A Domain-Decomposed Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.

2000-01-01

Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.

A New Approach to Parallel Dynamic Partitioning for Adaptive Unstructured Meshes

NASA Technical Reports Server (NTRS)

Heber, Gerd; Biswas, Rupak; Gao, Guang R.

1999-01-01

Classical mesh partitioning algorithms were designed for rather static situations, and their straightforward application in a dynamical framework may lead to unsatisfactory results, e.g., excessive data migration among processors. Furthermore, special attention should be paid to their amenability to parallelization. In this paper, a novel parallel method for the dynamic partitioning of adaptive unstructured meshes is described. It is based on a linear representation of the mesh using self-avoiding walks.

Adaptive mesh refinement and front-tracking for shear bands in an antiplane shear model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garaizar, F.X.; Trangenstein, J.

1998-09-01

In this paper the authors describe a numerical algorithm for the study of hear-band formation and growth in a two-dimensional antiplane shear of granular materials. The algorithm combines front-tracking techniques and adaptive mesh refinement. Tracking provides a more careful evolution of the band when coupled with special techniques to advance the ends of the shear band in the presence of a loss of hyperbolicity. The adaptive mesh refinement allows the computational effort to be concentrated in important areas of the deformation, such as the shear band and the elastic relief wave. The main challenges are the problems related to shearmore » bands that extend across several grid patches and the effects that a nonhyperbolic growth rate of the shear bands has in the refinement process. They give examples of the success of the algorithm for various levels of refinement.« less

A Moving Mesh Finite Element Algorithm for Singular Problems in Two and Three Space Dimensions

NASA Astrophysics Data System (ADS)

Li, Ruo; Tang, Tao; Zhang, Pingwen

2002-04-01

A framework for adaptive meshes based on the Hamilton-Schoen-Yau theory was proposed by Dvinsky. In a recent work (2001, J. Comput. Phys.170, 562-588), we extended Dvinsky's method to provide an efficient moving mesh algorithm which compared favorably with the previously proposed schemes in terms of simplicity and reliability. In this work, we will further extend the moving mesh methods based on harmonic maps to deal with mesh adaptation in three space dimensions. In obtaining the variational mesh, we will solve an optimization problem with some appropriate constraints, which is in contrast to the traditional method of solving the Euler-Lagrange equation directly. The key idea of this approach is to update the interior and boundary grids simultaneously, rather than considering them separately. Application of the proposed moving mesh scheme is illustrated with some two- and three-dimensional problems with large solution gradients. The numerical experiments show that our methods can accurately resolve detail features of singular problems in 3D.

A chimera grid scheme. [multiple overset body-conforming mesh system for finite difference adaptation to complex aircraft configurations

NASA Technical Reports Server (NTRS)

Steger, J. L.; Dougherty, F. C.; Benek, J. A.

1983-01-01

A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Oliker, Leonid; Sohn, Andrew

1996-01-01

Dynamic mesh adaption on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load imbalance among processors on a parallel machine. This paper describes the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution cost is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35% of the mesh is randomly adapted. For large-scale scientific computations, our load balancing strategy gives almost a sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remapper yields processor assignments that are less than 3% off the optimal solutions but requires only 1% of the computational time.

Kinetic solvers with adaptive mesh in phase space

NASA Astrophysics Data System (ADS)

Arslanbekov, Robert R.; Kolobov, Vladimir I.; Frolova, Anna A.

2013-12-01

An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a “tree of trees” (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.

Kinetic solvers with adaptive mesh in phase space.

PubMed

Arslanbekov, Robert R; Kolobov, Vladimir I; Frolova, Anna A

2013-12-01

An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a "tree of trees" (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.

Robust adaptive 3-D segmentation of vessel laminae from fluorescence confocal microscope images and parallel GPU implementation.

PubMed

Narayanaswamy, Arunachalam; Dwarakapuram, Saritha; Bjornsson, Christopher S; Cutler, Barbara M; Shain, William; Roysam, Badrinath

2010-03-01

This paper presents robust 3-D algorithms to segment vasculature that is imaged by labeling laminae, rather than the lumenal volume. The signal is weak, sparse, noisy, nonuniform, low-contrast, and exhibits gaps and spectral artifacts, so adaptive thresholding and Hessian filtering based methods are not effective. The structure deviates from a tubular geometry, so tracing algorithms are not effective. We propose a four step approach. The first step detects candidate voxels using a robust hypothesis test based on a model that assumes Poisson noise and locally planar geometry. The second step performs an adaptive region growth to extract weakly labeled and fine vessels while rejecting spectral artifacts. To enable interactive visualization and estimation of features such as statistical confidence, local curvature, local thickness, and local normal, we perform the third step. In the third step, we construct an accurate mesh representation using marching tetrahedra, volume-preserving smoothing, and adaptive decimation algorithms. To enable topological analysis and efficient validation, we describe a method to estimate vessel centerlines using a ray casting and vote accumulation algorithm which forms the final step of our algorithm. Our algorithm lends itself to parallel processing, and yielded an 8 x speedup on a graphics processor (GPU). On synthetic data, our meshes had average error per face (EPF) values of (0.1-1.6) voxels per mesh face for peak signal-to-noise ratios from (110-28 dB). Separately, the error from decimating the mesh to less than 1% of its original size, the EPF was less than 1 voxel/face. When validated on real datasets, the average recall and precision values were found to be 94.66% and 94.84%, respectively.

A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids

NASA Astrophysics Data System (ADS)

Percival, James; Pavlidis, Dimitrios; Xie, Zhihua; Alberini, Federico; Simmons, Mark; Pain, Christopher; Matar, Omar

2014-11-01

We present an investigation into the computational efficiency benefits of dynamic mesh adaptivity in the numerical simulation of transient multiphase fluid flow problems involving Non-Newtonian fluids. Such fluids appear in a range of industrial applications, from printing inks to toothpastes and introduce new challenges for mesh adaptivity due to the additional ``memory'' of viscoelastic fluids. Nevertheless, the multiscale nature of these flows implies huge potential benefits for a successful implementation. The study is performed using the open source package Fluidity, which couples an unstructured mesh control volume finite element solver for the multiphase Navier-Stokes equations to a dynamic anisotropic mesh adaptivity algorithm, based on estimated solution interpolation error criteria, and conservative mesh-to-mesh interpolation routine. The code is applied to problems involving rheologies ranging from simple Newtonian to shear-thinning to viscoelastic materials and verified against experimental data for various industrial and microfluidic flows. This work was undertaken as part of the EPSRC MEMPHIS programme grant EP/K003976/1.

An Adaptive Mesh Algorithm: Mapping the Mesh Variables

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scannapieco, Anthony J.

2016-07-25

Both thermodynamic and kinematic variables must be mapped. The kinematic variables are defined on a separate kinematic mesh; it is the duel mesh to the thermodynamic mesh. The map of the kinematic variables is done by calculating the contributions of kinematic variables on the old thermodynamic mesh, mapping the kinematic variable contributions onto the new thermodynamic mesh and then synthesizing the mapped kinematic variables on the new kinematic mesh. In this document the map of the thermodynamic variables will be described.

Application of adaptive gridding to magnetohydrodynamic flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schnack, D.D.; Lotatti, I.; Satyanarayana, P.

1996-12-31

The numerical simulation of the primitive, three-dimensional, time-dependent, resistive MHD equations on an unstructured, adaptive poloidal mesh using the TRIM code has been reported previously. The toroidal coordinate is approximated pseudo-spectrally with finite Fourier series and Fast-Fourier Transforms. The finite-volume algorithm preserves the magnetic field as solenoidal to round-off error, and also conserves mass, energy, and magnetic flux exactly. A semi-implicit method is used to allow for large time steps on the unstructured mesh. This is important for tokamak calculations where the relevant time scale is determined by the poloidal Alfven time. This also allows the viscosity to be treatedmore » implicitly. A conjugate-gradient method with pre-conditioning is used for matrix inversion. Applications to the growth and saturation of ideal instabilities in several toroidal fusion systems has been demonstrated. Recently we have concentrated on the details of the mesh adaption algorithm used in TRIM. We present several two-dimensional results relating to the use of grid adaptivity to track the evolution of hydrodynamic and MHD structures. Examples of plasma guns, opening switches, and supersonic flow over a magnetized sphere are presented. Issues relating to mesh adaption criteria are discussed.« less

Adaptive mesh refinement and load balancing based on multi-level block-structured Cartesian mesh

NASA Astrophysics Data System (ADS)

Misaka, Takashi; Sasaki, Daisuke; Obayashi, Shigeru

2017-11-01

We developed a framework for a distributed-memory parallel computer that enables dynamic data management for adaptive mesh refinement and load balancing. We employed simple data structure of the building cube method (BCM) where a computational domain is divided into multi-level cubic domains and each cube has the same number of grid points inside, realising a multi-level block-structured Cartesian mesh. Solution adaptive mesh refinement, which works efficiently with the help of the dynamic load balancing, was implemented by dividing cubes based on mesh refinement criteria. The framework was investigated with the Laplace equation in terms of adaptive mesh refinement, load balancing and the parallel efficiency. It was then applied to the incompressible Navier-Stokes equations to simulate a turbulent flow around a sphere. We considered wall-adaptive cube refinement where a non-dimensional wall distance y+ near the sphere is used for a criterion of mesh refinement. The result showed the load imbalance due to y+ adaptive mesh refinement was corrected by the present approach. To utilise the BCM framework more effectively, we also tested a cube-wise algorithm switching where an explicit and implicit time integration schemes are switched depending on the local Courant-Friedrichs-Lewy (CFL) condition in each cube.

Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Oliker, Leonid; Sohn, Andrew

1996-01-01

Dynamic mesh adaptation on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load inbalances among processors on a parallel machine. This paper described the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution coast is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35 percent of the mesh is randomly adapted. For large scale scientific computations, our load balancing strategy gives an almost sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remappier yields processor assignments that are less than 3 percent of the optimal solutions, but requires only 1 percent of the computational time.

Anisotropic mesh adaptation for marine ice-sheet modelling

NASA Astrophysics Data System (ADS)

Gillet-Chaulet, Fabien; Tavard, Laure; Merino, Nacho; Peyaud, Vincent; Brondex, Julien; Durand, Gael; Gagliardini, Olivier

2017-04-01

Improving forecasts of ice-sheets contribution to sea-level rise requires, amongst others, to correctly model the dynamics of the grounding line (GL), i.e. the line where the ice detaches from its underlying bed and goes afloat on the ocean. Many numerical studies, including the intercomparison exercises MISMIP and MISMIP3D, have shown that grid refinement in the GL vicinity is a key component to obtain reliable results. Improving model accuracy while maintaining the computational cost affordable has then been an important target for the development of marine icesheet models. Adaptive mesh refinement (AMR) is a method where the accuracy of the solution is controlled by spatially adapting the mesh size. It has become popular in models using the finite element method as they naturally deal with unstructured meshes, but block-structured AMR has also been successfully applied to model GL dynamics. The main difficulty with AMR is to find efficient and reliable estimators of the numerical error to control the mesh size. Here, we use the estimator proposed by Frey and Alauzet (2015). Based on the interpolation error, it has been found effective in practice to control the numerical error, and has some flexibility, such as its ability to combine metrics for different variables, that makes it attractive. Routines to compute the anisotropic metric defining the mesh size have been implemented in the finite element ice flow model Elmer/Ice (Gagliardini et al., 2013). The mesh adaptation is performed using the freely available library MMG (Dapogny et al., 2014) called from Elmer/Ice. Using a setup based on the inter-comparison exercise MISMIP+ (Asay-Davis et al., 2016), we study the accuracy of the solution when the mesh is adapted using various variables (ice thickness, velocity, basal drag, …). We show that combining these variables allows to reduce the number of mesh nodes by more than one order of magnitude, for the same numerical accuracy, when compared to uniform mesh refinement. For transient solutions where the GL is moving, we have implemented an algorithm where the computation is reiterated allowing to anticipate the GL displacement and to adapt the mesh to the transient solution. We discuss the performance and robustness of this algorithm.

A User's Guide to AMR1D: An Instructional Adaptive Mesh Refinement Code for Unstructured Grids

NASA Technical Reports Server (NTRS)

deFainchtein, Rosalinda

1996-01-01

This report documents the code AMR1D, which is currently posted on the World Wide Web (http://sdcd.gsfc.nasa.gov/ESS/exchange/contrib/de-fainchtein/adaptive _mesh_refinement.html). AMR1D is a one-dimensional finite element fluid-dynamics solver, capable of adaptive mesh refinement (AMR). It was written as an instructional tool for AMR on unstructured mesh codes. It is meant to illustrate the minimum requirements for AMR on more than one dimension. For that purpose, it uses the same type of data structure that would be necessary on a two-dimensional AMR code (loosely following the algorithm described by Lohner).

An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Han, Jianqiang; Tang, Huazhong

2007-01-01

This paper presents an adaptive moving mesh algorithm for two-dimensional (2D) ideal magnetohydrodynamics (MHD) that utilizes a staggered constrained transport technique to keep the magnetic field divergence-free. The algorithm consists of two independent parts: MHD evolution and mesh-redistribution. The first part is a high-resolution, divergence-free, shock-capturing scheme on a fixed quadrangular mesh, while the second part is an iterative procedure. In each iteration, mesh points are first redistributed, and then a conservative-interpolation formula is used to calculate the remapped cell-averages of the mass, momentum, and total energy on the resulting new mesh; the magnetic potential is remapped to the new mesh in a non-conservative way and is reconstructed to give a divergence-free magnetic field on the new mesh. Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy, track and resolve strong shock waves in ideal MHD problems, and preserve divergence-free property of the magnetic field. Numerical examples include the smooth Alfvén wave problem, 2D and 2.5D shock tube problems, two rotor problems, the stringent blast problem, and the cloud-shock interaction problem.

Fully implicit adaptive mesh refinement MHD algorithm

NASA Astrophysics Data System (ADS)

Philip, Bobby

2005-10-01

In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former results in stiffness due to the presence of very fast waves. The latter requires one to resolve the localized features that the system develops. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. To our knowledge, a scalable, fully implicit AMR algorithm has not been accomplished before for MHD. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technologyootnotetextL. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite --FAC-- algorithms) for scalability. We will demonstrate that the concept is indeed feasible, featuring optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations will be presented on a variety of problems.

Approaches to the automatic generation and control of finite element meshes

NASA Technical Reports Server (NTRS)

Shephard, Mark S.

1987-01-01

The algorithmic approaches being taken to the development of finite element mesh generators capable of automatically discretizing general domains without the need for user intervention are discussed. It is demonstrated that because of the modeling demands placed on a automatic mesh generator, all the approaches taken to date produce unstructured meshes. Consideration is also given to both a priori and a posteriori mesh control devices for automatic mesh generators as well as their integration with geometric modeling and adaptive analysis procedures.

Modelling atmospheric flows with adaptive moving meshes

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Smolarkiewicz, Piotr K.; Dörnbrack, Andreas

2012-04-01

An anelastic atmospheric flow solver has been developed that combines semi-implicit non-oscillatory forward-in-time numerics with a solution-adaptive mesh capability. A key feature of the solver is the unification of a mesh adaptation apparatus, based on moving mesh partial differential equations (PDEs), with the rigorous formulation of the governing anelastic PDEs in generalised time-dependent curvilinear coordinates. The solver development includes an enhancement of the flux-form multidimensional positive definite advection transport algorithm (MPDATA) - employed in the integration of the underlying anelastic PDEs - that ensures full compatibility with mass continuity under moving meshes. In addition, to satisfy the geometric conservation law (GCL) tensor identity under general moving meshes, a diagnostic approach is proposed based on the treatment of the GCL as an elliptic problem. The benefits of the solution-adaptive moving mesh technique for the simulation of multiscale atmospheric flows are demonstrated. The developed solver is verified for two idealised flow problems with distinct levels of complexity: passive scalar advection in a prescribed deformational flow, and the life cycle of a large-scale atmospheric baroclinic wave instability showing fine-scale phenomena of fronts and internal gravity waves.

A methodology for quadrilateral finite element mesh coarsening

DOE PAGES

Staten, Matthew L.; Benzley, Steven; Scott, Michael

2008-03-27

High fidelity finite element modeling of continuum mechanics problems often requires using all quadrilateral or all hexahedral meshes. The efficiency of such models is often dependent upon the ability to adapt a mesh to the physics of the phenomena. Adapting a mesh requires the ability to both refine and/or coarsen the mesh. The algorithms available to refine and coarsen triangular and tetrahedral meshes are very robust and efficient. However, the ability to locally and conformally refine or coarsen all quadrilateral and all hexahedral meshes presents many difficulties. Some research has been done on localized conformal refinement of quadrilateral and hexahedralmore » meshes. However, little work has been done on localized conformal coarsening of quadrilateral and hexahedral meshes. A general method which provides both localized conformal coarsening and refinement for quadrilateral meshes is presented in this paper. This method is based on restructuring the mesh with simplex manipulations to the dual of the mesh. Finally, this method appears to be extensible to hexahedral meshes in three dimensions.« less

Adaptive Control Parameters for Dispersal of Multi-Agent Mobile Ad Hoc Network (MANET) Swarms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kurt Derr; Milos Manic

A mobile ad hoc network is a collection of independent nodes that communicate wirelessly with one another. This paper investigates nodes that are swarm robots with communications and sensing capabilities. Each robot in the swarm may operate in a distributed and decentralized manner to achieve some goal. This paper presents a novel approach to dynamically adapting control parameters to achieve mesh configuration stability. The presented approach to robot interaction is based on spring force laws (attraction and repulsion laws) to create near-optimal mesh like configurations. In prior work, we presented the extended virtual spring mesh (EVSM) algorithm for the dispersionmore » of robot swarms. This paper extends the EVSM framework by providing the first known study on the effects of adaptive versus static control parameters on robot swarm stability. The EVSM algorithm provides the following novelties: 1) improved performance with adaptive control parameters and 2) accelerated convergence with high formation effectiveness. Simulation results show that 120 robots reach convergence using adaptive control parameters more than twice as fast as with static control parameters in a multiple obstacle environment.« less

Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.

2006-01-01

Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.

Parallel Tetrahedral Mesh Adaptation with Dynamic Load Balancing

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Biswas, Rupak; Gabow, Harold N.

1999-01-01

The ability to dynamically adapt an unstructured grid is a powerful tool for efficiently solving computational problems with evolving physical features. In this paper, we report on our experience parallelizing an edge-based adaptation scheme, called 3D_TAG. using message passing. Results show excellent speedup when a realistic helicopter rotor mesh is randomly refined. However. performance deteriorates when the mesh is refined using a solution-based error indicator since mesh adaptation for practical problems occurs in a localized region., creating a severe load imbalance. To address this problem, we have developed PLUM, a global dynamic load balancing framework for adaptive numerical computations. Even though PLUM primarily balances processor workloads for the solution phase, it reduces the load imbalance problem within mesh adaptation by repartitioning the mesh after targeting edges for refinement but before the actual subdivision. This dramatically improves the performance of parallel 3D_TAG since refinement occurs in a more load balanced fashion. We also present optimal and heuristic algorithms that, when applied to the default mapping of a parallel repartitioner, significantly reduce the data redistribution overhead. Finally, portability is examined by comparing performance on three state-of-the-art parallel machines.

Numerical Schemes for the Hamilton-Jacobi and Level Set Equations on Triangulated Domains

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Sethian, James A.

2006-01-01

Borrowing from techniques developed for conservation law equations, we have developed both monotone and higher order accurate numerical schemes which discretize the Hamilton-Jacobi and level set equations on triangulated domains. The use of unstructured meshes containing triangles (2D) and tetrahedra (3D) easily accommodates mesh adaptation to resolve disparate level set feature scales with a minimal number of solution unknowns. The minisymposium talk will discuss these algorithmic developments and present sample calculations using our adaptive triangulation algorithm applied to various moving interface problems such as etching, deposition, and curvature flow.

A hierarchical structure for automatic meshing and adaptive FEM analysis

NASA Technical Reports Server (NTRS)

Kela, Ajay; Saxena, Mukul; Perucchio, Renato

1987-01-01

A new algorithm for generating automatically, from solid models of mechanical parts, finite element meshes that are organized as spatially addressable quaternary trees (for 2-D work) or octal trees (for 3-D work) is discussed. Because such meshes are inherently hierarchical as well as spatially addressable, they permit efficient substructuring techniques to be used for both global analysis and incremental remeshing and reanalysis. The global and incremental techniques are summarized and some results from an experimental closed loop 2-D system in which meshing, analysis, error evaluation, and remeshing and reanalysis are done automatically and adaptively are presented. The implementation of 3-D work is briefly discussed.

An Adaptive Mesh Algorithm: Mesh Structure and Generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scannapieco, Anthony J.

2016-06-21

The purpose of Adaptive Mesh Refinement is to minimize spatial errors over the computational space not to minimize the number of computational elements. The additional result of the technique is that it may reduce the number of computational elements needed to retain a given level of spatial accuracy. Adaptive mesh refinement is a computational technique used to dynamically select, over a region of space, a set of computational elements designed to minimize spatial error in the computational model of a physical process. The fundamental idea is to increase the mesh resolution in regions where the physical variables are represented bymore » a broad spectrum of modes in k-space, hence increasing the effective global spectral coverage of those physical variables. In addition, the selection of the spatially distributed elements is done dynamically by cyclically adjusting the mesh to follow the spectral evolution of the system. Over the years three types of AMR schemes have evolved; block, patch and locally refined AMR. In block and patch AMR logical blocks of various grid sizes are overlaid to span the physical space of interest, whereas in locally refined AMR no logical blocks are employed but locally nested mesh levels are used to span the physical space. The distinction between block and patch AMR is that in block AMR the original blocks refine and coarsen entirely in time, whereas in patch AMR the patches change location and zone size with time. The type of AMR described herein is a locally refi ned AMR. In the algorithm described, at any point in physical space only one zone exists at whatever level of mesh that is appropriate for that physical location. The dynamic creation of a locally refi ned computational mesh is made practical by a judicious selection of mesh rules. With these rules the mesh is evolved via a mesh potential designed to concentrate the nest mesh in regions where the physics is modally dense, and coarsen zones in regions where the physics is modally sparse.« less

Solution adaptive grids applied to low Reynolds number flow

NASA Astrophysics Data System (ADS)

de With, G.; Holdø, A. E.; Huld, T. A.

2003-08-01

A numerical study has been undertaken to investigate the use of a solution adaptive grid for flow around a cylinder in the laminar flow regime. The main purpose of this work is twofold. The first aim is to investigate the suitability of a grid adaptation algorithm and the reduction in mesh size that can be obtained. Secondly, the uniform asymmetric flow structures are ideal to validate the mesh structures due to mesh refinement and consequently the selected refinement criteria. The refinement variable used in this work is a product of the rate of strain and the mesh cell size, and contains two variables Cm and Cstr which determine the order of each term. By altering the order of either one of these terms the refinement behaviour can be modified.

A constrained Delaunay discretization method for adaptively meshing highly discontinuous geological media

NASA Astrophysics Data System (ADS)

Wang, Yang; Ma, Guowei; Ren, Feng; Li, Tuo

2017-12-01

A constrained Delaunay discretization method is developed to generate high-quality doubly adaptive meshes of highly discontinuous geological media. Complex features such as three-dimensional discrete fracture networks (DFNs), tunnels, shafts, slopes, boreholes, water curtains, and drainage systems are taken into account in the mesh generation. The constrained Delaunay triangulation method is used to create adaptive triangular elements on planar fractures. Persson's algorithm (Persson, 2005), based on an analogy between triangular elements and spring networks, is enriched to automatically discretize a planar fracture into mesh points with varying density and smooth-quality gradient. The triangulated planar fractures are treated as planar straight-line graphs (PSLGs) to construct piecewise-linear complex (PLC) for constrained Delaunay tetrahedralization. This guarantees the doubly adaptive characteristic of the resulted mesh: the mesh is adaptive not only along fractures but also in space. The quality of elements is compared with the results from an existing method. It is verified that the present method can generate smoother elements and a better distribution of element aspect ratios. Two numerical simulations are implemented to demonstrate that the present method can be applied to various simulations of complex geological media that contain a large number of discontinuities.

Efficient generation of discontinuity-preserving adaptive triangulations from range images.

PubMed

Garcia, Miguel Angel; Sappa, Angel Domingo

2004-10-01

This paper presents an efficient technique for generating adaptive triangular meshes from range images. The algorithm consists of two stages. First, a user-defined number of points is adaptively sampled from the given range image. Those points are chosen by taking into account the surface shapes represented in the range image in such a way that points tend to group in areas of high curvature and to disperse in low-variation regions. This selection process is done through a noniterative, inherently parallel algorithm in order to gain efficiency. Once the image has been subsampled, the second stage applies a two and one half-dimensional Delaunay triangulation to obtain an initial triangular mesh. To favor the preservation of surface and orientation discontinuities (jump and crease edges) present in the original range image, the aforementioned triangular mesh is iteratively modified by applying an efficient edge flipping technique. Results with real range images show accurate triangular approximations of the given range images with low processing times.

Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Brislawn, Kristi D.; Brown, David L.; Chesshire, Geoffrey S.; Saltzman, Jeffrey S.

1995-01-01

Adaptive mesh refinement (AMR) in conjunction with higher-order upwind finite-difference methods have been used effectively on a variety of problems in two and three dimensions. In this paper we introduce an approach for resolving problems that involve complex geometries in which resolution of boundary geometry is important. The complex geometry is represented by using the method of overlapping grids, while local resolution is obtained by refining each component grid with the AMR algorithm, appropriately generalized for this situation. The CMPGRD algorithm introduced by Chesshire and Henshaw is used to automatically generate the overlapping grid structure for the underlying mesh.

Binary mesh partitioning for cache-efficient visualization.

PubMed

Tchiboukdjian, Marc; Danjean, Vincent; Raffin, Bruno

2010-01-01

One important bottleneck when visualizing large data sets is the data transfer between processor and memory. Cache-aware (CA) and cache-oblivious (CO) algorithms take into consideration the memory hierarchy to design cache efficient algorithms. CO approaches have the advantage to adapt to unknown and varying memory hierarchies. Recent CA and CO algorithms developed for 3D mesh layouts significantly improve performance of previous approaches, but they lack of theoretical performance guarantees. We present in this paper a {\\schmi O}(N\\log N) algorithm to compute a CO layout for unstructured but well shaped meshes. We prove that a coherent traversal of a N-size mesh in dimension d induces less than N/B+{\\schmi O}(N/M;{1/d}) cache-misses where B and M are the block size and the cache size, respectively. Experiments show that our layout computation is faster and significantly less memory consuming than the best known CO algorithm. Performance is comparable to this algorithm for classical visualization algorithm access patterns, or better when the BSP tree produced while computing the layout is used as an acceleration data structure adjusted to the layout. We also show that cache oblivious approaches lead to significant performance increases on recent GPU architectures.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cololla, P.

This review describes a structured approach to adaptivity. The Automated Mesh Refinement (ARM) algorithms developed by M Berger are described, touching on hyperbolic and parabolic applications. Adaptivity is achieved by overlaying finer grids only in areas flagged by a generalized error criterion. The author discusses some of the issues involved in abutting disparate-resolution grids, and demonstrates that suitable algorithms exist for dissipative as well as hyperbolic systems.

Adaptive Crack Modeling with Interface Solid Elements for Plain and Fiber Reinforced Concrete Structures.

PubMed

Zhan, Yijian; Meschke, Günther

2017-07-08

The effective analysis of the nonlinear behavior of cement-based engineering structures not only demands physically-reliable models, but also computationally-efficient algorithms. Based on a continuum interface element formulation that is suitable to capture complex cracking phenomena in concrete materials and structures, an adaptive mesh processing technique is proposed for computational simulations of plain and fiber-reinforced concrete structures to progressively disintegrate the initial finite element mesh and to add degenerated solid elements into the interfacial gaps. In comparison with the implementation where the entire mesh is processed prior to the computation, the proposed adaptive cracking model allows simulating the failure behavior of plain and fiber-reinforced concrete structures with remarkably reduced computational expense.

Adaptive Crack Modeling with Interface Solid Elements for Plain and Fiber Reinforced Concrete Structures

PubMed Central

Zhan, Yijian

2017-01-01

The effective analysis of the nonlinear behavior of cement-based engineering structures not only demands physically-reliable models, but also computationally-efficient algorithms. Based on a continuum interface element formulation that is suitable to capture complex cracking phenomena in concrete materials and structures, an adaptive mesh processing technique is proposed for computational simulations of plain and fiber-reinforced concrete structures to progressively disintegrate the initial finite element mesh and to add degenerated solid elements into the interfacial gaps. In comparison with the implementation where the entire mesh is processed prior to the computation, the proposed adaptive cracking model allows simulating the failure behavior of plain and fiber-reinforced concrete structures with remarkably reduced computational expense. PMID:28773130

Block structured adaptive mesh and time refinement for hybrid, hyperbolic + N-body systems

NASA Astrophysics Data System (ADS)

Miniati, Francesco; Colella, Phillip

2007-11-01

We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov’s method for hydrodynamics; a symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Serazio, C.; Chacon, L.; Lapenta, G.

2006-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. Crucial elements are the development of an effective multilevel treatment of the grid equation, and a robust, rigorous error estimator. For the latter, we explore the effectiveness of a coarse grid correction error estimator, which faithfully reproduces spatial truncation errors for conservative equations. We will show that the moving mesh approach is competitive vs. uniform grids both in accuracy (due to adaptivity) and efficiency. Results for a variety of models 1D and 2D geometries will be presented. L. Chac'on, G. Lapenta, J. Comput. Phys., 212 (2), 703 (2006) G. Lapenta, L. Chac'on, J. Comput. Phys., accepted (2006)

A Parallel Ghosting Algorithm for The Flexible Distributed Mesh Database

DOE PAGES

Mubarak, Misbah; Seol, Seegyoung; Lu, Qiukai; ...

2013-01-01

Critical to the scalability of parallel adaptive simulations are parallel control functions including load balancing, reduced inter-process communication and optimal data decomposition. In distributed meshes, many mesh-based applications frequently access neighborhood information for computational purposes which must be transmitted efficiently to avoid parallel performance degradation when the neighbors are on different processors. This article presents a parallel algorithm of creating and deleting data copies, referred to as ghost copies, which localize neighborhood data for computation purposes while minimizing inter-process communication. The key characteristics of the algorithm are: (1) It can create ghost copies of any permissible topological order in amore » 1D, 2D or 3D mesh based on selected adjacencies. (2) It exploits neighborhood communication patterns during the ghost creation process thus eliminating all-to-all communication. (3) For applications that need neighbors of neighbors, the algorithm can create n number of ghost layers up to a point where the whole partitioned mesh can be ghosted. Strong and weak scaling results are presented for the IBM BG/P and Cray XE6 architectures up to a core count of 32,768 processors. The algorithm also leads to scalable results when used in a parallel super-convergent patch recovery error estimator, an application that frequently accesses neighborhood data to carry out computation.« less

A parallel adaptive mesh refinement algorithm

NASA Technical Reports Server (NTRS)

Quirk, James J.; Hanebutte, Ulf R.

1993-01-01

Over recent years, Adaptive Mesh Refinement (AMR) algorithms which dynamically match the local resolution of the computational grid to the numerical solution being sought have emerged as powerful tools for solving problems that contain disparate length and time scales. In particular, several workers have demonstrated the effectiveness of employing an adaptive, block-structured hierarchical grid system for simulations of complex shock wave phenomena. Unfortunately, from the parallel algorithm developer's viewpoint, this class of scheme is quite involved; these schemes cannot be distilled down to a small kernel upon which various parallelizing strategies may be tested. However, because of their block-structured nature such schemes are inherently parallel, so all is not lost. In this paper we describe the method by which Quirk's AMR algorithm has been parallelized. This method is built upon just a few simple message passing routines and so it may be implemented across a broad class of MIMD machines. Moreover, the method of parallelization is such that the original serial code is left virtually intact, and so we are left with just a single product to support. The importance of this fact should not be underestimated given the size and complexity of the original algorithm.

Formulation and Implementation of Inflow/Outflow Boundary Conditions to Simulate Propulsive Effects

NASA Technical Reports Server (NTRS)

Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian

2018-01-01

Boundary conditions appropriate for simulating flow entering or exiting the computational domain to mimic propulsion effects have been implemented in an adaptive Cartesian simulation package. A robust iterative algorithm to control mass flow rate through an outflow boundary surface is presented, along with a formulation to explicitly specify mass flow rate through an inflow boundary surface. The boundary conditions have been applied within a mesh adaptation framework based on the method of adjoint-weighted residuals. This allows for proper adaptive mesh refinement when modeling propulsion systems. The new boundary conditions are demonstrated on several notional propulsion systems operating in flow regimes ranging from low subsonic to hypersonic. The examples show that the prescribed boundary state is more properly imposed as the mesh is refined. The mass-flowrate steering algorithm is shown to be an efficient approach in each example. To demonstrate the boundary conditions on a realistic complex aircraft geometry, two of the new boundary conditions are also applied to a modern low-boom supersonic demonstrator design with multiple flow inlets and outlets.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Chacon, Luis

2005-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. A crucial element is the development of an effective multilevel treatment of the grid equation.ootnotetextL. Chac'on, G. Lapenta, A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys., accepted (2005) We will show that such an approach is competitive vs. uniform grids both from the accuracy (due to adaptivity) and the efficiency standpoints. Results for a variety of models 1D and 2D geometries, including nonlinear diffusion, radiation-diffusion, Burgers equation, and gas dynamics will be presented.

Fully implicit adaptive mesh refinement algorithm for reduced MHD

NASA Astrophysics Data System (ADS)

Philip, Bobby; Pernice, Michael; Chacon, Luis

2006-10-01

In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technology to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite grid --FAC-- algorithms) for scalability. We demonstrate that the concept is indeed feasible, featuring near-optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations in challenging dissipation regimes will be presented on a variety of problems that benefit from this capability, including tearing modes, the island coalescence instability, and the tilt mode instability. L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) B. Philip, M. Pernice, and L. Chac'on, Lecture Notes in Computational Science and Engineering, accepted (2006)

Performance Analysis and Portability of the PLUM Load Balancing System

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Biswas, Rupak; Gabow, Harold N.

1998-01-01

The ability to dynamically adapt an unstructured mesh is a powerful tool for solving computational problems with evolving physical features; however, an efficient parallel implementation is rather difficult. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive numerical computations in a message-passing environment. PLUM requires that all data be globally redistributed after each mesh adaption to achieve load balance. We present an algorithm for minimizing this remapping overhead by guaranteeing an optimal processor reassignment. We also show that the data redistribution cost can be significantly reduced by applying our heuristic processor reassignment algorithm to the default mapping of the parallel partitioner. Portability is examined by comparing performance on a SP2, an Origin2000, and a T3E. Results show that PLUM can be successfully ported to different platforms without any code modifications.

Modelling the oscillations of the thermocline in a lake by means of a fully consistent and conservative 3D finite-element model with a vertically adaptive mesh

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Vallaeys, Valentin; Naithani, Jaya; Remacle, Jean-François; Legat, Vincent; Deleersnijder, Eric

2017-04-01

Vertical discretisation is crucial in the modelling of lake thermocline oscillations. For finite element methods, a simple way to increase the resolution close to the oscillating thermocline is to use vertical adaptive coordinates. With an Arbitrary Lagrangian-Eulerian (ALE) formulation, the mesh can be adapted to increase the resolution in regions with strong shear or stratification. In such an application, consistency and conservativity must be strictly enforced. SLIM 3D, a discontinuous-Galerkin finite element model for shallow-water flows (www.climate.be/slim, e.g. Kärnä et al., 2013, Delandmeter et al., 2015), was designed to be strictly consistent and conservative in its discrete formulation. In this context, special care must be paid to the coupling of the external and internal modes of the model and the moving mesh algorithm. In this framework, the mesh can be adapted arbitrarily in the vertical direction. Two moving mesh algorithms were implemented: the first one computes an a-priori optimal mesh; the second one diffuses vertically the mesh (Burchard et al., 2004, Hofmeister et al., 2010). The criteria used to define the optimal mesh and the diffusion function are related to a suitable measure of shear and stratification. We will present in detail the design of the model and how the consistency and conservativity is obtained. Then we will apply it to both idealised benchmarks and the wind-forced thermocline oscillations in Lake Tanganyika (Naithani et al. 2002). References Tuomas Kärnä, Vincent Legat and Eric Deleersnijder. A baroclinic discontinuous Galerkin finite element model for coastal flows, Ocean Modelling, 61:1-20, 2013. Philippe Delandmeter, Stephen E Lewis, Jonathan Lambrechts, Eric Deleersnijder, Vincent Legat and Eric Wolanski. The transport and fate of riverine fine sediment exported to a semi-open system. Estuarine, Coastal and Shelf Science, 167:336-346, 2015. Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids in one-dimensional numerical ocean models. Ocean Modelling, 6:51-81, 2004. Richard Hofmeister, Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids for 3d numerical ocean models. Ocean Modelling, 33:70-86, 2010. Jaya Naithani, Eric Deleersnijder and Pierre-Denis Plisnier. Origin of intraseasonal variability in Lake Tanganyika. Geophysical Research Letters, 29(23), doi:10.1029/2002GL015843, 2002.

Adaptive Mesh Refinement in Curvilinear Body-Fitted Grid Systems

NASA Technical Reports Server (NTRS)

Steinthorsson, Erlendur; Modiano, David; Colella, Phillip

1995-01-01

To be truly compatible with structured grids, an AMR algorithm should employ a block structure for the refined grids to allow flow solvers to take advantage of the strengths of unstructured grid systems, such as efficient solution algorithms for implicit discretizations and multigrid schemes. One such algorithm, the AMR algorithm of Berger and Colella, has been applied to and adapted for use with body-fitted structured grid systems. Results are presented for a transonic flow over a NACA0012 airfoil (AGARD-03 test case) and a reflection of a shock over a double wedge.

Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.; Ovall, J.; Holst, M.

2014-12-01

We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented adaptive refinement code named MARE2DEM. We demonstrate the performance and parallel scaling of this algorithm on a medium-scale computing cluster with a marine controlled-source EM example that includes a 3D array of receivers located over a 3D model that includes significant seafloor bathymetry variations and a heterogeneous subsurface.

Adaptive Finite Element Methods for Continuum Damage Modeling

NASA Technical Reports Server (NTRS)

Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.

1995-01-01

The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.

An object-oriented and quadrilateral-mesh based solution adaptive algorithm for compressible multi-fluid flows

NASA Astrophysics Data System (ADS)

Zheng, H. W.; Shu, C.; Chew, Y. T.

2008-07-01

In this paper, an object-oriented and quadrilateral-mesh based solution adaptive algorithm for the simulation of compressible multi-fluid flows is presented. The HLLC scheme (Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored) is extended to adaptively solve the compressible multi-fluid flows under complex geometry on unstructured mesh. It is also extended to the second-order of accuracy by using MUSCL extrapolation. The node, edge and cell are arranged in such an object-oriented manner that each of them inherits from a basic object. A home-made double link list is designed to manage these objects so that the inserting of new objects and removing of the existing objects (nodes, edges and cells) are independent of the number of objects and only of the complexity of O( 1). In addition, the cells with different levels are further stored in different lists. This avoids the recursive calculation of solution of mother (non-leaf) cells. Thus, high efficiency is obtained due to these features. Besides, as compared to other cell-edge adaptive methods, the separation of nodes would reduce the memory requirement of redundant nodes, especially in the cases where the level number is large or the space dimension is three. Five two-dimensional examples are used to examine its performance. These examples include vortex evolution problem, interface only problem under structured mesh and unstructured mesh, bubble explosion under the water, bubble-shock interaction, and shock-interface interaction inside the cylindrical vessel. Numerical results indicate that there is no oscillation of pressure and velocity across the interface and it is feasible to apply it to solve compressible multi-fluid flows with large density ratio (1000) and strong shock wave (the pressure ratio is 10,000) interaction with the interface.

Adaptive mesh refinement for characteristic grids

NASA Astrophysics Data System (ADS)

Thornburg, Jonathan

2011-05-01

I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive, and the best-known past Berger-Oliger characteristic AMR algorithm, that of Pretorius and Lehner (J Comp Phys 198:10, 2004), recurses on individual "diamond" characteristic grid cells. This leads to the use of fine-grained memory management, with individual grid cells kept in two-dimensional linked lists at each refinement level. This complicates the implementation and adds overhead in both space and time. Here I describe a Berger-Oliger characteristic AMR algorithm which instead recurses on null slices. This algorithm is very similar to the usual Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory management, allowing entire null slices to be stored in contiguous arrays in memory. The algorithm is very efficient in both space and time. I describe discretizations yielding both second and fourth order global accuracy. My code implementing the algorithm described here is included in the electronic supplementary materials accompanying this paper, and is freely available to other researchers under the terms of the GNU general public license.

Heating and Large Scale Dynamics of the Solar Corona

NASA Technical Reports Server (NTRS)

Schnack, Dalton D.

2000-01-01

The effort was concentrated in the areas: coronal heating mechanism, unstructured adaptive grid algorithms, numerical modeling of magnetic reconnection in the MRX experiment: effect of toroidal magnetic field and finite pressure, effect of OHMIC heating and vertical magnetic field, effect of dynamic MESH adaption.

Space-time adaptive solution of inverse problems with the discrete adjoint method

NASA Astrophysics Data System (ADS)

Alexe, Mihai; Sandu, Adrian

2014-08-01

This paper develops a framework for the construction and analysis of discrete adjoint sensitivities in the context of time dependent, adaptive grid, adaptive step models. Discrete adjoints are attractive in practice since they can be generated with low effort using automatic differentiation. However, this approach brings several important challenges. The space-time adjoint of the forward numerical scheme may be inconsistent with the continuous adjoint equations. A reduction in accuracy of the discrete adjoint sensitivities may appear due to the inter-grid transfer operators. Moreover, the optimization algorithm may need to accommodate state and gradient vectors whose dimensions change between iterations. This work shows that several of these potential issues can be avoided through a multi-level optimization strategy using discontinuous Galerkin (DG) hp-adaptive discretizations paired with Runge-Kutta (RK) time integration. We extend the concept of dual (adjoint) consistency to space-time RK-DG discretizations, which are then shown to be well suited for the adaptive solution of time-dependent inverse problems. Furthermore, we prove that DG mesh transfer operators on general meshes are also dual consistent. This allows the simultaneous derivation of the discrete adjoint for both the numerical solver and the mesh transfer logic with an automatic code generation mechanism such as algorithmic differentiation (AD), potentially speeding up development of large-scale simulation codes. The theoretical analysis is supported by numerical results reported for a two-dimensional non-stationary inverse problem.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hewett, D.W.; Yu-Jiuan Chen

The authors describe how they hold onto orthogonal mesh discretization when dealing with curved boundaries. Special difference operators were constructed to approximate numerical zones split by the domain boundary; the operators are particularly simple for this rectangular mesh. The authors demonstrated that this simple numerical approach, termed Dynamic Alternating Direction Implicit, turned out to be considerably more efficient than more complex grid-adaptive algorithms that were tried previously.

An implementation of a chemical and thermal nonequilibrium flow solver on unstructured meshes and application to blunt bodies

NASA Technical Reports Server (NTRS)

Prabhu, Ramadas K.

1994-01-01

This paper presents a nonequilibrium flow solver, implementation of the algorithm on unstructured meshes, and application to hypersonic flow past blunt bodies. Air is modeled as a mixture of five chemical species, namely O2, N2, O, NO, and N, having two temperatures namely translational and vibrational. The solution algorithm is a cell centered, point implicit upwind scheme that employs Roe's flux difference splitting technique. Implementation of this algorithm on unstructured meshes is described. The computer code is applied to solve Mach 15 flow with and without a Type IV shock interference on a cylindrical body of 2.5mm radius representing a cowl lip. Adaptively generated meshes are employed, and the meshes are refined several times until the solution exhibits detailed flow features and surface pressure and heat flux distributions. Effects of a catalytic wall on surface heat flux distribution are studied. For the Mach 15 Type IV shock interference flow, present results showed a peak heat flux of 544 MW/m2 for a fully catalytic wall and 431 MW/m(exp 2) for a noncatalytic wall. Some of the results are compared with available computational data.

Three dimensional unstructured multigrid for the Euler equations

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1991-01-01

The three dimensional Euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy. The driving algorithm consists of an explicit vertex-based finite element scheme, which employs an edge-based data structure to assemble the residuals. The multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady-state of the fine grid solution. Variables, residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm. The preprocessing operation is shown to require a negligible fraction of the CPU time required by the overall solution procedure, while gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350,000 vertices. Solutions using globally regenerated fine meshes as well as adaptively refined meshes are given.

Multiscale Simulations of Magnetic Island Coalescence

NASA Technical Reports Server (NTRS)

Dorelli, John C.

2010-01-01

We describe a new interactive parallel Adaptive Mesh Refinement (AMR) framework written in the Python programming language. This new framework, PyAMR, hides the details of parallel AMR data structures and algorithms (e.g., domain decomposition, grid partition, and inter-process communication), allowing the user to focus on the development of algorithms for advancing the solution of a systems of partial differential equations on a single uniform mesh. We demonstrate the use of PyAMR by simulating the pairwise coalescence of magnetic islands using the resistive Hall MHD equations. Techniques for coupling different physics models on different levels of the AMR grid hierarchy are discussed.

Mesh refinement in finite element analysis by minimization of the stiffness matrix trace

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.

1989-01-01

Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kurt Derr

Mobile Ad hoc NETworks (MANETs) are distributed self-organizing networks that can change locations and configure themselves on the fly. This paper focuses on an algorithmic approach for the deployment of a MANET within an enclosed area, such as a building in a disaster scenario, which can provide a robust communication infrastructure for search and rescue operations. While a virtual spring mesh (VSM) algorithm provides scalable, self-organizing, and fault-tolerant capabilities required by aMANET, the VSM lacks the MANET's capabilities of deployment mechanisms for blanket coverage of an area and does not provide an obstacle avoidance mechanism. This paper presents a newmore » technique, an extended VSM (EVSM) algorithm that provides the following novelties: (1) new control laws for exploration and expansion to provide blanket coverage, (2) virtual adaptive springs enabling the mesh to expand as necessary, (3) adapts to communications disturbances by varying the density and movement of mobile nodes, and (4) new metrics to assess the performance of the EVSM algorithm. Simulation results show that EVSM provides up to 16% more coverage and is 3.5 times faster than VSM in environments with eight obstacles.« less

A short note on the use of the red-black tree in Cartesian adaptive mesh refinement algorithms

NASA Astrophysics Data System (ADS)

Hasbestan, Jaber J.; Senocak, Inanc

2017-12-01

Mesh adaptivity is an indispensable capability to tackle multiphysics problems with large disparity in time and length scales. With the availability of powerful supercomputers, there is a pressing need to extend time-proven computational techniques to extreme-scale problems. Cartesian adaptive mesh refinement (AMR) is one such method that enables simulation of multiscale, multiphysics problems. AMR is based on construction of octrees. Originally, an explicit tree data structure was used to generate and manipulate an adaptive Cartesian mesh. At least eight pointers are required in an explicit approach to construct an octree. Parent-child relationships are then used to traverse the tree. An explicit octree, however, is expensive in terms of memory usage and the time it takes to traverse the tree to access a specific node. For these reasons, implicit pointerless methods have been pioneered within the computer graphics community, motivated by applications requiring interactivity and realistic three dimensional visualization. Lewiner et al. [1] provides a concise review of pointerless approaches to generate an octree. Use of a hash table and Z-order curve are two key concepts in pointerless methods that we briefly discuss next.

High-resolution multi-code implementation of unsteady Navier-Stokes flow solver based on paralleled overset adaptive mesh refinement and high-order low-dissipation hybrid schemes

NASA Astrophysics Data System (ADS)

Li, Gaohua; Fu, Xiang; Wang, Fuxin

2017-10-01

The low-dissipation high-order accurate hybrid up-winding/central scheme based on fifth-order weighted essentially non-oscillatory (WENO) and sixth-order central schemes, along with the Spalart-Allmaras (SA)-based delayed detached eddy simulation (DDES) turbulence model, and the flow feature-based adaptive mesh refinement (AMR), are implemented into a dual-mesh overset grid infrastructure with parallel computing capabilities, for the purpose of simulating vortex-dominated unsteady detached wake flows with high spatial resolutions. The overset grid assembly (OGA) process based on collection detection theory and implicit hole-cutting algorithm achieves an automatic coupling for the near-body and off-body solvers, and the error-and-try method is used for obtaining a globally balanced load distribution among the composed multiple codes. The results of flows over high Reynolds cylinder and two-bladed helicopter rotor show that the combination of high-order hybrid scheme, advanced turbulence model, and overset adaptive mesh refinement can effectively enhance the spatial resolution for the simulation of turbulent wake eddies.

Transport Protocols for Wireless Mesh Networks

NASA Astrophysics Data System (ADS)

Eddie Law, K. L.

Transmission control protocol (TCP) provides reliable connection-oriented services between any two end systems on the Internet. With TCP congestion control algorithm, multiple TCP connections can share network and link resources simultaneously. These TCP congestion control mechanisms have been operating effectively in wired networks. However, performance of TCP connections degrades rapidly in wireless and lossy networks. To sustain the throughput performance of TCP connections in wireless networks, design modifications may be required accordingly in the TCP flow control algorithm, and potentially, in association with other protocols in other layers for proper adaptations. In this chapter, we explain the limitations of the latest TCP congestion control algorithm, and then review some popular designs for TCP connections to operate effectively in wireless mesh network infrastructure.

Reconstruction and simplification of urban scene models based on oblique images

NASA Astrophysics Data System (ADS)

Liu, J.; Guo, B.

2014-08-01

We describe a multi-view stereo reconstruction and simplification algorithms for urban scene models based on oblique images. The complexity, diversity, and density within the urban scene, it increases the difficulty to build the city models using the oblique images. But there are a lot of flat surfaces existing in the urban scene. One of our key contributions is that a dense matching algorithm based on Self-Adaptive Patch in view of the urban scene is proposed. The basic idea of matching propagating based on Self-Adaptive Patch is to build patches centred by seed points which are already matched. The extent and shape of the patches can adapt to the objects of urban scene automatically: when the surface is flat, the extent of the patch would become bigger; while the surface is very rough, the extent of the patch would become smaller. The other contribution is that the mesh generated by Graph Cuts is 2-manifold surface satisfied the half edge data structure. It is solved by clustering and re-marking tetrahedrons in s-t graph. The purpose of getting 2- manifold surface is to simply the mesh by edge collapse algorithm which can preserve and stand out the features of buildings.

Adaptive Wavelet Modeling of Geophysical Data

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H.; Dahmen, W.; Vorloeper, J.

2009-12-01

Despite the ever-increasing power of modern computers, realistic modeling of complex three-dimensional Earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modeling approaches includes either finite difference or non-adaptive finite element algorithms, and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behavior of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modeled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet based approach that is applicable to a large scope of problems, also including nonlinear problems. To the best of our knowledge such algorithms have not yet been applied in geophysics. Adaptive wavelet algorithms offer several attractive features: (i) for a given subsurface model, they allow the forward modeling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient, and (iii) the modeling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving three-dimensional geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best fit subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectrical modeling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with spatially highly variable electrical conductivities. The linear dependency of the modeling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementation.

Adaptive grid methods for RLV environment assessment and nozzle analysis

NASA Technical Reports Server (NTRS)

Thornburg, Hugh J.

1996-01-01

Rapid access to highly accurate data about complex configurations is needed for multi-disciplinary optimization and design. In order to efficiently meet these requirements a closer coupling between the analysis algorithms and the discretization process is needed. In some cases, such as free surface, temporally varying geometries, and fluid structure interaction, the need is unavoidable. In other cases the need is to rapidly generate and modify high quality grids. Techniques such as unstructured and/or solution-adaptive methods can be used to speed the grid generation process and to automatically cluster mesh points in regions of interest. Global features of the flow can be significantly affected by isolated regions of inadequately resolved flow. These regions may not exhibit high gradients and can be difficult to detect. Thus excessive resolution in certain regions does not necessarily increase the accuracy of the overall solution. Several approaches have been employed for both structured and unstructured grid adaption. The most widely used involve grid point redistribution, local grid point enrichment/derefinement or local modification of the actual flow solver. However, the success of any one of these methods ultimately depends on the feature detection algorithm used to determine solution domain regions which require a fine mesh for their accurate representation. Typically, weight functions are constructed to mimic the local truncation error and may require substantial user input. Most problems of engineering interest involve multi-block grids and widely disparate length scales. Hence, it is desirable that the adaptive grid feature detection algorithm be developed to recognize flow structures of different type as well as differing intensity, and adequately address scaling and normalization across blocks. These weight functions can then be used to construct blending functions for algebraic redistribution, interpolation functions for unstructured grid generation, forcing functions to attract/repel points in an elliptic system, or to trigger local refinement, based upon application of an equidistribution principle. The popularity of solution-adaptive techniques is growing in tandem with unstructured methods. The difficultly of precisely controlling mesh densities and orientations with current unstructured grid generation systems has driven the use of solution-adaptive meshing. Use of derivatives of density or pressure are widely used for construction of such weight functions, and have been proven very successful for inviscid flows with shocks. However, less success has been realized for flowfields with viscous layers, vortices or shocks of disparate strength. It is difficult to maintain the appropriate mesh point spacing in the various regions which require a fine spacing for adequate resolution. Mesh points often migrate from important regions due to refinement of dominant features. An example of this is the well know tendency of adaptive methods to increase the resolution of shocks in the flowfield around airfoils, but in the incorrect location due to inadequate resolution of the stagnation region. This problem has been the motivation for this research.

Unstructured Mesh Methods for the Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Peraire, Jaime; Bibb, K. L. (Technical Monitor)

2001-01-01

This report describes the research work undertaken at the Massachusetts Institute of Technology. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of hypersonic viscous flows about re-entry vehicles. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use, of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the, code which incorporates real gas effects, has been produced. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. In figures I and 2, we show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although these initial results were encouraging, it became apparent that in order to develop a fully functional capability for viscous flows, several advances in gridding, solution accuracy, robustness and efficiency were required. As part of this research we have developed: 1) automatic meshing techniques and the corresponding computer codes have been delivered to NASA and implemented into the GridEx system, 2) a finite element algorithm for the solution of the viscous compressible flow equations which can solve flows all the way down to the incompressible limit and that can use higher order (quadratic) approximations leading to highly accurate answers, and 3) and iterative algebraic multigrid solution techniques.

Tangle-Free Mesh Motion for Ablation Simulations

NASA Technical Reports Server (NTRS)

Droba, Justin

2016-01-01

Problems involving mesh motion-which should not be mistakenly associated with moving mesh methods, a class of adaptive mesh redistribution techniques-are of critical importance in numerical simulations of the thermal response of melting and ablative materials. Ablation is the process by which material vaporizes or otherwise erodes due to strong heating. Accurate modeling of such materials is of the utmost importance in design of passive thermal protection systems ("heatshields") for spacecraft, the layer of the vehicle that ensures survival of crew and craft during re-entry. In an explicit mesh motion approach, a complete thermal solve is first performed. Afterwards, the thermal response is used to determine surface recession rates. These values are then used to generate boundary conditions for an a posteriori correction designed to update the location of the mesh nodes. Most often, linear elastic or biharmonic equations are used to model this material response, traditionally in a finite element framework so that complex geometries can be simulated. A simple scheme for moving the boundary nodes involves receding along the surface normals. However, for all but the simplest problem geometries, evolution in time following such a scheme will eventually bring the mesh to intersect and "tangle" with itself, inducing failure. This presentation demonstrates a comprehensive and sophisticated scheme that analyzes the local geometry of each node with help from user-provided clues to eliminate the tangle and enable simulations on a wide-class of difficult problem geometries. The method developed is demonstrated for linear elastic equations but is general enough that it may be adapted to other modeling equations. The presentation will explicate the inner workings of the tangle-free mesh motion algorithm for both two and three-dimensional meshes. It will show abstract examples of the method's success, including a verification problem that demonstrates its accuracy and correctness. The focus of the presentation will be on the algorithm; specifics on how the techniques may be used in spacecraft design will be not discussed.

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit

2018-07-01

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n -sided polygon, the quadratic serendipity elements have 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n ( n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements obtained by our greedy algorithms can be further refined using an L 2 -optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.

3D forward modeling and response analysis for marine CSEMs towed by two ships

NASA Astrophysics Data System (ADS)

Zhang, Bo; Yin, Chang-Chun; Liu, Yun-He; Ren, Xiu-Yan; Qi, Yan-Fu; Cai, Jing

2018-03-01

A dual-ship-towed marine electromagnetic (EM) system is a new marine exploration technology recently being developed in China. Compared with traditional marine EM systems, the new system tows the transmitters and receivers using two ships, rendering it unnecessary to position EM receivers at the seafloor in advance. This makes the system more flexible, allowing for different configurations (e.g., in-line, broadside, and azimuthal and concentric scanning) that can produce more detailed underwater structural information. We develop a three-dimensional goal-oriented adaptive forward modeling method for the new marine EM system and analyze the responses for four survey configurations. Oceanbottom topography has a strong effect on the marine EM responses; thus, we develop a forward modeling algorithm based on the finite-element method and unstructured grids. To satisfy the requirements for modeling the moving transmitters of a dual-ship-towed EM system, we use a single mesh for each of the transmitter locations. This mitigates the mesh complexity by refining the grids near the transmitters and minimizes the computational cost. To generate a rational mesh while maintaining the accuracy for single transmitter, we develop a goal-oriented adaptive method with separate mesh refinements for areas around the transmitting source and those far away. To test the modeling algorithm and accuracy, we compare the EM responses calculated by the proposed algorithm and semi-analytical results and from published sources. Furthermore, by analyzing the EM responses for four survey configurations, we are confirm that compared with traditional marine EM systems with only in-line array, a dual-ship-towed marine system can collect more data.

Three-dimensional geoelectric modelling with optimal work/accuracy rate using an adaptive wavelet algorithm

NASA Astrophysics Data System (ADS)

Plattner, A.; Maurer, H. R.; Vorloeper, J.; Dahmen, W.

2010-08-01

Despite the ever-increasing power of modern computers, realistic modelling of complex 3-D earth models is still a challenging task and requires substantial computing resources. The overwhelming majority of current geophysical modelling approaches includes either finite difference or non-adaptive finite element algorithms and variants thereof. These numerical methods usually require the subsurface to be discretized with a fine mesh to accurately capture the behaviour of the physical fields. However, this may result in excessive memory consumption and computing times. A common feature of most of these algorithms is that the modelled data discretizations are independent of the model complexity, which may be wasteful when there are only minor to moderate spatial variations in the subsurface parameters. Recent developments in the theory of adaptive numerical solvers have the potential to overcome this problem. Here, we consider an adaptive wavelet-based approach that is applicable to a large range of problems, also including nonlinear problems. In comparison with earlier applications of adaptive solvers to geophysical problems we employ here a new adaptive scheme whose core ingredients arose from a rigorous analysis of the overall asymptotically optimal computational complexity, including in particular, an optimal work/accuracy rate. Our adaptive wavelet algorithm offers several attractive features: (i) for a given subsurface model, it allows the forward modelling domain to be discretized with a quasi minimal number of degrees of freedom, (ii) sparsity of the associated system matrices is guaranteed, which makes the algorithm memory efficient and (iii) the modelling accuracy scales linearly with computing time. We have implemented the adaptive wavelet algorithm for solving 3-D geoelectric problems. To test its performance, numerical experiments were conducted with a series of conductivity models exhibiting varying degrees of structural complexity. Results were compared with a non-adaptive finite element algorithm, which incorporates an unstructured mesh to best-fitting subsurface boundaries. Such algorithms represent the current state-of-the-art in geoelectric modelling. An analysis of the numerical accuracy as a function of the number of degrees of freedom revealed that the adaptive wavelet algorithm outperforms the finite element solver for simple and moderately complex models, whereas the results become comparable for models with high spatial variability of electrical conductivities. The linear dependence of the modelling error and the computing time proved to be model-independent. This feature will allow very efficient computations using large-scale models as soon as our experimental code is optimized in terms of its implementation.

Computations of Unsteady Viscous Compressible Flows Using Adaptive Mesh Refinement in Curvilinear Body-fitted Grid Systems

NASA Technical Reports Server (NTRS)

Steinthorsson, E.; Modiano, David; Colella, Phillip

1994-01-01

A methodology for accurate and efficient simulation of unsteady, compressible flows is presented. The cornerstones of the methodology are a special discretization of the Navier-Stokes equations on structured body-fitted grid systems and an efficient solution-adaptive mesh refinement technique for structured grids. The discretization employs an explicit multidimensional upwind scheme for the inviscid fluxes and an implicit treatment of the viscous terms. The mesh refinement technique is based on the AMR algorithm of Berger and Colella. In this approach, cells on each level of refinement are organized into a small number of topologically rectangular blocks, each containing several thousand cells. The small number of blocks leads to small overhead in managing data, while their size and regular topology means that a high degree of optimization can be achieved on computers with vector processors.

AMR on the CM-2

NASA Technical Reports Server (NTRS)

Berger, Marsha J.; Saltzman, Jeff S.

1992-01-01

We describe the development of a structured adaptive mesh algorithm (AMR) for the Connection Machine-2 (CM-2). We develop a data layout scheme that preserves locality even for communication between fine and coarse grids. On 8K of a 32K machine we achieve performance slightly less than 1 CPU of the Cray Y-MP. We apply our algorithm to an inviscid compressible flow problem.

Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation

PubMed Central

Gao, Zhanheng; Yu, Zeyun; Holst, Michael

2012-01-01

Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing “bad” triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method. PMID:23144522

Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations

PubMed Central

Feischl, Michael; Gantner, Gregor; Praetorius, Dirk

2015-01-01

We consider the Galerkin boundary element method (BEM) for weakly-singular integral equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the unknown Galerkin BEM error. The required assumptions are weak and allow for piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. In particular, our analysis gives a first contribution to adaptive BEM in the frame of isogeometric analysis (IGABEM), for which we formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments underline the theoretical findings and show that the proposed adaptive strategy leads to optimal convergence. PMID:26085698

A novel adaptive algorithm for 3D finite element analysis to model extracortical bone growth.

PubMed

Cheong, Vee San; Blunn, Gordon W; Coathup, Melanie J; Fromme, Paul

2018-02-01

Extracortical bone growth with osseointegration of bone onto the shaft of massive bone tumour implants is an important clinical outcome for long-term implant survival. A new computational algorithm combining geometrical shape changes and bone adaptation in 3D Finite Element simulations has been developed, using a soft tissue envelope mesh, a novel concept of osteoconnectivity, and bone remodelling theory. The effects of varying the initial tissue density, spatial influence function and time step were investigated. The methodology demonstrated good correspondence to radiological results for a segmental prosthesis.

Marine Controlled-Source Electromagnetic 2D Inversion for synthetic models.

NASA Astrophysics Data System (ADS)

Liu, Y.; Li, Y.

2016-12-01

We present a 2D inverse algorithm for frequency domain marine controlled-source electromagnetic (CSEM) data, which is based on the regularized Gauss-Newton approach. As a forward solver, our parallel adaptive finite element forward modeling program is employed. It is a self-adaptive, goal-oriented grid refinement algorithm in which a finite element analysis is performed on a sequence of refined meshes. The mesh refinement process is guided by a dual error estimate weighting to bias refinement towards elements that affect the solution at the EM receiver locations. With the use of the direct solver (MUMPS), we can effectively compute the electromagnetic fields for multi-sources and parametric sensitivities. We also implement the parallel data domain decomposition approach of Key and Ovall (2011), with the goal of being able to compute accurate responses in parallel for complicated models and a full suite of data parameters typical of offshore CSEM surveys. All minimizations are carried out by using the Gauss-Newton algorithm and model perturbations at each iteration step are obtained by using the Inexact Conjugate Gradient iteration method. Synthetic test inversions are presented.

ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve☆

PubMed Central

Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk

2014-01-01

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments. PMID:24748725

On an adaptive preconditioned Crank-Nicolson MCMC algorithm for infinite dimensional Bayesian inference

NASA Astrophysics Data System (ADS)

Hu, Zixi; Yao, Zhewei; Li, Jinglai

2017-03-01

Many scientific and engineering problems require to perform Bayesian inference for unknowns of infinite dimension. In such problems, many standard Markov Chain Monte Carlo (MCMC) algorithms become arbitrary slow under the mesh refinement, which is referred to as being dimension dependent. To this end, a family of dimensional independent MCMC algorithms, known as the preconditioned Crank-Nicolson (pCN) methods, were proposed to sample the infinite dimensional parameters. In this work we develop an adaptive version of the pCN algorithm, where the covariance operator of the proposal distribution is adjusted based on sampling history to improve the simulation efficiency. We show that the proposed algorithm satisfies an important ergodicity condition under some mild assumptions. Finally we provide numerical examples to demonstrate the performance of the proposed method.

Update on Development of Mesh Generation Algorithms in MeshKit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jain, Rajeev; Vanderzee, Evan; Mahadevan, Vijay

2015-09-30

MeshKit uses a graph-based design for coding all its meshing algorithms, which includes the Reactor Geometry (and mesh) Generation (RGG) algorithms. This report highlights the developmental updates of all the algorithms, results and future work. Parallel versions of algorithms, documentation and performance results are reported. RGG GUI design was updated to incorporate new features requested by the users; boundary layer generation and parallel RGG support were added to the GUI. Key contributions to the release, upgrade and maintenance of other SIGMA1 libraries (CGM and MOAB) were made. Several fundamental meshing algorithms for creating a robust parallel meshing pipeline in MeshKitmore » are under development. Results and current status of automated, open-source and high quality nuclear reactor assembly mesh generation algorithms such as trimesher, quadmesher, interval matching and multi-sweeper are reported.« less

An efficicient data structure for three-dimensional vertex based finite volume method

NASA Astrophysics Data System (ADS)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

Development of an Unstructured Mesh Code for Flows About Complete Vehicles

NASA Technical Reports Server (NTRS)

Peraire, Jaime; Gupta, K. K. (Technical Monitor)

2001-01-01

This report describes the research work undertaken at the Massachusetts Institute of Technology, under NASA Research Grant NAG4-157. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of flow simulations about complete vehicle configurations. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms, flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the code which incorporates real gas effects, has been produced. The FELISA system is also a component of the STARS aeroservoelastic system developed at NASA Dryden. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. We show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although this initial results were encouraging it became apparent that in order to develop a fully functional capability for viscous flows, several advances in solution accuracy, robustness and efficiency were required. In this grant we set out to investigate some novel methodologies that could lead to the required improvements. In particular we focused on two fronts: (1) finite element methods and (2) iterative algebraic multigrid solution techniques.

Thickness distribution of a cooling pyroclastic flow deposit on Augustine Volcano, Alaska: Optimization using InSAR, FEMs, and an adaptive mesh algorithm

USGS Publications Warehouse

Masterlark, Timothy; Lu, Zhong; Rykhus, Russell P.

2006-01-01

Interferometric synthetic aperture radar (InSAR) imagery documents the consistent subsidence, during the interval 1992–1999, of a pyroclastic flow deposit (PFD) emplaced during the 1986 eruption of Augustine Volcano, Alaska. We construct finite element models (FEMs) that simulate thermoelastic contraction of the PFD to account for the observed subsidence. Three-dimensional problem domains of the FEMs include a thermoelastic PFD embedded in an elastic substrate. The thickness of the PFD is initially determined from the difference between post- and pre-eruption digital elevation models (DEMs). The initial excess temperature of the PFD at the time of deposition, 640 °C, is estimated from FEM predictions and an InSAR image via standard least-squares inverse methods. Although the FEM predicts the major features of the observed transient deformation, systematic prediction errors (RMSE = 2.2 cm) are most likely associated with errors in the a priori PFD thickness distribution estimated from the DEM differences. We combine an InSAR image, FEMs, and an adaptive mesh algorithm to iteratively optimize the geometry of the PFD with respect to a minimized misfit between the predicted thermoelastic deformation and observed deformation. Prediction errors from an FEM, which includes an optimized PFD geometry and the initial excess PFD temperature estimated from the least-squares analysis, are sub-millimeter (RMSE = 0.3 mm). The average thickness (9.3 m), maximum thickness (126 m), and volume (2.1 × 107m3) of the PFD, estimated using the adaptive mesh algorithm, are about twice as large as the respective estimations for the a priori PFD geometry. Sensitivity analyses suggest unrealistic PFD thickness distributions are required for initial excess PFD temperatures outside of the range 500–800 °C.

Quinoa - Adaptive Computational Fluid Dynamics, 0.2

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bakosi, Jozsef; Gonzalez, Francisco; Rogers, Brandon

Quinoa is a set of computational tools that enables research and numerical analysis in fluid dynamics. At this time it remains a test-bed to experiment with various algorithms using fully asynchronous runtime systems. Currently, Quinoa consists of the following tools: (1) Walker, a numerical integrator for systems of stochastic differential equations in time. It is a mathematical tool to analyze and design the behavior of stochastic differential equations. It allows the estimation of arbitrary coupled statistics and probability density functions and is currently used for the design of statistical moment approximations for multiple mixing materials in variable-density turbulence. (2) Inciter,more » an overdecomposition-aware finite element field solver for partial differential equations using 3D unstructured grids. Inciter is used to research asynchronous mesh-based algorithms and to experiment with coupling asynchronous to bulk-synchronous parallel code. Two planned new features of Inciter, compared to the previous release (LA-CC-16-015), to be implemented in 2017, are (a) a simple Navier-Stokes solver for ideal single-material compressible gases, and (b) solution-adaptive mesh refinement (AMR), which enables dynamically concentrating compute resources to regions with interesting physics. Using the NS-AMR problem we plan to explore how to scale such high-load-imbalance simulations, representative of large production multiphysics codes, to very large problems on very large computers using an asynchronous runtime system. (3) RNGTest, a test harness to subject random number generators to stringent statistical tests enabling quantitative ranking with respect to their quality and computational cost. (4) UnitTest, a unit test harness, running hundreds of tests per second, capable of testing serial, synchronous, and asynchronous functions. (5) MeshConv, a mesh file converter that can be used to convert 3D tetrahedron meshes from and to either of the following formats: Gmsh, (http://www.geuz.org/gmsh), Netgen, (http://sourceforge.net/apps/mediawiki/netgen-mesher), ExodusII, (http://sourceforge.net/projects/exodusii), HyperMesh, (http://www.altairhyperworks.com/product/HyperMesh).« less

Implementation of a flexible and scalable particle-in-cell method for massively parallel computations in the mantle convection code ASPECT

NASA Astrophysics Data System (ADS)

Gassmöller, Rene; Bangerth, Wolfgang

2016-04-01

Particle-in-cell methods have a long history and many applications in geodynamic modelling of mantle convection, lithospheric deformation and crustal dynamics. They are primarily used to track material information, the strain a material has undergone, the pressure-temperature history a certain material region has experienced, or the amount of volatiles or partial melt present in a region. However, their efficient parallel implementation - in particular combined with adaptive finite-element meshes - is complicated due to the complex communication patterns and frequent reassignment of particles to cells. Consequently, many current scientific software packages accomplish this efficient implementation by specifically designing particle methods for a single purpose, like the advection of scalar material properties that do not evolve over time (e.g., for chemical heterogeneities). Design choices for particle integration, data storage, and parallel communication are then optimized for this single purpose, making the code relatively rigid to changing requirements. Here, we present the implementation of a flexible, scalable and efficient particle-in-cell method for massively parallel finite-element codes with adaptively changing meshes. Using a modular plugin structure, we allow maximum flexibility of the generation of particles, the carried tracer properties, the advection and output algorithms, and the projection of properties to the finite-element mesh. We present scaling tests ranging up to tens of thousands of cores and tens of billions of particles. Additionally, we discuss efficient load-balancing strategies for particles in adaptive meshes with their strengths and weaknesses, local particle-transfer between parallel subdomains utilizing existing communication patterns from the finite element mesh, and the use of established parallel output algorithms like the HDF5 library. Finally, we show some relevant particle application cases, compare our implementation to a modern advection-field approach, and demonstrate under which conditions which method is more efficient. We implemented the presented methods in ASPECT (aspect.dealii.org), a freely available open-source community code for geodynamic simulations. The structure of the particle code is highly modular, and segregated from the PDE solver, and can thus be easily transferred to other programs, or adapted for various application cases.

Adaptive Grid Refinement for Atmospheric Boundary Layer Simulations

NASA Astrophysics Data System (ADS)

van Hooft, Antoon; van Heerwaarden, Chiel; Popinet, Stephane; van der linden, Steven; de Roode, Stephan; van de Wiel, Bas

2017-04-01

We validate and benchmark an adaptive mesh refinement (AMR) algorithm for numerical simulations of the atmospheric boundary layer (ABL). The AMR technique aims to distribute the computational resources efficiently over a domain by refining and coarsening the numerical grid locally and in time. This can be beneficial for studying cases in which length scales vary significantly in time and space. We present the results for a case describing the growth and decay of a convective boundary layer. The AMR results are benchmarked against two runs using a fixed, fine meshed grid. First, with the same numerical formulation as the AMR-code and second, with a code dedicated to ABL studies. Compared to the fixed and isotropic grid runs, the AMR algorithm can coarsen and refine the grid such that accurate results are obtained whilst using only a fraction of the grid cells. Performance wise, the AMR run was cheaper than the fixed and isotropic grid run with similar numerical formulations. However, for this specific case, the dedicated code outperformed both aforementioned runs.

Wavelet-based Adaptive Mesh Refinement Method for Global Atmospheric Chemical Transport Modeling

NASA Astrophysics Data System (ADS)

Rastigejev, Y.

2011-12-01

Numerical modeling of global atmospheric chemical transport presents enormous computational difficulties, associated with simulating a wide range of time and spatial scales. The described difficulties are exacerbated by the fact that hundreds of chemical species and thousands of chemical reactions typically are used for chemical kinetic mechanism description. These computational requirements very often forces researches to use relatively crude quasi-uniform numerical grids with inadequate spatial resolution that introduces significant numerical diffusion into the system. It was shown that this spurious diffusion significantly distorts the pollutant mixing and transport dynamics for typically used grid resolution. The described numerical difficulties have to be systematically addressed considering that the demand for fast, high-resolution chemical transport models will be exacerbated over the next decade by the need to interpret satellite observations of tropospheric ozone and related species. In this study we offer dynamically adaptive multilevel Wavelet-based Adaptive Mesh Refinement (WAMR) method for numerical modeling of atmospheric chemical evolution equations. The adaptive mesh refinement is performed by adding and removing finer levels of resolution in the locations of fine scale development and in the locations of smooth solution behavior accordingly. The algorithm is based on the mathematically well established wavelet theory. This allows us to provide error estimates of the solution that are used in conjunction with an appropriate threshold criteria to adapt the non-uniform grid. Other essential features of the numerical algorithm include: an efficient wavelet spatial discretization that allows to minimize the number of degrees of freedom for a prescribed accuracy, a fast algorithm for computing wavelet amplitudes, and efficient and accurate derivative approximations on an irregular grid. The method has been tested for a variety of benchmark problems including numerical simulation of transpacific traveling pollution plumes. The generated pollution plumes are diluted due to turbulent mixing as they are advected downwind. Despite this dilution, it was recently discovered that pollution plumes in the remote troposphere can preserve their identity as well-defined structures for two weeks or more as they circle the globe. Present Global Chemical Transport Models (CTMs) implemented for quasi-uniform grids are completely incapable of reproducing these layered structures due to high numerical plume dilution caused by numerical diffusion combined with non-uniformity of atmospheric flow. It is shown that WAMR algorithm solutions of comparable accuracy as conventional numerical techniques are obtained with more than an order of magnitude reduction in number of grid points, therefore the adaptive algorithm is capable to produce accurate results at a relatively low computational cost. The numerical simulations demonstrate that WAMR algorithm applied the traveling plume problem accurately reproduces the plume dynamics unlike conventional numerical methods that utilizes quasi-uniform numerical grids.

A novel partitioning method for block-structured adaptive meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, Lin, E-mail: lin.fu@tum.de; Litvinov, Sergej, E-mail: sergej.litvinov@aer.mw.tum.de; Hu, Xiangyu Y., E-mail: xiangyu.hu@tum.de

We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtainmore » the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.« less

A novel partitioning method for block-structured adaptive meshes

NASA Astrophysics Data System (ADS)

Fu, Lin; Litvinov, Sergej; Hu, Xiangyu Y.; Adams, Nikolaus A.

2017-07-01

We propose a novel partitioning method for block-structured adaptive meshes utilizing the meshless Lagrangian particle concept. With the observation that an optimum partitioning has high analogy to the relaxation of a multi-phase fluid to steady state, physically motivated model equations are developed to characterize the background mesh topology and are solved by multi-phase smoothed-particle hydrodynamics. In contrast to well established partitioning approaches, all optimization objectives are implicitly incorporated and achieved during the particle relaxation to stationary state. Distinct partitioning sub-domains are represented by colored particles and separated by a sharp interface with a surface tension model. In order to obtain the particle relaxation, special viscous and skin friction models, coupled with a tailored time integration algorithm are proposed. Numerical experiments show that the present method has several important properties: generation of approximately equal-sized partitions without dependence on the mesh-element type, optimized interface communication between distinct partitioning sub-domains, continuous domain decomposition which is physically localized and implicitly incremental. Therefore it is particularly suitable for load-balancing of high-performance CFD simulations.

An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

NASA Astrophysics Data System (ADS)

Papoutsakis, Andreas; Sazhin, Sergei S.; Begg, Steven; Danaila, Ionut; Luddens, Francky

2018-06-01

We present an Adaptive Mesh Refinement (AMR) method suitable for hybrid unstructured meshes that allows for local refinement and de-refinement of the computational grid during the evolution of the flow. The adaptive implementation of the Discontinuous Galerkin (DG) method introduced in this work (ForestDG) is based on a topological representation of the computational mesh by a hierarchical structure consisting of oct- quad- and binary trees. Adaptive mesh refinement (h-refinement) enables us to increase the spatial resolution of the computational mesh in the vicinity of the points of interest such as interfaces, geometrical features, or flow discontinuities. The local increase in the expansion order (p-refinement) at areas of high strain rates or vorticity magnitude results in an increase of the order of accuracy in the region of shear layers and vortices. A graph of unitarian-trees, representing hexahedral, prismatic and tetrahedral elements is used for the representation of the initial domain. The ancestral elements of the mesh can be split into self-similar elements allowing each tree to grow branches to an arbitrary level of refinement. The connectivity of the elements, their genealogy and their partitioning are described by linked lists of pointers. An explicit calculation of these relations, presented in this paper, facilitates the on-the-fly splitting, merging and repartitioning of the computational mesh by rearranging the links of each node of the tree with a minimal computational overhead. The modal basis used in the DG implementation facilitates the mapping of the fluxes across the non conformal faces. The AMR methodology is presented and assessed using a series of inviscid and viscous test cases. Also, the AMR methodology is used for the modelling of the interaction between droplets and the carrier phase in a two-phase flow. This approach is applied to the analysis of a spray injected into a chamber of quiescent air, using the Eulerian-Lagrangian approach. This enables us to refine the computational mesh in the vicinity of the droplet parcels and accurately resolve the coupling between the two phases.

New algorithms for field-theoretic block copolymer simulations: Progress on using adaptive-mesh refinement and sparse matrix solvers in SCFT calculations

NASA Astrophysics Data System (ADS)

Sides, Scott; Jamroz, Ben; Crockett, Robert; Pletzer, Alexander

2012-02-01

Self-consistent field theory (SCFT) for dense polymer melts has been highly successful in describing complex morphologies in block copolymers. Field-theoretic simulations such as these are able to access large length and time scales that are difficult or impossible for particle-based simulations such as molecular dynamics. The modified diffusion equations that arise as a consequence of the coarse-graining procedure in the SCF theory can be efficiently solved with a pseudo-spectral (PS) method that uses fast-Fourier transforms on uniform Cartesian grids. However, PS methods can be difficult to apply in many block copolymer SCFT simulations (eg. confinement, interface adsorption) in which small spatial regions might require finer resolution than most of the simulation grid. Progress on using new solver algorithms to address these problems will be presented. The Tech-X Chompst project aims at marrying the best of adaptive mesh refinement with linear matrix solver algorithms. The Tech-X code PolySwift++ is an SCFT simulation platform that leverages ongoing development in coupling Chombo, a package for solving PDEs via block-structured AMR calculations and embedded boundaries, with PETSc, a toolkit that includes a large assortment of sparse linear solvers.

4D cone-beam CT reconstruction using multi-organ meshes for sliding motion modeling

NASA Astrophysics Data System (ADS)

Zhong, Zichun; Gu, Xuejun; Mao, Weihua; Wang, Jing

2016-02-01

A simultaneous motion estimation and image reconstruction (SMEIR) strategy was proposed for 4D cone-beam CT (4D-CBCT) reconstruction and showed excellent results in both phantom and lung cancer patient studies. In the original SMEIR algorithm, the deformation vector field (DVF) was defined on voxel grid and estimated by enforcing a global smoothness regularization term on the motion fields. The objective of this work is to improve the computation efficiency and motion estimation accuracy of SMEIR for 4D-CBCT through developing a multi-organ meshing model. Feature-based adaptive meshes were generated to reduce the number of unknowns in the DVF estimation and accurately capture the organ shapes and motion. Additionally, the discontinuity in the motion fields between different organs during respiration was explicitly considered in the multi-organ mesh model. This will help with the accurate visualization and motion estimation of the tumor on the organ boundaries in 4D-CBCT. To further improve the computational efficiency, a GPU-based parallel implementation was designed. The performance of the proposed algorithm was evaluated on a synthetic sliding motion phantom, a 4D NCAT phantom, and four lung cancer patients. The proposed multi-organ mesh based strategy outperformed the conventional Feldkamp-Davis-Kress, iterative total variation minimization, original SMEIR and single meshing method based on both qualitative and quantitative evaluations.

4D cone-beam CT reconstruction using multi-organ meshes for sliding motion modeling.

PubMed

Zhong, Zichun; Gu, Xuejun; Mao, Weihua; Wang, Jing

2016-02-07

A simultaneous motion estimation and image reconstruction (SMEIR) strategy was proposed for 4D cone-beam CT (4D-CBCT) reconstruction and showed excellent results in both phantom and lung cancer patient studies. In the original SMEIR algorithm, the deformation vector field (DVF) was defined on voxel grid and estimated by enforcing a global smoothness regularization term on the motion fields. The objective of this work is to improve the computation efficiency and motion estimation accuracy of SMEIR for 4D-CBCT through developing a multi-organ meshing model. Feature-based adaptive meshes were generated to reduce the number of unknowns in the DVF estimation and accurately capture the organ shapes and motion. Additionally, the discontinuity in the motion fields between different organs during respiration was explicitly considered in the multi-organ mesh model. This will help with the accurate visualization and motion estimation of the tumor on the organ boundaries in 4D-CBCT. To further improve the computational efficiency, a GPU-based parallel implementation was designed. The performance of the proposed algorithm was evaluated on a synthetic sliding motion phantom, a 4D NCAT phantom, and four lung cancer patients. The proposed multi-organ mesh based strategy outperformed the conventional Feldkamp-Davis-Kress, iterative total variation minimization, original SMEIR and single meshing method based on both qualitative and quantitative evaluations.

4D cone-beam CT reconstruction using multi-organ meshes for sliding motion modeling

PubMed Central

Zhong, Zichun; Gu, Xuejun; Mao, Weihua; Wang, Jing

2016-01-01

A simultaneous motion estimation and image reconstruction (SMEIR) strategy was proposed for 4D cone-beam CT (4D-CBCT) reconstruction and showed excellent results in both phantom and lung cancer patient studies. In the original SMEIR algorithm, the deformation vector field (DVF) was defined on voxel grid and estimated by enforcing a global smoothness regularization term on the motion fields. The objective of this work is to improve the computation efficiency and motion estimation accuracy of SMEIR for 4D-CBCT through developing a multi-organ meshing model. Feature-based adaptive meshes were generated to reduce the number of unknowns in the DVF estimation and accurately capture the organ shapes and motion. Additionally, the discontinuity in the motion fields between different organs during respiration was explicitly considered in the multi-organ mesh model. This will help with the accurate visualization and motion estimation of the tumor on the organ boundaries in 4D-CBCT. To further improve the computational efficiency, a GPU-based parallel implementation was designed. The performance of the proposed algorithm was evaluated on a synthetic sliding motion phantom, a 4D NCAT phantom, and four lung cancer patients. The proposed multi-organ mesh based strategy outperformed the conventional Feldkamp–Davis–Kress, iterative total variation minimization, original SMEIR and single meshing method based on both qualitative and quantitative evaluations. PMID:26758496

Discrete Data Transfer Technique for Fluid-Structure Interaction

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2007-01-01

This paper presents a general three-dimensional algorithm for data transfer between dissimilar meshes. The algorithm is suitable for applications of fluid-structure interaction and other high-fidelity multidisciplinary analysis and optimization. Because the algorithm is independent of the mesh topology, we can treat structured and unstructured meshes in the same manner. The algorithm is fast and accurate for transfer of scalar or vector fields between dissimilar surface meshes. The algorithm is also applicable for the integration of a scalar field (e.g., coefficients of pressure) on one mesh and injection of the resulting vectors (e.g., force vectors) onto another mesh. The author has implemented the algorithm in a C++ computer code. This paper contains a complete formulation of the algorithm with a few selected results.

A dynamically adaptive multigrid algorithm for the incompressible Navier-Stokes equations: Validation and model problems

NASA Technical Reports Server (NTRS)

Thompson, C. P.; Leaf, G. K.; Vanrosendale, J.

1991-01-01

An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction.

Incremental update of electrostatic interactions in adaptively restrained particle simulations.

PubMed

Edorh, Semeho Prince A; Redon, Stéphane

2018-04-06

The computation of long-range potentials is one of the demanding tasks in Molecular Dynamics. During the last decades, an inventive panoply of methods was developed to reduce the CPU time of this task. In this work, we propose a fast method dedicated to the computation of the electrostatic potential in adaptively restrained systems. We exploit the fact that, in such systems, only some particles are allowed to move at each timestep. We developed an incremental algorithm derived from a multigrid-based alternative to traditional Fourier-based methods. Our algorithm was implemented inside LAMMPS, a popular molecular dynamics simulation package. We evaluated the method on different systems. We showed that the new algorithm's computational complexity scales with the number of active particles in the simulated system, and is able to outperform the well-established Particle Particle Particle Mesh (P3M) for adaptively restrained simulations. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

An Anisotropic A posteriori Error Estimator for CFD

NASA Astrophysics Data System (ADS)

Feijóo, Raúl A.; Padra, Claudio; Quintana, Fernando

In this article, a robust anisotropic adaptive algorithm is presented, to solve compressible-flow equations using a stabilized CFD solver and automatic mesh generators. The association includes a mesh generator, a flow solver, and an a posteriori error-estimator code. The estimator was selected among several choices available (Almeida et al. (2000). Comput. Methods Appl. Mech. Engng, 182, 379-400; Borges et al. (1998). "Computational mechanics: new trends and applications". Proceedings of the 4th World Congress on Computational Mechanics, Bs.As., Argentina) giving a powerful computational tool. The main aim is to capture solution discontinuities, in this case, shocks, using the least amount of computational resources, i.e. elements, compatible with a solution of good quality. This leads to high aspect-ratio elements (stretching). To achieve this, a directional error estimator was specifically selected. The numerical results show good behavior of the error estimator, resulting in strongly-adapted meshes in few steps, typically three or four iterations, enough to capture shocks using a moderate and well-distributed amount of elements.

Tree-based solvers for adaptive mesh refinement code FLASH - I: gravity and optical depths

NASA Astrophysics Data System (ADS)

Wünsch, R.; Walch, S.; Dinnbier, F.; Whitworth, A.

2018-04-01

We describe an OctTree algorithm for the MPI parallel, adaptive mesh refinement code FLASH, which can be used to calculate the gas self-gravity, and also the angle-averaged local optical depth, for treating ambient diffuse radiation. The algorithm communicates to the different processors only those parts of the tree that are needed to perform the tree-walk locally. The advantage of this approach is a relatively low memory requirement, important in particular for the optical depth calculation, which needs to process information from many different directions. This feature also enables a general tree-based radiation transport algorithm that will be described in a subsequent paper, and delivers excellent scaling up to at least 1500 cores. Boundary conditions for gravity can be either isolated or periodic, and they can be specified in each direction independently, using a newly developed generalization of the Ewald method. The gravity calculation can be accelerated with the adaptive block update technique by partially re-using the solution from the previous time-step. Comparison with the FLASH internal multigrid gravity solver shows that tree-based methods provide a competitive alternative, particularly for problems with isolated or mixed boundary conditions. We evaluate several multipole acceptance criteria (MACs) and identify a relatively simple approximate partial error MAC which provides high accuracy at low computational cost. The optical depth estimates are found to agree very well with those of the RADMC-3D radiation transport code, with the tree-solver being much faster. Our algorithm is available in the standard release of the FLASH code in version 4.0 and later.

Predicting mesh density for adaptive modelling of the global atmosphere.

PubMed

Weller, Hilary

2009-11-28

The shallow water equations are solved using a mesh of polygons on the sphere, which adapts infrequently to the predicted future solution. Infrequent mesh adaptation reduces the cost of adaptation and load-balancing and will thus allow for more accurate mapping on adaptation. We simulate the growth of a barotropically unstable jet adapting the mesh every 12 h. Using an adaptation criterion based largely on the gradient of the vorticity leads to a mesh with around 20 per cent of the cells of a uniform mesh that gives equivalent results. This is a similar proportion to previous studies of the same test case with mesh adaptation every 1-20 min. The prediction of the mesh density involves solving the shallow water equations on a coarse mesh in advance of the locally refined mesh in order to estimate where features requiring higher resolution will grow, decay or move to. The adaptation criterion consists of two parts: that resolved on the coarse mesh, and that which is not resolved and so is passively advected on the coarse mesh. This combination leads to a balance between resolving features controlled by the large-scale dynamics and maintaining fine-scale features.

An upwind method for the solution of the 3D Euler and Navier-Stokes equations on adaptively refined meshes

NASA Astrophysics Data System (ADS)

Aftosmis, Michael J.

1992-10-01

A new node based upwind scheme for the solution of the 3D Navier-Stokes equations on adaptively refined meshes is presented. The method uses a second-order upwind TVD scheme to integrate the convective terms, and discretizes the viscous terms with a new compact central difference technique. Grid adaptation is achieved through directional division of hexahedral cells in response to evolving features as the solution converges. The method is advanced in time with a multistage Runge-Kutta time stepping scheme. Two- and three-dimensional examples establish the accuracy of the inviscid and viscous discretization. These investigations highlight the ability of the method to produce crisp shocks, while accurately and economically resolving viscous layers. The representation of these and other structures is shown to be comparable to that obtained by structured methods. Further 3D examples demonstrate the ability of the adaptive algorithm to effectively locate and resolve multiple scale features in complex 3D flows with many interacting, viscous, and inviscid structures.

Introducing Enabling Computational Tools to the Climate Sciences: Multi-Resolution Climate Modeling with Adaptive Cubed-Sphere Grids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jablonowski, Christiane

The research investigates and advances strategies how to bridge the scale discrepancies between local, regional and global phenomena in climate models without the prohibitive computational costs of global cloud-resolving simulations. In particular, the research explores new frontiers in computational geoscience by introducing high-order Adaptive Mesh Refinement (AMR) techniques into climate research. AMR and statically-adapted variable-resolution approaches represent an emerging trend for atmospheric models and are likely to become the new norm in future-generation weather and climate models. The research advances the understanding of multi-scale interactions in the climate system and showcases a pathway how to model these interactions effectively withmore » advanced computational tools, like the Chombo AMR library developed at the Lawrence Berkeley National Laboratory. The research is interdisciplinary and combines applied mathematics, scientific computing and the atmospheric sciences. In this research project, a hierarchy of high-order atmospheric models on cubed-sphere computational grids have been developed that serve as an algorithmic prototype for the finite-volume solution-adaptive Chombo-AMR approach. The foci of the investigations have lied on the characteristics of both static mesh adaptations and dynamically-adaptive grids that can capture flow fields of interest like tropical cyclones. Six research themes have been chosen. These are (1) the introduction of adaptive mesh refinement techniques into the climate sciences, (2) advanced algorithms for nonhydrostatic atmospheric dynamical cores, (3) an assessment of the interplay between resolved-scale dynamical motions and subgrid-scale physical parameterizations, (4) evaluation techniques for atmospheric model hierarchies, (5) the comparison of AMR refinement strategies and (6) tropical cyclone studies with a focus on multi-scale interactions and variable-resolution modeling. The results of this research project demonstrate significant advances in all six research areas. The major conclusions are that statically-adaptive variable-resolution modeling is currently becoming mature in the climate sciences, and that AMR holds outstanding promise for future-generation weather and climate models on high-performance computing architectures.« less

3-D inversion of airborne electromagnetic data parallelized and accelerated by local mesh and adaptive soundings

NASA Astrophysics Data System (ADS)

Yang, Dikun; Oldenburg, Douglas W.; Haber, Eldad

2014-03-01

Airborne electromagnetic (AEM) methods are highly efficient tools for assessing the Earth's conductivity structures in a large area at low cost. However, the configuration of AEM measurements, which typically have widely distributed transmitter-receiver pairs, makes the rigorous modelling and interpretation extremely time-consuming in 3-D. Excessive overcomputing can occur when working on a large mesh covering the entire survey area and inverting all soundings in the data set. We propose two improvements. The first is to use a locally optimized mesh for each AEM sounding for the forward modelling and calculation of sensitivity. This dedicated local mesh is small with fine cells near the sounding location and coarse cells far away in accordance with EM diffusion and the geometric decay of the signals. Once the forward problem is solved on the local meshes, the sensitivity for the inversion on the global mesh is available through quick interpolation. Using local meshes for AEM forward modelling avoids unnecessary computing on fine cells on a global mesh that are far away from the sounding location. Since local meshes are highly independent, the forward modelling can be efficiently parallelized over an array of processors. The second improvement is random and dynamic down-sampling of the soundings. Each inversion iteration only uses a random subset of the soundings, and the subset is reselected for every iteration. The number of soundings in the random subset, determined by an adaptive algorithm, is tied to the degree of model regularization. This minimizes the overcomputing caused by working with redundant soundings. Our methods are compared against conventional methods and tested with a synthetic example. We also invert a field data set that was previously considered to be too large to be practically inverted in 3-D. These examples show that our methodology can dramatically reduce the processing time of 3-D inversion to a practical level without losing resolution. Any existing modelling technique can be included into our framework of mesh decoupling and adaptive sampling to accelerate large-scale 3-D EM inversions.

Modeling NIF experimental designs with adaptive mesh refinement and Lagrangian hydrodynamics

NASA Astrophysics Data System (ADS)

Koniges, A. E.; Anderson, R. W.; Wang, P.; Gunney, B. T. N.; Becker, R.; Eder, D. C.; MacGowan, B. J.; Schneider, M. B.

2006-06-01

Incorporation of adaptive mesh refinement (AMR) into Lagrangian hydrodynamics algorithms allows for the creation of a highly powerful simulation tool effective for complex target designs with three-dimensional structure. We are developing an advanced modeling tool that includes AMR and traditional arbitrary Lagrangian-Eulerian (ALE) techniques. Our goal is the accurate prediction of vaporization, disintegration and fragmentation in National Ignition Facility (NIF) experimental target elements. Although our focus is on minimizing the generation of shrapnel in target designs and protecting the optics, the general techniques are applicable to modern advanced targets that include three-dimensional effects such as those associated with capsule fill tubes. Several essential computations in ordinary radiation hydrodynamics need to be redesigned in order to allow for AMR to work well with ALE, including algorithms associated with radiation transport. Additionally, for our goal of predicting fragmentation, we include elastic/plastic flow into our computations. We discuss the integration of these effects into a new ALE-AMR simulation code. Applications of this newly developed modeling tool as well as traditional ALE simulations in two and three dimensions are applied to NIF early-light target designs.

A cellular automaton - finite volume method for the simulation of dendritic and eutectic growth in binary alloys using an adaptive mesh refinement

NASA Astrophysics Data System (ADS)

Dobravec, Tadej; Mavrič, Boštjan; Šarler, Božidar

2017-11-01

A two-dimensional model to simulate the dendritic and eutectic growth in binary alloys is developed. A cellular automaton method is adopted to track the movement of the solid-liquid interface. The diffusion equation is solved in the solid and liquid phases by using an explicit finite volume method. The computational domain is divided into square cells that can be hierarchically refined or coarsened using an adaptive mesh based on the quadtree algorithm. Such a mesh refines the regions of the domain near the solid-liquid interface, where the highest concentration gradients are observed. In the regions where the lowest concentration gradients are observed the cells are coarsened. The originality of the work is in the novel, adaptive approach to the efficient and accurate solution of the posed multiscale problem. The model is verified and assessed by comparison with the analytical results of the Lipton-Glicksman-Kurz model for the steady growth of a dendrite tip and the Jackson-Hunt model for regular eutectic growth. Several examples of typical microstructures are simulated and the features of the method as well as further developments are discussed.

Implementation of tetrahedral-mesh geometry in Monte Carlo radiation transport code PHITS

NASA Astrophysics Data System (ADS)

Furuta, Takuya; Sato, Tatsuhiko; Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Brown, Justin L.; Bolch, Wesley E.

2017-06-01

A new function to treat tetrahedral-mesh geometry was implemented in the particle and heavy ion transport code systems. To accelerate the computational speed in the transport process, an original algorithm was introduced to initially prepare decomposition maps for the container box of the tetrahedral-mesh geometry. The computational performance was tested by conducting radiation transport simulations of 100 MeV protons and 1 MeV photons in a water phantom represented by tetrahedral mesh. The simulation was repeated with varying number of meshes and the required computational times were then compared with those of the conventional voxel representation. Our results show that the computational costs for each boundary crossing of the region mesh are essentially equivalent for both representations. This study suggests that the tetrahedral-mesh representation offers not only a flexible description of the transport geometry but also improvement of computational efficiency for the radiation transport. Due to the adaptability of tetrahedrons in both size and shape, dosimetrically equivalent objects can be represented by tetrahedrons with a much fewer number of meshes as compared its voxelized representation. Our study additionally included dosimetric calculations using a computational human phantom. A significant acceleration of the computational speed, about 4 times, was confirmed by the adoption of a tetrahedral mesh over the traditional voxel mesh geometry.

Implementation of tetrahedral-mesh geometry in Monte Carlo radiation transport code PHITS.

PubMed

Furuta, Takuya; Sato, Tatsuhiko; Han, Min Cheol; Yeom, Yeon Soo; Kim, Chan Hyeong; Brown, Justin L; Bolch, Wesley E

2017-06-21

A new function to treat tetrahedral-mesh geometry was implemented in the particle and heavy ion transport code systems. To accelerate the computational speed in the transport process, an original algorithm was introduced to initially prepare decomposition maps for the container box of the tetrahedral-mesh geometry. The computational performance was tested by conducting radiation transport simulations of 100 MeV protons and 1 MeV photons in a water phantom represented by tetrahedral mesh. The simulation was repeated with varying number of meshes and the required computational times were then compared with those of the conventional voxel representation. Our results show that the computational costs for each boundary crossing of the region mesh are essentially equivalent for both representations. This study suggests that the tetrahedral-mesh representation offers not only a flexible description of the transport geometry but also improvement of computational efficiency for the radiation transport. Due to the adaptability of tetrahedrons in both size and shape, dosimetrically equivalent objects can be represented by tetrahedrons with a much fewer number of meshes as compared its voxelized representation. Our study additionally included dosimetric calculations using a computational human phantom. A significant acceleration of the computational speed, about 4 times, was confirmed by the adoption of a tetrahedral mesh over the traditional voxel mesh geometry.

Mesh Algorithms for PDE with Sieve I: Mesh Distribution

DOE PAGES

Knepley, Matthew G.; Karpeev, Dmitry A.

2009-01-01

We have developed a new programming framework, called Sieve, to support parallel numerical partial differential equation(s) (PDE) algorithms operating over distributed meshes. We have also developed a reference implementation of Sieve in C++ as a library of generic algorithms operating on distributed containers conforming to the Sieve interface. Sieve makes instances of the incidence relation, or arrows, the conceptual first-class objects represented in the containers. Further, generic algorithms acting on this arrow container are systematically used to provide natural geometric operations on the topology and also, through duality, on the data. Finally, coverings and duality are used to encode notmore » only individual meshes, but all types of hierarchies underlying PDE data structures, including multigrid and mesh partitions. In order to demonstrate the usefulness of the framework, we show how the mesh partition data can be represented and manipulated using the same fundamental mechanisms used to represent meshes. We present the complete description of an algorithm to encode a mesh partition and then distribute a mesh, which is independent of the mesh dimension, element shape, or embedding. Moreover, data associated with the mesh can be similarly distributed with exactly the same algorithm. The use of a high level of abstraction within the Sieve leads to several benefits in terms of code reuse, simplicity, and extensibility. We discuss these benefits and compare our approach to other existing mesh libraries.« less

High-Performance Java Codes for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Riley, Christopher; Chatterjee, Siddhartha; Biswas, Rupak; Biegel, Bryan (Technical Monitor)

2001-01-01

The computational science community is reluctant to write large-scale computationally -intensive applications in Java due to concerns over Java's poor performance, despite the claimed software engineering advantages of its object-oriented features. Naive Java implementations of numerical algorithms can perform poorly compared to corresponding Fortran or C implementations. To achieve high performance, Java applications must be designed with good performance as a primary goal. This paper presents the object-oriented design and implementation of two real-world applications from the field of Computational Fluid Dynamics (CFD): a finite-volume fluid flow solver (LAURA, from NASA Langley Research Center), and an unstructured mesh adaptation algorithm (2D_TAG, from NASA Ames Research Center). This work builds on our previous experience with the design of high-performance numerical libraries in Java. We examine the performance of the applications using the currently available Java infrastructure and show that the Java version of the flow solver LAURA performs almost within a factor of 2 of the original procedural version. Our Java version of the mesh adaptation algorithm 2D_TAG performs within a factor of 1.5 of its original procedural version on certain platforms. Our results demonstrate that object-oriented software design principles are not necessarily inimical to high performance.

Constrained-transport Magnetohydrodynamics with Adaptive Mesh Refinement in CHARM

NASA Astrophysics Data System (ADS)

Miniati, Francesco; Martin, Daniel F.

2011-07-01

We present the implementation of a three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the piecewise-parabolic method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a constrained-transport (CT) method. The so-called multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem, and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.

SAGE: The Self-Adaptive Grid Code. 3

NASA Technical Reports Server (NTRS)

Davies, Carol B.; Venkatapathy, Ethiraj

1999-01-01

The multi-dimensional self-adaptive grid code, SAGE, is an important tool in the field of computational fluid dynamics (CFD). It provides an efficient method to improve the accuracy of flow solutions while simultaneously reducing computer processing time. Briefly, SAGE enhances an initial computational grid by redistributing the mesh points into more appropriate locations. The movement of these points is driven by an equal-error-distribution algorithm that utilizes the relationship between high flow gradients and excessive solution errors. The method also provides a balance between clustering points in the high gradient regions and maintaining the smoothness and continuity of the adapted grid, The latest version, Version 3, includes the ability to change the boundaries of a given grid to more efficiently enclose flow structures and provides alternative redistribution algorithms.

Three-Dimensional Stable Nonorthogonal FDTD Algorithm with Adaptive Mesh Refinement for Solving Maxwell’s Equations

DTIC Science & Technology

2013-03-01

Räisänen. An efficient FDTD algorithm for the analysis of microstrip patch antennas printed on a general anisotropic dielectric substrate. IEEE...applications [3, 21, 22], including antenna , microwave circuits, geophysics, optics, etc. The Ground Penetrating Radar (GPR) is a popular and...IEEE Trans. Antennas Propag., 41:994–999, 1993. 16 [6] S. G. Garcia, T. M. Hung-Bao, R. G. Martin, and B. G. Olmedo. On the application of finite

A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation

NASA Astrophysics Data System (ADS)

Vergez, Guillaume; Danaila, Ionut; Auliac, Sylvain; Hecht, Frédéric

2016-12-01

We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily code various numerical algorithms. Two robust and optimized numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are used to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models.

Method of modifying a volume mesh using sheet insertion

DOEpatents

Borden, Michael J [Albuquerque, NM; Shepherd, Jason F [Albuquerque, NM

2006-08-29

A method and machine-readable medium provide a technique to modify a hexahedral finite element volume mesh using dual generation and sheet insertion. After generating a dual of a volume stack (mesh), a predetermined algorithm may be followed to modify (refine) the volume mesh of hexahedral elements. The predetermined algorithm may include the steps of locating a sheet of hexahedral mesh elements, determining a plurality of hexahedral elements within the sheet to refine, shrinking the plurality of elements, and inserting a new sheet of hexahedral elements adjacently to modify the volume mesh. Additionally, another predetermined algorithm using mesh cutting may be followed to modify a volume mesh.

An adaptive mesh refinement-multiphase lattice Boltzmann flux solver for simulation of complex binary fluid flows

NASA Astrophysics Data System (ADS)

Yuan, H. Z.; Wang, Y.; Shu, C.

2017-12-01

This paper presents an adaptive mesh refinement-multiphase lattice Boltzmann flux solver (AMR-MLBFS) for effective simulation of complex binary fluid flows at large density ratios. In this method, an AMR algorithm is proposed by introducing a simple indicator on the root block for grid refinement and two possible statuses for each block. Unlike available block-structured AMR methods, which refine their mesh by spawning or removing four child blocks simultaneously, the present method is able to refine its mesh locally by spawning or removing one to four child blocks independently when the refinement indicator is triggered. As a result, the AMR mesh used in this work can be more focused on the flow region near the phase interface and its size is further reduced. In each block of mesh, the recently proposed MLBFS is applied for the solution of the flow field and the level-set method is used for capturing the fluid interface. As compared with existing AMR-lattice Boltzmann models, the present method avoids both spatial and temporal interpolations of density distribution functions so that converged solutions on different AMR meshes and uniform grids can be obtained. The proposed method has been successfully validated by simulating a static bubble immersed in another fluid, a falling droplet, instabilities of two-layered fluids, a bubble rising in a box, and a droplet splashing on a thin film with large density ratios and high Reynolds numbers. Good agreement with the theoretical solution, the uniform-grid result, and/or the published data has been achieved. Numerical results also show its effectiveness in saving computational time and virtual memory as compared with computations on uniform meshes.

Adaptive radial basis function mesh deformation using data reduction

NASA Astrophysics Data System (ADS)

Gillebaart, T.; Blom, D. S.; van Zuijlen, A. H.; Bijl, H.

2016-09-01

Radial Basis Function (RBF) mesh deformation is one of the most robust mesh deformation methods available. Using the greedy (data reduction) method in combination with an explicit boundary correction, results in an efficient method as shown in literature. However, to ensure the method remains robust, two issues are addressed: 1) how to ensure that the set of control points remains an accurate representation of the geometry in time and 2) how to use/automate the explicit boundary correction, while ensuring a high mesh quality. In this paper, we propose an adaptive RBF mesh deformation method, which ensures the set of control points always represents the geometry/displacement up to a certain (user-specified) criteria, by keeping track of the boundary error throughout the simulation and re-selecting when needed. Opposed to the unit displacement and prescribed displacement selection methods, the adaptive method is more robust, user-independent and efficient, for the cases considered. Secondly, the analysis of a single high aspect ratio cell is used to formulate an equation for the correction radius needed, depending on the characteristics of the correction function used, maximum aspect ratio, minimum first cell height and boundary error. Based on the analysis two new radial basis correction functions are derived and proposed. This proposed automated procedure is verified while varying the correction function, Reynolds number (and thus first cell height and aspect ratio) and boundary error. Finally, the parallel efficiency is studied for the two adaptive methods, unit displacement and prescribed displacement for both the CPU as well as the memory formulation with a 2D oscillating and translating airfoil with oscillating flap, a 3D flexible locally deforming tube and deforming wind turbine blade. Generally, the memory formulation requires less work (due to the large amount of work required for evaluating RBF's), but the parallel efficiency reduces due to the limited bandwidth available between CPU and memory. In terms of parallel efficiency/scaling the different studied methods perform similarly, with the greedy algorithm being the bottleneck. In terms of absolute computational work the adaptive methods are better for the cases studied due to their more efficient selection of the control points. By automating most of the RBF mesh deformation, a robust, efficient and almost user-independent mesh deformation method is presented.

Dynamic mesh adaption for triangular and tetrahedral grids

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Strawn, Roger

1993-01-01

The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.

A new multiscale air quality transport model (Fluidity, 4.1.9) using fully unstructured anisotropic adaptive mesh technology

NASA Astrophysics Data System (ADS)

Zheng, J.; Zhu, J.; Wang, Z.; Fang, F.; Pain, C. C.; Xiang, J.

2015-06-01

A new anisotropic hr-adaptive mesh technique has been applied to modelling of multiscale transport phenomena, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been setup for two-dimensional (2-D) transport phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes.

Inverse modeling of rainfall infiltration with a dual permeability approach using different matrix-fracture coupling variants.

NASA Astrophysics Data System (ADS)

Blöcher, Johanna; Kuraz, Michal

2017-04-01

In this contribution we propose implementations of the dual permeability model with different inter-domain exchange descriptions and metaheuristic optimization algorithms for parameter identification and mesh optimization. We compare variants of the coupling term with different numbers of parameters to test if a reduction of parameters is feasible. This can reduce parameter uncertainty in inverse modeling, but also allow for different conceptual models of the domain and matrix coupling. The different variants of the dual permeability model are implemented in the open-source objective library DRUtES written in FORTRAN 2003/2008 in 1D and 2D. For parameter identification we use adaptations of the particle swarm optimization (PSO) and Teaching-learning-based optimization (TLBO), which are population-based metaheuristics with different learning strategies. These are high-level stochastic-based search algorithms that don't require gradient information or a convex search space. Despite increasing computing power and parallel processing, an overly fine mesh is not feasible for parameter identification. This creates the need to find a mesh that optimizes both accuracy and simulation time. We use a bi-objective PSO algorithm to generate a Pareto front of optimal meshes to account for both objectives. The dual permeability model and the optimization algorithms were tested on virtual data and field TDR sensor readings. The TDR sensor readings showed a very steep increase during rapid rainfall events and a subsequent steep decrease. This was theorized to be an effect of artificial macroporous envelopes surrounding TDR sensors creating an anomalous region with distinct local soil hydraulic properties. One of our objectives is to test how well the dual permeability model can describe this infiltration behavior and what coupling term would be most suitable.

Percept User Manual.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Carnes, Brian; Kennon, Stephen Ray

2017-05-01

This document is the main user guide for the Sierra/Percept capabilities including the mesh_adapt and mesh_transfer tools. Basic capabilities for uniform mesh refinement (UMR) and mesh transfers are discussed. Examples are used to provide illustration. Future versions of this manual will include more advanced features such as geometry and mesh smoothing. Additionally, all the options for the mesh_adapt code will be described in detail. Capabilities for local adaptivity in the context of offline adaptivity will also be included. This page intentionally left blank.

Adaptive mesh optimization and nonrigid motion recovery based image registration for wide-field-of-view ultrasound imaging.

PubMed

Tan, Chaowei; Wang, Bo; Liu, Paul; Liu, Dong

2008-01-01

Wide field of view (WFOV) imaging mode obtains an ultrasound image over an area much larger than the real time window normally available. As the probe is moved over the region of interest, new image frames are combined with prior frames to form a panorama image. Image registration techniques are used to recover the probe motion, eliminating the need for a position sensor. Speckle patterns, which are inherent in ultrasound imaging, change, or become decorrelated, as the scan plane moves, so we pre-smooth the image to reduce the effects of speckle in registration, as well as reducing effects from thermal noise. Because we wish to track the movement of features such as structural boundaries, we use an adaptive mesh over the entire smoothed image to home in on areas with feature. Motion estimation using blocks centered at the individual mesh nodes generates a field of motion vectors. After angular correction of motion vectors, we model the overall movement between frames as a nonrigid deformation. The polygon filling algorithm for precise, persistence-based spatial compounding constructs the final speckle reduced WFOV image.

Efficient low-bit-rate adaptive mesh-based motion compensation technique

NASA Astrophysics Data System (ADS)

Mahmoud, Hanan A.; Bayoumi, Magdy A.

2001-08-01

This paper proposes a two-stage global motion estimation method using a novel quadtree block-based motion estimation technique and an active mesh model. In the first stage, motion parameters are estimated by fitting block-based motion vectors computed using a new efficient quadtree technique, that divides a frame into equilateral triangle blocks using the quad-tree structure. Arbitrary partition shapes are achieved by allowing 4-to-1, 3-to-1 and 2-1 merge/combine of sibling blocks having the same motion vector . In the second stage, the mesh is constructed using an adaptive triangulation procedure that places more triangles over areas with high motion content, these areas are estimated during the first stage. finally the motion compensation is achieved by using a novel algorithm that is carried by both the encoder and the decoder to determine the optimal triangulation of the resultant partitions followed by affine mapping at the encoder. Computer simulation results show that the proposed method gives better performance that the conventional ones in terms of the peak signal-to-noise ration (PSNR) and the compression ratio (CR).

Adaptive triangular mesh generation

NASA Technical Reports Server (NTRS)

Erlebacher, G.; Eiseman, P. R.

1984-01-01

A general adaptive grid algorithm is developed on triangular grids. The adaptivity is provided by a combination of node addition, dynamic node connectivity and a simple node movement strategy. While the local restructuring process and the node addition mechanism take place in the physical plane, the nodes are displaced on a monitor surface, constructed from the salient features of the physical problem. An approximation to mean curvature detects changes in the direction of the monitor surface, and provides the pulling force on the nodes. Solutions to the axisymmetric Grad-Shafranov equation demonstrate the capturing, by triangles, of the plasma-vacuum interface in a free-boundary equilibrium configuration.

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

NASA Astrophysics Data System (ADS)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

Adaptive Meshing Techniques for Viscous Flow Calculations on Mixed Element Unstructured Meshes

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1997-01-01

An adaptive refinement strategy based on hierarchical element subdivision is formulated and implemented for meshes containing arbitrary mixtures of tetrahendra, hexahendra, prisms and pyramids. Special attention is given to keeping memory overheads as low as possible. This procedure is coupled with an algebraic multigrid flow solver which operates on mixed-element meshes. Inviscid flows as well as viscous flows are computed an adaptively refined tetrahedral, hexahedral, and hybrid meshes. The efficiency of the method is demonstrated by generating an adapted hexahedral mesh containing 3 million vertices on a relatively inexpensive workstation.

An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies

NASA Technical Reports Server (NTRS)

Quirk, James J.

1992-01-01

In this paper we describe an approach for dealing with arbitrary complex, two dimensional geometries, the so-called cartesian boundary method. Conceptually, the cartesian boundary method is quite simple. Solid bodies blank out areas of a background, cartesian mesh, and the resultant cut cells are singled out for special attention. However, there are several obstacles that must be overcome in order to achieve a practical scheme. We present a general strategy that overcomes these obstacles, together with some details of our successful conversion of an adaptive mesh algorithm from a body-fitted code to a cartesian boundary code.

PELEC

DOE Office of Scientific and Technical Information (OSTI.GOV)

2017-05-17

PeleC is an adaptive-mesh compressible hydrodynamics code for reacting flows. It solves the compressible Navier-Stokes with multispecies transport in a block structured framework. The resulting algorithm is well suited for flows with localized resolution requirements and robust to discontinuities. User controllable refinement crieteria has the potential to result in extremely small numerical dissipation and dispersion, making this code appropriate for both research and applied usage. The code is built on the AMReX library which facilitates hierarchical parallelism and manages distributed memory parallism. PeleC algorithms are implemented to express shared memory parallelism.

Adjoint Algorithm for CAD-Based Shape Optimization Using a Cartesian Method

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2004-01-01

Adjoint solutions of the governing flow equations are becoming increasingly important for the development of efficient analysis and optimization algorithms. A well-known use of the adjoint method is gradient-based shape optimization. Given an objective function that defines some measure of performance, such as the lift and drag functionals, its gradient is computed at a cost that is essentially independent of the number of design variables (geometric parameters that control the shape). More recently, emerging adjoint applications focus on the analysis problem, where the adjoint solution is used to drive mesh adaptation, as well as to provide estimates of functional error bounds and corrections. The attractive feature of this approach is that the mesh-adaptation procedure targets a specific functional, thereby localizing the mesh refinement and reducing computational cost. Our focus is on the development of adjoint-based optimization techniques for a Cartesian method with embedded boundaries.12 In contrast t o implementations on structured and unstructured grids, Cartesian methods decouple the surface discretization from the volume mesh. This feature makes Cartesian methods well suited for the automated analysis of complex geometry problems, and consequently a promising approach to aerodynamic optimization. Melvin et developed an adjoint formulation for the TRANAIR code, which is based on the full-potential equation with viscous corrections. More recently, Dadone and Grossman presented an adjoint formulation for the Euler equations. In both approaches, a boundary condition is introduced to approximate the effects of the evolving surface shape that results in accurate gradient computation. Central to automated shape optimization algorithms is the issue of geometry modeling and control. The need to optimize complex, "real-life" geometry provides a strong incentive for the use of parametric-CAD systems within the optimization procedure. In previous work, we presented an effective optimization framework that incorporates a direct-CAD interface. In this work, we enhance the capabilities of this framework with efficient gradient computations using the discrete adjoint method. We present details of the adjoint numerical implementation, which reuses the domain decomposition, multigrid, and time-marching schemes of the flow solver. Furthermore, we explain and demonstrate the use of CAD in conjunction with the Cartesian adjoint approach. The final paper will contain a number of complex geometry, industrially relevant examples with many design variables to demonstrate the effectiveness of the adjoint method on Cartesian meshes.

Towards a new multiscale air quality transport model using the fully unstructured anisotropic adaptive mesh technology of Fluidity (version 4.1.9)

NASA Astrophysics Data System (ADS)

Zheng, J.; Zhu, J.; Wang, Z.; Fang, F.; Pain, C. C.; Xiang, J.

2015-10-01

An integrated method of advanced anisotropic hr-adaptive mesh and discretization numerical techniques has been, for first time, applied to modelling of multiscale advection-diffusion problems, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been set up for two-dimensional (2-D) advection phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes. Performance achieved in 3-D simulation of power plant plumes indicates that this new adaptive multiscale model has the potential to provide accurate air quality modelling solutions effectively.

Mesh quality oriented 3D geometric vascular modeling based on parallel transport frame.

PubMed

Guo, Jixiang; Li, Shun; Chui, Yim Pan; Qin, Jing; Heng, Pheng Ann

2013-08-01

While a number of methods have been proposed to reconstruct geometrically and topologically accurate 3D vascular models from medical images, little attention has been paid to constantly maintain high mesh quality of these models during the reconstruction procedure, which is essential for many subsequent applications such as simulation-based surgical training and planning. We propose a set of methods to bridge this gap based on parallel transport frame. An improved bifurcation modeling method and two novel trifurcation modeling methods are developed based on 3D Bézier curve segments in order to ensure the continuous surface transition at furcations. In addition, a frame blending scheme is implemented to solve the twisting problem caused by frame mismatch of two successive furcations. A curvature based adaptive sampling scheme combined with a mesh quality guided frame tilting algorithm is developed to construct an evenly distributed, non-concave and self-intersection free surface mesh for vessels with distinct radius and high curvature. Extensive experiments demonstrate that our methodology can generate vascular models with better mesh quality than previous methods in terms of surface mesh quality criteria. Copyright © 2013 Elsevier Ltd. All rights reserved.

Hexahedral Mesh Untangling

DOE Office of Scientific and Technical Information (OSTI.GOV)

KNUPP,PATRICK

2000-12-13

We investigate a well-motivated mesh untangling objective function whose optimization automatically produces non-inverted elements when possible. Examples show the procedure is highly effective on simplicial meshes and on non-simplicial (e.g., hexahedral) meshes constructed via mapping or sweeping algorithms. The current whisker-weaving (WW) algorithm in CUBIT usually produces hexahedral meshes that are unsuitable for analyses due to inverted elements. The majority of these meshes cannot be untangled using the new objective function. The most likely source of the difficulty is poor mesh topology.

Method of modifying a volume mesh using sheet extraction

DOEpatents

Borden, Michael J [Albuquerque, NM; Shepherd, Jason F [Albuquerque, NM

2007-02-20

A method and machine-readable medium provide a technique to modify a hexahedral finite element volume mesh using dual generation and sheet extraction. After generating a dual of a volume stack (mesh), a predetermined algorithm may be followed to modify the volume mesh of hexahedral elements. The predetermined algorithm may include the steps of determining a sheet of hexahedral mesh elements, generating nodes for merging, and merging the nodes to delete the sheet of hexahedral mesh elements and modify the volume mesh.

An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Flaherty, Joseph E.; Arney, David C.

1993-01-01

We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.

Unstructured and adaptive mesh generation for high Reynolds number viscous flows

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1991-01-01

A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes.

Unstructured mesh adaptivity for urban flooding modelling

NASA Astrophysics Data System (ADS)

Hu, R.; Fang, F.; Salinas, P.; Pain, C. C.

2018-05-01

Over the past few decades, urban floods have been gaining more attention due to their increase in frequency. To provide reliable flooding predictions in urban areas, various numerical models have been developed to perform high-resolution flood simulations. However, the use of high-resolution meshes across the whole computational domain causes a high computational burden. In this paper, a 2D control-volume and finite-element flood model using adaptive unstructured mesh technology has been developed. This adaptive unstructured mesh technique enables meshes to be adapted optimally in time and space in response to the evolving flow features, thus providing sufficient mesh resolution where and when it is required. It has the advantage of capturing the details of local flows and wetting and drying front while reducing the computational cost. Complex topographic features are represented accurately during the flooding process. For example, the high-resolution meshes around the buildings and steep regions are placed when the flooding water reaches these regions. In this work a flooding event that happened in 2002 in Glasgow, Scotland, United Kingdom has been simulated to demonstrate the capability of the adaptive unstructured mesh flooding model. The simulations have been performed using both fixed and adaptive unstructured meshes, and then results have been compared with those published 2D and 3D results. The presented method shows that the 2D adaptive mesh model provides accurate results while having a low computational cost.

An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm in curvilinear geometry

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.; Barnes, D. C.

2012-03-01

A recent proof-of-principle study proposes an energy- and charge-conserving, fully implicit particle-in-cell algorithm in one dimension [1], which is able to use timesteps comparable to the dynamical timescale of interest. Here, we generalize the method to employ non-uniform meshes via a curvilinear map. The key enabling technology is a hybrid particle pusher [2], with particle positions updated in logical space and particle velocities updated in physical space. The self-adaptive, charge-conserving particle mover of Ref. [1] is extended to the non-uniform mesh case. The fully implicit implementation, using a Jacobian-free Newton-Krylov iterative solver, remains exactly charge- and energy-conserving. The extension of the formulation to multiple dimensions will be discussed. We present numerical experiments of 1D electrostatic, long-timescale ion-acoustic wave and ion-acoustic shock wave simulations, demonstrating that charge and energy are conserved to round-off for arbitrary mesh non-uniformity, and that the total momentum remains well conserved.[4pt] [1] Chen, Chac'on, Barnes, J. Comput. Phys. 230 (2011). [0pt] [2] Camporeale and Delzanno, Bull. Am. Phys. Soc. 56(6) (2011); Wang, et al., J. Plasma Physics, 61 (1999).

Comparison Between Three Different Types of Routing Algorithms of Network on Chip

NASA Astrophysics Data System (ADS)

Soni, Neetu; Deshmukh, Khemraj

Network on Chip (NoC) is an on-chip communication technology in which a large number of processing elements and storage blocks are integrated on a single chip. Due to scalability, adaptive nature, well resource utilization NoCs have become popular in and has efficiently replaced SoCs. NoCs performance depends mainly on the type of routing algorithm chosen. In this paper three different types of routing algorithms are being compared firstly one is deterministic routing (XY routing algorithm), secondly three partially adaptive routing (West-first, North-last and Negative-first) and two adaptive routing (DyAD, OE) are being compared with respect to Packet Injection Rate (PIR) of load for random traffic pattern for 4 × 4 mesh topology. All these comparison and simulation is done in NOXIM 2.3.1 simulator which is a cycle accurate systemC based simulator. The distribution of packets is Poisson type with Buffer depth (number of buffers) of input channel FIFO is 8. Packet size is taken as 8 bytes. The simulation time is taken 50,000 cycles. We found that XY routing is better when the PIR is low. The partially adaptive routing is good when the PIR is moderate. DyAD routing is suited when the load i.e. PIR is high.

Smart algorithms and adaptive methods in computational fluid dynamics

NASA Astrophysics Data System (ADS)

Tinsley Oden, J.

1989-05-01

A review is presented of the use of smart algorithms which employ adaptive methods in processing large amounts of data in computational fluid dynamics (CFD). Smart algorithms use a rationally based set of criteria for automatic decision making in an attempt to produce optimal simulations of complex fluid dynamics problems. The information needed to make these decisions is not known beforehand and evolves in structure and form during the numerical solution of flow problems. Once the code makes a decision based on the available data, the structure of the data may change, and criteria may be reapplied in order to direct the analysis toward an acceptable end. Intelligent decisions are made by processing vast amounts of data that evolve unpredictably during the calculation. The basic components of adaptive methods and their application to complex problems of fluid dynamics are reviewed. The basic components of adaptive methods are: (1) data structures, that is what approaches are available for modifying data structures of an approximation so as to reduce errors; (2) error estimation, that is what techniques exist for estimating error evolution in a CFD calculation; and (3) solvers, what algorithms are available which can function in changing meshes. Numerical examples which demonstrate the viability of these approaches are presented.

A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.

PubMed

Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J

2009-11-28

In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.

A heuristic re-mapping algorithm reducing inter-level communication in SAMR applications.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Steensland, Johan; Ray, Jaideep

2003-07-01

This paper aims at decreasing execution time for large-scale structured adaptive mesh refinement (SAMR) applications by proposing a new heuristic re-mapping algorithm and experimentally showing its effectiveness in reducing inter-level communication. Tests were done for five different SAMR applications. The overall goal is to engineer a dynamically adaptive meta-partitioner capable of selecting and configuring the most appropriate partitioning strategy at run-time based on current system and application state. Such a metapartitioner can significantly reduce execution times for general SAMR applications. Computer simulations of physical phenomena are becoming increasingly popular as they constitute an important complement to real-life testing. In manymore » cases, such simulations are based on solving partial differential equations by numerical methods. Adaptive methods are crucial to efficiently utilize computer resources such as memory and CPU. But even with adaption, the simulations are computationally demanding and yield huge data sets. Thus parallelization and the efficient partitioning of data become issues of utmost importance. Adaption causes the workload to change dynamically, calling for dynamic (re-) partitioning to maintain efficient resource utilization. The proposed heuristic algorithm reduced inter-level communication substantially. Since the complexity of the proposed algorithm is low, this decrease comes at a relatively low cost. As a consequence, we draw the conclusion that the proposed re-mapping algorithm would be useful to lower overall execution times for many large SAMR applications. Due to its usefulness and its parameterization, the proposed algorithm would constitute a natural and important component of the meta-partitioner.« less

A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake

NASA Astrophysics Data System (ADS)

Bercea, Gheorghe-Teodor; McRae, Andrew T. T.; Ham, David A.; Mitchell, Lawrence; Rathgeber, Florian; Nardi, Luigi; Luporini, Fabio; Kelly, Paul H. J.

2016-10-01

We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells. Applications of extruded meshes include, but are not limited to, the representation of three-dimensional high aspect ratio domains employed by geophysical finite element simulations. These meshes are structured in the extruded direction. The algorithm presented here exploits this structure to avoid the performance penalty traditionally associated with unstructured meshes. We evaluate the implementation of this algorithm in the Firedrake finite element system on a range of low compute intensity operations which constitute worst cases for data layout performance exploration. The experiments show that having structure along the extruded direction enables the cost of the indirect data accesses to be amortized after 10-20 layers as long as the underlying mesh is well ordered. We characterize the resulting spatial and temporal reuse in a representative set of both continuous-Galerkin and discontinuous-Galerkin discretizations. On meshes with realistic numbers of layers the performance achieved is between 70 and 90 % of a theoretical hardware-specific limit.

An object-oriented approach for parallel self adaptive mesh refinement on block structured grids

NASA Technical Reports Server (NTRS)

Lemke, Max; Witsch, Kristian; Quinlan, Daniel

1993-01-01

Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently.

High-Fidelity Geometric Modeling and Mesh Generation for Mechanics Characterization of Polycrystalline Materials

DTIC Science & Technology

2014-10-26

From the parameterization results, we extract adaptive and anisotropic T-meshes for the further T- spline surface construction. Finally, a gradient flow...field-based method [7, 12] to generate adaptive and anisotropic quadrilateral meshes, which can be used as the control mesh for high-order T- spline ...parameterization results, we extract adaptive and anisotropic T-meshes for the further T- spline surface construction. Finally, a gradient flow-based

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

NASA Technical Reports Server (NTRS)

Slack, David C.; Walters, Robert W.; Lohner, R.

1990-01-01

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Lung lobe modeling and segmentation with individualized surface meshes

NASA Astrophysics Data System (ADS)

Blaffert, Thomas; Barschdorf, Hans; von Berg, Jens; Dries, Sebastian; Franz, Astrid; Klinder, Tobias; Lorenz, Cristian; Renisch, Steffen; Wiemker, Rafael

2008-03-01

An automated segmentation of lung lobes in thoracic CT images is of interest for various diagnostic purposes like the quantification of emphysema or the localization of tumors within the lung. Although the separating lung fissures are visible in modern multi-slice CT-scanners, their contrast in the CT-image often does not separate the lobes completely. This makes it impossible to build a reliable segmentation algorithm without additional information. Our approach uses general anatomical knowledge represented in a geometrical mesh model to construct a robust lobe segmentation, which even gives reasonable estimates of lobe volumes if fissures are not visible at all. The paper describes the generation of the lung model mesh including lobes by an average volume model, its adaptation to individual patient data using a special fissure feature image, and a performance evaluation over a test data set showing an average segmentation accuracy of 1 to 3 mm.

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

Progress in the Simulation of Steady and Time-Dependent Flows with 3D Parallel Unstructured Cartesian Methods

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Murman, S. M.; Kwak, Dochan (Technical Monitor)

2002-01-01

The proposed paper will present recent extensions in the development of an efficient Euler solver for adaptively-refined Cartesian meshes with embedded boundaries. The paper will focus on extensions of the basic method to include solution adaptation, time-dependent flow simulation, and arbitrary rigid domain motion. The parallel multilevel method makes use of on-the-fly parallel domain decomposition to achieve extremely good scalability on large numbers of processors, and is coupled with an automatic coarse mesh generation algorithm for efficient processing by a multigrid smoother. Numerical results are presented demonstrating parallel speed-ups of up to 435 on 512 processors. Solution-based adaptation may be keyed off truncation error estimates using tau-extrapolation or a variety of feature detection based refinement parameters. The multigrid method is extended to for time-dependent flows through the use of a dual-time approach. The extension to rigid domain motion uses an Arbitrary Lagrangian-Eulerlarian (ALE) formulation, and results will be presented for a variety of two- and three-dimensional example problems with both simple and complex geometry.

Mesh-free data transfer algorithms for partitioned multiphysics problems: Conservation, accuracy, and parallelism

DOE PAGES

Slattery, Stuart R.

2015-12-02

In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothnessmore » and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.« less

Adaptively Refined Euler and Navier-Stokes Solutions with a Cartesian-Cell Based Scheme

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian-cell based scheme with adaptive mesh refinement for solving the Euler and Navier-Stokes equations in two dimensions has been developed and tested. Grids about geometrically complicated bodies were generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells were created using polygon-clipping algorithms. The grid was stored in a binary-tree data structure which provided a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations were solved on the resulting grids using an upwind, finite-volume formulation. The inviscid fluxes were found in an upwinded manner using a linear reconstruction of the cell primitives, providing the input states to an approximate Riemann solver. The viscous fluxes were formed using a Green-Gauss type of reconstruction upon a co-volume surrounding the cell interface. Data at the vertices of this co-volume were found in a linearly K-exact manner, which ensured linear K-exactness of the gradients. Adaptively-refined solutions for the inviscid flow about a four-element airfoil (test case 3) were compared to theory. Laminar, adaptively-refined solutions were compared to accepted computational, experimental and theoretical results.

Sensitivity field distributions for segmental bioelectrical impedance analysis based on real human anatomy

NASA Astrophysics Data System (ADS)

Danilov, A. A.; Kramarenko, V. K.; Nikolaev, D. V.; Rudnev, S. G.; Salamatova, V. Yu; Smirnov, A. V.; Vassilevski, Yu V.

2013-04-01

In this work, an adaptive unstructured tetrahedral mesh generation technology is applied for simulation of segmental bioimpedance measurements using high-resolution whole-body model of the Visible Human Project man. Sensitivity field distributions for a conventional tetrapolar, as well as eight- and ten-electrode measurement configurations are obtained. Based on the ten-electrode configuration, we suggest an algorithm for monitoring changes in the upper lung area.

A moving mesh unstaggered constrained transport scheme for magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Mocz, Philip; Pakmor, Rüdiger; Springel, Volker; Vogelsberger, Mark; Marinacci, Federico; Hernquist, Lars

2016-11-01

We present a constrained transport (CT) algorithm for solving the 3D ideal magnetohydrodynamic (MHD) equations on a moving mesh, which maintains the divergence-free condition on the magnetic field to machine-precision. Our CT scheme uses an unstructured representation of the magnetic vector potential, making the numerical method simple and computationally efficient. The scheme is implemented in the moving mesh code AREPO. We demonstrate the performance of the approach with simulations of driven MHD turbulence, a magnetized disc galaxy, and a cosmological volume with primordial magnetic field. We compare the outcomes of these experiments to those obtained with a previously implemented Powell divergence-cleaning scheme. While CT and the Powell technique yield similar results in idealized test problems, some differences are seen in situations more representative of astrophysical flows. In the turbulence simulations, the Powell cleaning scheme artificially grows the mean magnetic field, while CT maintains this conserved quantity of ideal MHD. In the disc simulation, CT gives slower magnetic field growth rate and saturates to equipartition between the turbulent kinetic energy and magnetic energy, whereas Powell cleaning produces a dynamically dominant magnetic field. Such difference has been observed in adaptive-mesh refinement codes with CT and smoothed-particle hydrodynamics codes with divergence-cleaning. In the cosmological simulation, both approaches give similar magnetic amplification, but Powell exhibits more cell-level noise. CT methods in general are more accurate than divergence-cleaning techniques, and, when coupled to a moving mesh can exploit the advantages of automatic spatial/temporal adaptivity and reduced advection errors, allowing for improved astrophysical MHD simulations.

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

DOE PAGES

Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett; ...

2017-01-01

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

Documentation for MeshKit - Reactor Geometry (&mesh) Generator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jain, Rajeev; Mahadevan, Vijay

2015-09-30

This report gives documentation for using MeshKit’s Reactor Geometry (and mesh) Generator (RGG) GUI and also briefly documents other algorithms and tools available in MeshKit. RGG is a program designed to aid in modeling and meshing of complex/large hexagonal and rectilinear reactor cores. RGG uses Argonne’s SIGMA interfaces, Qt and VTK to produce an intuitive user interface. By integrating a 3D view of the reactor with the meshing tools and combining them into one user interface, RGG streamlines the task of preparing a simulation mesh and enables real-time feedback that reduces accidental scripting mistakes that could waste hours of meshing.more » RGG interfaces with MeshKit tools to consolidate the meshing process, meaning that going from model to mesh is as easy as a button click. This report is designed to explain RGG v 2.0 interface and provide users with the knowledge and skills to pilot RGG successfully. Brief documentation of MeshKit source code, tools and other algorithms available are also presented for developers to extend and add new algorithms to MeshKit. RGG tools work in serial and parallel and have been used to model complex reactor core models consisting of conical pins, load pads, several thousands of axially varying material properties of instrumentation pins and other interstices meshes.« less

An advancing front Delaunay triangulation algorithm designed for robustness

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1992-01-01

A new algorithm is described for generating an unstructured mesh about an arbitrary two-dimensional configuration. Mesh points are generated automatically by the algorithm in a manner which ensures a smooth variation of elements, and the resulting triangulation constitutes the Delaunay triangulation of these points. The algorithm combines the mathematical elegance and efficiency of Delaunay triangulation algorithms with the desirable point placement features, boundary integrity, and robustness traditionally associated with advancing-front-type mesh generation strategies. The method offers increased robustness over previous algorithms in that it cannot fail regardless of the initial boundary point distribution and the prescribed cell size distribution throughout the flow-field.

An improved three-dimension reconstruction method based on guided filter and Delaunay

NASA Astrophysics Data System (ADS)

Liu, Yilin; Su, Xiu; Liang, Haitao; Xu, Huaiyuan; Wang, Yi; Chen, Xiaodong

2018-01-01

Binocular stereo vision is becoming a research hotspot in the area of image processing. Based on traditional adaptive-weight stereo matching algorithm, we improve the cost volume by averaging the AD (Absolute Difference) of RGB color channels and adding x-derivative of the grayscale image to get the cost volume. Then we use guided filter in the cost aggregation step and weighted median filter for post-processing to address the edge problem. In order to get the location in real space, we combine the deep information with the camera calibration to project each pixel in 2D image to 3D coordinate matrix. We add the concept of projection to region-growing algorithm for surface reconstruction, its specific operation is to project all the points to a 2D plane through the normals of clouds and return the results back to 3D space according to these connection relationship among the points in 2D plane. During the triangulation in 2D plane, we use Delaunay algorithm because it has optimal quality of mesh. We configure OpenCV and pcl on Visual Studio for testing, and the experimental results show that the proposed algorithm have higher computational accuracy of disparity and can realize the details of the real mesh model.

Impact of MPEG-4 3D mesh coding on watermarking algorithms for polygonal 3D meshes

NASA Astrophysics Data System (ADS)

Funk, Wolfgang

2004-06-01

The MPEG-4 multimedia standard addresses the scene-based composition of audiovisual objects. Natural and synthetic multimedia content can be mixed and transmitted over narrow and broadband communication channels. Synthetic natural hybrid coding (SNHC) within MPEG-4 provides tools for 3D mesh coding (3DMC). We investigate the robustness of two different 3D watermarking algorithms for polygonal meshes with respect to 3DMC. The first algorithm is a blind detection scheme designed for labelling applications that require high bandwidth and low robustness. The second algorithm is a robust non-blind one-bit watermarking scheme intended for copyright protection applications. Both algorithms have been proposed by Benedens. We expect 3DMC to have an impact on the watermarked 3D meshes, as the algorithms used for our simulations work on vertex coordinates to encode the watermark. We use the 3DMC implementation provided with the MPEG-4 reference software and the Princeton Shape Benchmark model database for our simulations. The watermarked models are sent through the 3DMC encoder and decoder, and the watermark decoding process is performed. For each algorithm under consideration we examine the detection properties as a function of the quantization of the vertex coordinates.

TU-AB-202-05: GPU-Based 4D Deformable Image Registration Using Adaptive Tetrahedral Mesh Modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhong, Z; Zhuang, L; Gu, X

Purpose: Deformable image registration (DIR) has been employed today as an automated and effective segmentation method to transfer tumor or organ contours from the planning image to daily images, instead of manual segmentation. However, the computational time and accuracy of current DIR approaches are still insufficient for online adaptive radiation therapy (ART), which requires real-time and high-quality image segmentation, especially in a large datasets of 4D-CT images. The objective of this work is to propose a new DIR algorithm, with fast computational speed and high accuracy, by using adaptive feature-based tetrahedral meshing and GPU-based parallelization. Methods: The first step ismore » to generate the adaptive tetrahedral mesh based on the image features of a reference phase of 4D-CT, so that the deformation can be well captured and accurately diffused from the mesh vertices to voxels of the image volume. Subsequently, the deformation vector fields (DVF) and other phases of 4D-CT can be obtained by matching each phase of the target 4D-CT images with the corresponding deformed reference phase. The proposed 4D DIR method is implemented on GPU, resulting in significantly increasing the computational efficiency due to its parallel computing ability. Results: A 4D NCAT digital phantom was used to test the efficiency and accuracy of our method. Both the image and DVF results show that the fine structures and shapes of lung are well preserved, and the tumor position is well captured, i.e., 3D distance error is 1.14 mm. Compared to the previous voxel-based CPU implementation of DIR, such as demons, the proposed method is about 160x faster for registering a 10-phase 4D-CT with a phase dimension of 256×256×150. Conclusion: The proposed 4D DIR method uses feature-based mesh and GPU-based parallelism, which demonstrates the capability to compute both high-quality image and motion results, with significant improvement on the computational speed.« less

3D CSEM inversion based on goal-oriented adaptive finite element method

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with complex geological scenarios by applying it to the inversion of synthetic marine controlled source EM data generated for a complex 3D offshore model with significant seafloor topography.

Adjoint-Based Mesh Adaptation for the Sonic Boom Signature Loudness

NASA Technical Reports Server (NTRS)

Rallabhandi, Sriram K.; Park, Michael A.

2017-01-01

The mesh adaptation functionality of FUN3D is utilized to obtain a mesh optimized to calculate sonic boom ground signature loudness. During this process, the coupling between the discrete-adjoints of the computational fluid dynamics tool FUN3D and the atmospheric propagation tool sBOOM is exploited to form the error estimate. This new mesh adaptation methodology will allow generation of suitable meshes adapted to reduce the estimated errors in the ground loudness, which is an optimization metric employed in supersonic aircraft design. This new output-based adaptation could allow new insights into meshing for sonic boom analysis and design, and complements existing output-based adaptation techniques such as adaptation to reduce estimated errors in off-body pressure functional. This effort could also have implications for other coupled multidisciplinary adjoint capabilities (e.g., aeroelasticity) as well as inclusion of propagation specific parameters such as prevailing winds or non-standard atmospheric conditions. Results are discussed in the context of existing methods and appropriate conclusions are drawn as to the efficacy and efficiency of the developed capability.

Topography compensation for haptization of a mesh object and its stiffness distribution.

PubMed

Yim, Sunghoon; Jeon, Seokhee; Choi, Seungmoon

2015-01-01

This work was motivated by the need for perceptualizing nano-scale scientific data, e.g., those acquired by a scanning probe microscope, where collocated topography and stiffness distribution of a surface can be measured. Previous research showed that when the topography of a surface with spatially varying stiffness is rendered using the conventional penalty-based haptic rendering method, the topography perceived by the user could be significantly distorted from its original model. In the worst case, a higher region with a smaller stiffness value can be perceived to be lower than a lower region with a larger stiffness value. This problem was explained by the theory of force constancy: the user tends to maintain an invariant contact force when s/he strokes the surface to perceive its topography. In this paper, we present a haptization algorithm that can render the shape of a mesh surface and its stiffness distribution with high perceptual accuracy. Our algorithm adaptively changes the surface topography on the basis of the force constancy theory to deliver adequate shape information to the user while preserving the stiffness perception. We also evaluated the performance of the proposed haptization algorithm in comparison to the constraint-based algorithm by examining relevant proximal stimuli and carrying out a user experiment. Results demonstrated that our algorithm could improve the perceptual accuracy of shape and reduce the exploration time, thereby leading to more accurate and efficient haptization.

Patch-based Adaptive Mesh Refinement for Multimaterial Hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lomov, I; Pember, R; Greenough, J

2005-10-18

We present a patch-based direct Eulerian adaptive mesh refinement (AMR) algorithm for modeling real equation-of-state, multimaterial compressible flow with strength. Our approach to AMR uses a hierarchical, structured grid approach first developed by (Berger and Oliger 1984), (Berger and Oliger 1984). The grid structure is dynamic in time and is composed of nested uniform rectangular grids of varying resolution. The integration scheme on the grid hierarchy is a recursive procedure in which the coarse grids are advanced, then the fine grids are advanced multiple steps to reach the same time, and finally the coarse and fine grids are synchronized tomore » remove conservation errors during the separate advances. The methodology presented here is based on a single grid algorithm developed for multimaterial gas dynamics by (Colella et al. 1993), refined by(Greenough et al. 1995), and extended to the solution of solid mechanics problems with significant strength by (Lomov and Rubin 2003). The single grid algorithm uses a second-order Godunov scheme with an approximate single fluid Riemann solver and a volume-of-fluid treatment of material interfaces. The method also uses a non-conservative treatment of the deformation tensor and an acoustic approximation for shear waves in the Riemann solver. This departure from a strict application of the higher-order Godunov methodology to the equation of solid mechanics is justified due to the fact that highly nonlinear behavior of shear stresses is rare. This algorithm is implemented in two codes, Geodyn and Raptor, the latter of which is a coupled rad-hydro code. The present discussion will be solely concerned with hydrodynamics modeling. Results from a number of simulations for flows with and without strength will be presented.« less

3D numerical simulations of oblique droplet impact onto a deep liquid pool

NASA Astrophysics Data System (ADS)

Gelderblom, Hanneke; Reijers, Sten A.; Gielen, Marise; Sleutel, Pascal; Lohse, Detlef; Xie, Zhihua; Pain, Christopher C.; Matar, Omar K.

2017-11-01

We study the fluid dynamics of three-dimensional oblique droplet impact, which results in phenomena that include splashing and cavity formation. An adaptive, unstructured mesh modelling framework is employed here, which can modify and adapt unstructured meshes to better represent the underlying physics of droplet dynamics, and reduce computational effort without sacrificing accuracy. The numerical framework consists of a mixed control-volume and finite-element formulation, a volume-of-fluid-type method for the interface-capturing based on a compressive control-volume advection method. The framework also features second-order finite-element methods, and a force-balanced algorithm for the surface tension implementation, minimising the spurious velocities often found in many simulations involving capillary-driven flows. The numerical results generated using this framework are compared with high-speed images of the interfacial shapes of the deformed droplet, and the cavity formed upon impact, yielding good agreement. EPSRC, UK, MEMPHIS program Grant (EP/K003976/1), RAEng Research Chair (OKM).

Newmark local time stepping on high-performance computing architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rietmann, Max, E-mail: max.rietmann@erdw.ethz.ch; Institute of Geophysics, ETH Zurich; Grote, Marcus, E-mail: marcus.grote@unibas.ch

In multi-scale complex media, finite element meshes often require areas of local refinement, creating small elements that can dramatically reduce the global time-step for wave-propagation problems due to the CFL condition. Local time stepping (LTS) algorithms allow an explicit time-stepping scheme to adapt the time-step to the element size, allowing near-optimal time-steps everywhere in the mesh. We develop an efficient multilevel LTS-Newmark scheme and implement it in a widely used continuous finite element seismic wave-propagation package. In particular, we extend the standard LTS formulation with adaptations to continuous finite element methods that can be implemented very efficiently with very strongmore » element-size contrasts (more than 100x). Capable of running on large CPU and GPU clusters, we present both synthetic validation examples and large scale, realistic application examples to demonstrate the performance and applicability of the method and implementation on thousands of CPU cores and hundreds of GPUs.« less

Parallel implementation of a Lagrangian-based model on an adaptive mesh in C++: Application to sea-ice

NASA Astrophysics Data System (ADS)

Samaké, Abdoulaye; Rampal, Pierre; Bouillon, Sylvain; Ólason, Einar

2017-12-01

We present a parallel implementation framework for a new dynamic/thermodynamic sea-ice model, called neXtSIM, based on the Elasto-Brittle rheology and using an adaptive mesh. The spatial discretisation of the model is done using the finite-element method. The temporal discretisation is semi-implicit and the advection is achieved using either a pure Lagrangian scheme or an Arbitrary Lagrangian Eulerian scheme (ALE). The parallel implementation presented here focuses on the distributed-memory approach using the message-passing library MPI. The efficiency and the scalability of the parallel algorithms are illustrated by the numerical experiments performed using up to 500 processor cores of a cluster computing system. The performance obtained by the proposed parallel implementation of the neXtSIM code is shown being sufficient to perform simulations for state-of-the-art sea ice forecasting and geophysical process studies over geographical domain of several millions squared kilometers like the Arctic region.

Laminar and turbulent flow computations of Type 4 shock-shock interference aerothermal loads using unstructured grids

NASA Technical Reports Server (NTRS)

Vemaganti, Gururaja R.

1994-01-01

This report presents computations for the Type 4 shock-shock interference flow under laminar and turbulent conditions using unstructured grids. Mesh adaptation was accomplished by remeshing, refinement, and mesh movement. Two two-equation turbulence models were used to analyze turbulent flows. The mean flow governing equations and the turbulence governing equations are solved in a coupled manner. The solution algorithm and the details pertaining to its implementation on unstructured grids are described. Computations were performed at two different freestream Reynolds numbers at a freestream Mach number of 11. Effects of the variation in the impinging shock location are studied. The comparison of the results in terms of wall heat flux and wall pressure distributions is presented.

A Fast and Scalable Algorithm for Calculating the Achievable Capacity of a Wireless Mesh Network

DTIC Science & Technology

2016-04-10

to interference from a given transmission . We then use our algorithm to perform a network capacity analysis comparing different wireless technologies...A Fast and Scalable Algorithm for Calculating the Achievable Capacity of a Wireless Mesh Network Greg Kuperman, Jun Sun, and Aradhana Narula-Tam MIT...the maximum achievable capacity of a multi-hop wireless mesh network subject to interference constraints. Being able to quickly determine the maximum

Parallel deterministic neutronics with AMR in 3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clouse, C.; Ferguson, J.; Hendrickson, C.

1997-12-31

AMTRAN, a three dimensional Sn neutronics code with adaptive mesh refinement (AMR) has been parallelized over spatial domains and energy groups and runs on the Meiko CS-2 with MPI message passing. Block refined AMR is used with linear finite element representations for the fluxes, which allows for a straight forward interpretation of fluxes at block interfaces with zoning differences. The load balancing algorithm assumes 8 spatial domains, which minimizes idle time among processors.

Advanced adaptive computational methods for Navier-Stokes simulations in rotorcraft aerodynamics

NASA Technical Reports Server (NTRS)

Stowers, S. T.; Bass, J. M.; Oden, J. T.

1993-01-01

A phase 2 research and development effort was conducted in area transonic, compressible, inviscid flows with an ultimate goal of numerically modeling complex flows inherent in advanced helicopter blade designs. The algorithms and methodologies therefore are classified as adaptive methods, which are error estimation techniques for approximating the local numerical error, and automatically refine or unrefine the mesh so as to deliver a given level of accuracy. The result is a scheme which attempts to produce the best possible results with the least number of grid points, degrees of freedom, and operations. These types of schemes automatically locate and resolve shocks, shear layers, and other flow details to an accuracy level specified by the user of the code. The phase 1 work involved a feasibility study of h-adaptive methods for steady viscous flows, with emphasis on accurate simulation of vortex initiation, migration, and interaction. Phase 2 effort focused on extending these algorithms and methodologies to a three-dimensional topology.

Physiology driven adaptivity for the numerical solution of the bidomain equations.

PubMed

Whiteley, Jonathan P

2007-09-01

Previous work [Whiteley, J. P. IEEE Trans. Biomed. Eng. 53:2139-2147, 2006] derived a stable, semi-implicit numerical scheme for solving the bidomain equations. This scheme allows the timestep used when solving the bidomain equations numerically to be chosen by accuracy considerations rather than stability considerations. In this study we modify this scheme to allow an adaptive numerical solution in both time and space. The spatial mesh size is determined by the gradient of the transmembrane and extracellular potentials while the timestep is determined by the values of: (i) the fast sodium current; and (ii) the calcium release from junctional sarcoplasmic reticulum to myoplasm current. For two-dimensional simulations presented here, combining the numerical algorithm in the paper cited above with the adaptive algorithm presented here leads to an increase in computational efficiency by a factor of around 250 over previous work, together with significantly less computational memory being required. The speedup for three-dimensional simulations is likely to be more impressive.

Application of Parallel Adjoint-Based Error Estimation and Anisotropic Grid Adaptation for Three-Dimensional Aerospace Configurations

NASA Technical Reports Server (NTRS)

Lee-Rausch, E. M.; Park, M. A.; Jones, W. T.; Hammond, D. P.; Nielsen, E. J.

2005-01-01

This paper demonstrates the extension of error estimation and adaptation methods to parallel computations enabling larger, more realistic aerospace applications and the quantification of discretization errors for complex 3-D solutions. Results were shown for an inviscid sonic-boom prediction about a double-cone configuration and a wing/body segmented leading edge (SLE) configuration where the output function of the adjoint was pressure integrated over a part of the cylinder in the near field. After multiple cycles of error estimation and surface/field adaptation, a significant improvement in the inviscid solution for the sonic boom signature of the double cone was observed. Although the double-cone adaptation was initiated from a very coarse mesh, the near-field pressure signature from the final adapted mesh compared very well with the wind-tunnel data which illustrates that the adjoint-based error estimation and adaptation process requires no a priori refinement of the mesh. Similarly, the near-field pressure signature for the SLE wing/body sonic boom configuration showed a significant improvement from the initial coarse mesh to the final adapted mesh in comparison with the wind tunnel results. Error estimation and field adaptation results were also presented for the viscous transonic drag prediction of the DLR-F6 wing/body configuration, and results were compared to a series of globally refined meshes. Two of these globally refined meshes were used as a starting point for the error estimation and field-adaptation process where the output function for the adjoint was the total drag. The field-adapted results showed an improvement in the prediction of the drag in comparison with the finest globally refined mesh and a reduction in the estimate of the remaining drag error. The adjoint-based adaptation parameter showed a need for increased resolution in the surface of the wing/body as well as a need for wake resolution downstream of the fuselage and wing trailing edge in order to achieve the requested drag tolerance. Although further adaptation was required to meet the requested tolerance, no further cycles were computed in order to avoid large discrepancies between the surface mesh spacing and the refined field spacing.

Method of generating a surface mesh

DOEpatents

Shepherd, Jason F [Albuquerque, NM; Benzley, Steven [Provo, UT; Grover, Benjamin T [Tracy, CA

2008-03-04

A method and machine-readable medium provide a technique to generate and modify a quadrilateral finite element surface mesh using dual creation and modification. After generating a dual of a surface (mesh), a predetermined algorithm may be followed to generate and modify a surface mesh of quadrilateral elements. The predetermined algorithm may include the steps of generating two-dimensional cell regions in dual space, determining existing nodes in primal space, generating new nodes in the dual space, and connecting nodes to form the quadrilateral elements (faces) for the generated and modifiable surface mesh.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Slattery, Stuart R.

In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothnessmore » and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.« less

Carpet: Adaptive Mesh Refinement for the Cactus Framework

NASA Astrophysics Data System (ADS)

Schnetter, Erik; Hawley, Scott; Hawke, Ian

2016-11-01

Carpet is an adaptive mesh refinement and multi-patch driver for the Cactus Framework (ascl:1102.013). Cactus is a software framework for solving time-dependent partial differential equations on block-structured grids, and Carpet acts as driver layer providing adaptive mesh refinement, multi-patch capability, as well as parallelization and efficient I/O.

PARAMESH: A Parallel Adaptive Mesh Refinement Community Toolkit

NASA Technical Reports Server (NTRS)

MacNeice, Peter; Olson, Kevin M.; Mobarry, Clark; deFainchtein, Rosalinda; Packer, Charles

1999-01-01

In this paper, we describe a community toolkit which is designed to provide parallel support with adaptive mesh capability for a large and important class of computational models, those using structured, logically cartesian meshes. The package of Fortran 90 subroutines, called PARAMESH, is designed to provide an application developer with an easy route to extend an existing serial code which uses a logically cartesian structured mesh into a parallel code with adaptive mesh refinement. Alternatively, in its simplest use, and with minimal effort, it can operate as a domain decomposition tool for users who want to parallelize their serial codes, but who do not wish to use adaptivity. The package can provide them with an incremental evolutionary path for their code, converting it first to uniformly refined parallel code, and then later if they so desire, adding adaptivity.

A multigrid method for steady Euler equations on unstructured adaptive grids

NASA Technical Reports Server (NTRS)

Riemslagh, Kris; Dick, Erik

1993-01-01

A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.

Adapting to life: ocean biogeochemical modelling and adaptive remeshing

NASA Astrophysics Data System (ADS)

Hill, J.; Popova, E. E.; Ham, D. A.; Piggott, M. D.; Srokosz, M.

2014-05-01

An outstanding problem in biogeochemical modelling of the ocean is that many of the key processes occur intermittently at small scales, such as the sub-mesoscale, that are not well represented in global ocean models. This is partly due to their failure to resolve sub-mesoscale phenomena, which play a significant role in vertical nutrient supply. Simply increasing the resolution of the models may be an inefficient computational solution to this problem. An approach based on recent advances in adaptive mesh computational techniques may offer an alternative. Here the first steps in such an approach are described, using the example of a simple vertical column (quasi-1-D) ocean biogeochemical model. We present a novel method of simulating ocean biogeochemical behaviour on a vertically adaptive computational mesh, where the mesh changes in response to the biogeochemical and physical state of the system throughout the simulation. We show that the model reproduces the general physical and biological behaviour at three ocean stations (India, Papa and Bermuda) as compared to a high-resolution fixed mesh simulation and to observations. The use of an adaptive mesh does not increase the computational error, but reduces the number of mesh elements by a factor of 2-3. Unlike previous work the adaptivity metric used is flexible and we show that capturing the physical behaviour of the model is paramount to achieving a reasonable solution. Adding biological quantities to the adaptivity metric further refines the solution. We then show the potential of this method in two case studies where we change the adaptivity metric used to determine the varying mesh sizes in order to capture the dynamics of chlorophyll at Bermuda and sinking detritus at Papa. We therefore demonstrate that adaptive meshes may provide a suitable numerical technique for simulating seasonal or transient biogeochemical behaviour at high vertical resolution whilst minimising the number of elements in the mesh. More work is required to move this to fully 3-D simulations.

Watermarking on 3D mesh based on spherical wavelet transform.

PubMed

Jin, Jian-Qiu; Dai, Min-Ya; Bao, Hu-Jun; Peng, Qun-Sheng

2004-03-01

In this paper we propose a robust watermarking algorithm for 3D mesh. The algorithm is based on spherical wavelet transform. Our basic idea is to decompose the original mesh into a series of details at different scales by using spherical wavelet transform; the watermark is then embedded into the different levels of details. The embedding process includes: global sphere parameterization, spherical uniform sampling, spherical wavelet forward transform, embedding watermark, spherical wavelet inverse transform, and at last resampling the mesh watermarked to recover the topological connectivity of the original model. Experiments showed that our algorithm can improve the capacity of the watermark and the robustness of watermarking against attacks.

Stress adapted embroidered meshes with a graded pattern design for abdominal wall hernia repair

NASA Astrophysics Data System (ADS)

Hahn, J.; Bittrich, L.; Breier, A.; Spickenheuer, A.

2017-10-01

Abdominal wall hernias are one of the most relevant injuries of the digestive system with 25 million patients in 2013. Surgery is recommended primarily using allogenic non-absorbable wrap-knitted meshes. These meshes have in common that their stress-strain behaviour is not adapted to the anisotropic behaviour of native abdominal wall tissue. The ideal mesh should possess an adequate mechanical behaviour and a suitable porosity at the same time. An alternative fabrication method to wrap-knitting is the embroidery technology with a high flexibility in pattern design and adaption of mechanical properties. In this study, a pattern generator was created for pattern designs consisting of a base and a reinforcement pattern. The embroidered mesh structures demonstrated different structural and mechanical characteristics. Additionally, the investigation of the mechanical properties exhibited an anisotropic mechanical behaviour for the embroidered meshes. As a result, the investigated pattern generator and the embroidery technology allow the production of stress adapted mesh structures that are a promising approach for hernia reconstruction.

Procedure for Adapting Direct Simulation Monte Carlo Meshes

NASA Technical Reports Server (NTRS)

Woronowicz, Michael S.; Wilmoth, Richard G.; Carlson, Ann B.; Rault, Didier F. G.

1992-01-01

A technique is presented for adapting computational meshes used in the G2 version of the direct simulation Monte Carlo method. The physical ideas underlying the technique are discussed, and adaptation formulas are developed for use on solutions generated from an initial mesh. The effect of statistical scatter on adaptation is addressed, and results demonstrate the ability of this technique to achieve more accurate results without increasing necessary computational resources.

A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Lou, John Z.; Norton, Charles D.; Cwik, Thomas A.

1999-01-01

The design and implementation of Pyramid, a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described. This software library can be easily used in a variety of unstructured parallel computational applications, including parallel finite element, parallel finite volume, and parallel visualization applications using triangular or tetrahedral meshes. The library contains a suite of well-designed and efficiently implemented modules that perform operations in a typical PAMR process. Among these are mesh quality control during successive parallel adaptive refinement (typically guided by a local-error estimator), parallel load-balancing, and parallel mesh partitioning using the ParMeTiS partitioner. The Pyramid library is implemented in Fortran 90 with an interface to the Message-Passing Interface (MPI) library, supporting code efficiency, modularity, and portability. An EM waveguide filter application, adaptively refined using the Pyramid library, is illustrated.

Finite-element 3D simulation tools for high-current relativistic electron beams

NASA Astrophysics Data System (ADS)

Humphries, Stanley; Ekdahl, Carl

2002-08-01

The DARHT second-axis injector is a challenge for computer simulations. Electrons are subject to strong beam-generated forces. The fields are fully three-dimensional and accurate calculations at surfaces are critical. We describe methods applied in OmniTrak, a 3D finite-element code suite that can address DARHT and the full range of charged-particle devices. The system handles mesh generation, electrostatics, magnetostatics and self-consistent particle orbits. The MetaMesh program generates meshes of conformal hexahedrons to fit any user geometry. The code has the unique ability to create structured conformal meshes with cubic logic. Organized meshes offer advantages in speed and memory utilization in the orbit and field solutions. OmniTrak is a versatile charged-particle code that handles 3D electric and magnetic field solutions on independent meshes. The program can update both 3D field solutions from the calculated beam space-charge and current-density. We shall describe numerical methods for orbit tracking on a hexahedron mesh. Topics include: 1) identification of elements along the particle trajectory, 2) fast searches and adaptive field calculations, 3) interpolation methods to terminate orbits on material surfaces, 4) automatic particle generation on multiple emission surfaces to model space-charge-limited emission and field emission, 5) flexible Child law algorithms, 6) implementation of the dual potential model for 3D magnetostatics, and 7) assignment of charge and current from model particle orbits for self-consistent fields.

Unstructured Polyhedral Mesh Thermal Radiation Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palmer, T.S.; Zika, M.R.; Madsen, N.K.

2000-07-27

Unstructured mesh particle transport and diffusion methods are gaining wider acceptance as mesh generation, scientific visualization and linear solvers improve. This paper describes an algorithm that is currently being used in the KULL code at Lawrence Livermore National Laboratory to solve the radiative transfer equations. The algorithm employs a point-centered diffusion discretization on arbitrary polyhedral meshes in 3D. We present the results of a few test problems to illustrate the capabilities of the radiation diffusion module.

Efficiently Sorting Zoo-Mesh Data Sets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cook, R; Max, N; Silva, C

The authors describe the SXMPVO algorithm for performing a visibility ordering zoo-meshed polyhedra. The algorithm runs in practice in linear time and the visibility ordering which it produces is exact.

Quality factors and local adaption (with applications in Eulerian hydrodynamics)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crowley, W.P.

1992-06-17

Adapting the mesh to suit the solution is a technique commonly used for solving both ode`s and pde`s. For Lagrangian hydrodynamics, ALE and Free-Lagrange are examples of structured and unstructured adaptive methods. For Eulerian hydrodynamics the two basic approaches are the macro-unstructuring technique pioneered by Oliger and Berger and the micro-structuring technique due to Lohner and others. Here we will describe a new micro-unstructuring technique, LAM, (for Local Adaptive Mesh) as applied to Eulerian hydrodynamics. The LAM technique consists of two independent parts: (1) the time advance scheme is a variation on the artificial viscosity method; (2) the adaption schememore » uses a micro-unstructured mesh with quadrilateral mesh elements. The adaption scheme makes use of quality factors and the relation between these and truncation errors is discussed. The time advance scheme; the adaption strategy; and the effect of different adaption parameters on numerical solutions are described.« less

Quality factors and local adaption (with applications in Eulerian hydrodynamics)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Crowley, W.P.

1992-06-17

Adapting the mesh to suit the solution is a technique commonly used for solving both ode's and pde's. For Lagrangian hydrodynamics, ALE and Free-Lagrange are examples of structured and unstructured adaptive methods. For Eulerian hydrodynamics the two basic approaches are the macro-unstructuring technique pioneered by Oliger and Berger and the micro-structuring technique due to Lohner and others. Here we will describe a new micro-unstructuring technique, LAM, (for Local Adaptive Mesh) as applied to Eulerian hydrodynamics. The LAM technique consists of two independent parts: (1) the time advance scheme is a variation on the artificial viscosity method; (2) the adaption schememore » uses a micro-unstructured mesh with quadrilateral mesh elements. The adaption scheme makes use of quality factors and the relation between these and truncation errors is discussed. The time advance scheme; the adaption strategy; and the effect of different adaption parameters on numerical solutions are described.« less

Adaptive Shape Functions and Internal Mesh Adaptation for Modelling Progressive Failure in Adhesively Bonded Joints

NASA Technical Reports Server (NTRS)

Stapleton, Scott; Gries, Thomas; Waas, Anthony M.; Pineda, Evan J.

2014-01-01

Enhanced finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.

The Clawpack Community of Codes

NASA Astrophysics Data System (ADS)

Mandli, K. T.; LeVeque, R. J.; Ketcheson, D.; Ahmadia, A. J.

2014-12-01

Clawpack, the Conservation Laws Package, has long been one of the standards for solving hyperbolic conservation laws but over the years has extended well beyond this role. Today a community of open-source codes have been developed that address a multitude of different needs including non-conservative balance laws, high-order accurate methods, and parallelism while remaining extensible and easy to use, largely by the judicious use of Python and the original Fortran codes that it wraps. This talk will present some of the recent developments in projects under the Clawpack umbrella, notably the GeoClaw and PyClaw projects. GeoClaw was originally developed as a tool for simulating tsunamis using adaptive mesh refinement but has since encompassed a large number of other geophysically relevant flows including storm surge and debris-flows. PyClaw originated as a Python version of the original Clawpack algorithms but has since been both a testing ground for new algorithmic advances in the Clawpack framework but also an easily extensible framework for solving hyperbolic balance laws. Some of these extensions include the addition of WENO high-order methods, massively parallel capabilities, and adaptive mesh refinement technologies, made possible largely by the flexibility of the Python language and community libraries such as NumPy and PETSc. Because of the tight integration with Python tecnologies, both packages have benefited also from the focus on reproducibility in the Python community, notably IPython notebooks.

Multiresolution strategies for the numerical solution of optimal control problems

NASA Astrophysics Data System (ADS)

Jain, Sachin

There exist many numerical techniques for solving optimal control problems but less work has been done in the field of making these algorithms run faster and more robustly. The main motivation of this work is to solve optimal control problems accurately in a fast and efficient way. Optimal control problems are often characterized by discontinuities or switchings in the control variables. One way of accurately capturing the irregularities in the solution is to use a high resolution (dense) uniform grid. This requires a large amount of computational resources both in terms of CPU time and memory. Hence, in order to accurately capture any irregularities in the solution using a few computational resources, one can refine the mesh locally in the region close to an irregularity instead of refining the mesh uniformly over the whole domain. Therefore, a novel multiresolution scheme for data compression has been designed which is shown to outperform similar data compression schemes. Specifically, we have shown that the proposed approach results in fewer grid points in the grid compared to a common multiresolution data compression scheme. The validity of the proposed mesh refinement algorithm has been verified by solving several challenging initial-boundary value problems for evolution equations in 1D. The examples have demonstrated the stability and robustness of the proposed algorithm. The algorithm adapted dynamically to any existing or emerging irregularities in the solution by automatically allocating more grid points to the region where the solution exhibited sharp features and fewer points to the region where the solution was smooth. Thereby, the computational time and memory usage has been reduced significantly, while maintaining an accuracy equivalent to the one obtained using a fine uniform mesh. Next, a direct multiresolution-based approach for solving trajectory optimization problems is developed. The original optimal control problem is transcribed into a nonlinear programming (NLP) problem that is solved using standard NLP codes. The novelty of the proposed approach hinges on the automatic calculation of a suitable, nonuniform grid over which the NLP problem is solved, which tends to increase numerical efficiency and robustness. Control and/or state constraints are handled with ease, and without any additional computational complexity. The proposed algorithm is based on a simple and intuitive method to balance several conflicting objectives, such as accuracy of the solution, convergence, and speed of the computations. The benefits of the proposed algorithm over uniform grid implementations are demonstrated with the help of several nontrivial examples. Furthermore, two sequential multiresolution trajectory optimization algorithms for solving problems with moving targets and/or dynamically changing environments have been developed. For such problems, high accuracy is desirable only in the immediate future, yet the ultimate mission objectives should be accommodated as well. An intelligent trajectory generation for such situations is thus enabled by introducing the idea of multigrid temporal resolution to solve the associated trajectory optimization problem on a non-uniform grid across time that is adapted to: (i) immediate future, and (ii) potential discontinuities in the state and control variables.

Aerodynamics of Engine-Airframe Interaction

NASA Technical Reports Server (NTRS)

Caughey, D. A.

1986-01-01

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm.

Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees

PubMed Central

Bronson, Jonathan; Levine, Joshua A.; Whitaker, Ross

2014-01-01

We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach. PMID:24356365

Active structural acoustic control of helicopter interior multifrequency noise using input-output-based hybrid control

NASA Astrophysics Data System (ADS)

Ma, Xunjun; Lu, Yang; Wang, Fengjiao

2017-09-01

This paper presents the recent advances in reduction of multifrequency noise inside helicopter cabin using an active structural acoustic control system, which is based on active gearbox struts technical approach. To attenuate the multifrequency gearbox vibrations and resulting noise, a new scheme of discrete model predictive sliding mode control has been proposed based on controlled auto-regressive moving average model. Its implementation only needs input/output data, hence a broader frequency range of controlled system is modelled and the burden on the state observer design is released. Furthermore, a new iteration form of the algorithm is designed, improving the developing efficiency and run speed. To verify the algorithm's effectiveness and self-adaptability, experiments of real-time active control are performed on a newly developed helicopter model system. The helicopter model can generate gear meshing vibration/noise similar to a real helicopter with specially designed gearbox and active struts. The algorithm's control abilities are sufficiently checked by single-input single-output and multiple-input multiple-output experiments via different feedback strategies progressively: (1) control gear meshing noise through attenuating vibrations at the key points on the transmission path, (2) directly control the gear meshing noise in the cabin using the actuators. Results confirm that the active control system is practical for cancelling multifrequency helicopter interior noise, which also weakens the frequency-modulation of the tones. For many cases, the attenuations of the measured noise exceed the level of 15 dB, with maximum reduction reaching 31 dB. Also, the control process is demonstrated to be smoother and faster.

The Feasibility of Adaptive Unstructured Computations On Petaflops Systems

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Oliker, Leonid; Heber, Gerd; Gao, Guang; Saini, Subhash (Technical Monitor)

1999-01-01

This viewgraph presentation covers the advantages of mesh adaptation, unstructured grids, and dynamic load balancing. It illustrates parallel adaptive communications, and explains PLUM (Parallel dynamic load balancing for adaptive unstructured meshes), and PSAW (Proper Self Avoiding Walks).

Parallel deterministic transport sweeps of structured and unstructured meshes with overloaded mesh decompositions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pautz, Shawn D.; Bailey, Teresa S.

Here, the efficiency of discrete ordinates transport sweeps depends on the scheduling algorithm, the domain decomposition, the problem to be solved, and the computational platform. Sweep scheduling algorithms may be categorized by their approach to several issues. In this paper we examine the strategy of domain overloading for mesh partitioning as one of the components of such algorithms. In particular, we extend the domain overloading strategy, previously defined and analyzed for structured meshes, to the general case of unstructured meshes. We also present computational results for both the structured and unstructured domain overloading cases. We find that an appropriate amountmore » of domain overloading can greatly improve the efficiency of parallel sweeps for both structured and unstructured partitionings of the test problems examined on up to 10 5 processor cores.« less

Parallel deterministic transport sweeps of structured and unstructured meshes with overloaded mesh decompositions

DOE PAGES

Pautz, Shawn D.; Bailey, Teresa S.

2016-11-29

Here, the efficiency of discrete ordinates transport sweeps depends on the scheduling algorithm, the domain decomposition, the problem to be solved, and the computational platform. Sweep scheduling algorithms may be categorized by their approach to several issues. In this paper we examine the strategy of domain overloading for mesh partitioning as one of the components of such algorithms. In particular, we extend the domain overloading strategy, previously defined and analyzed for structured meshes, to the general case of unstructured meshes. We also present computational results for both the structured and unstructured domain overloading cases. We find that an appropriate amountmore » of domain overloading can greatly improve the efficiency of parallel sweeps for both structured and unstructured partitionings of the test problems examined on up to 10 5 processor cores.« less

Development of a solution adaptive unstructured scheme for quasi-3D inviscid flows through advanced turbomachinery cascades

NASA Technical Reports Server (NTRS)

Usab, William J., Jr.; Jiang, Yi-Tsann

1991-01-01

The objective of the present research is to develop a general solution adaptive scheme for the accurate prediction of inviscid quasi-three-dimensional flow in advanced compressor and turbine designs. The adaptive solution scheme combines an explicit finite-volume time-marching scheme for unstructured triangular meshes and an advancing front triangular mesh scheme with a remeshing procedure for adapting the mesh as the solution evolves. The unstructured flow solver has been tested on a series of two-dimensional airfoil configurations including a three-element analytic test case presented here. Mesh adapted quasi-three-dimensional Euler solutions are presented for three spanwise stations of the NASA rotor 67 transonic fan. Computed solutions are compared with available experimental data.

Simulating Soft Shadows with Graphics Hardware,

DTIC Science & Technology

1997-01-15

This radiance texture is analogous to the mesh of radiosity values computed in a radiosity algorithm. Unlike a radiosity algorithm, however, our...discretely. Several researchers have explored continuous visibility methods for soft shadow computation and radiosity mesh generation. With this approach...times of several seconds [9]. Most radiosity methods discretize each surface into a mesh of elements and then use discrete methods such as ray

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Lesoinne, Michel

1993-01-01

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Efficiently computing exact geodesic loops within finite steps.

PubMed

Xin, Shi-Qing; He, Ying; Fu, Chi-Wing

2012-06-01

Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.

A mesh regeneration method using quadrilateral and triangular elements for compressible flows

NASA Technical Reports Server (NTRS)

Vemaganti, G. R.; Thornton, E. A.

1989-01-01

An adaptive remeshing method using both triangular and quadrilateral elements suitable for high-speed viscous flows is presented. For inviscid flows, the method generates completely unstructured meshes. For viscous flows, structured meshes are generated for boundary layers, and unstructured meshes are generated for inviscid flow regions. Examples of inviscid and viscous adaptations for high-speed flows are presented.

Parallel Adaptive Mesh Refinement for High-Order Finite-Volume Schemes in Computational Fluid Dynamics

NASA Astrophysics Data System (ADS)

Schwing, Alan Michael

For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable comparisons across a range of regimes. Unsteady and steady applications are considered in both subsonic and supersonic flows. Inviscid and viscous simulations achieve similar results at a much reduced cost when employing dynamic mesh adaptation. Several techniques for guiding adaptation are compared. Detailed analysis of statistics from the instrumented solver enable understanding of the costs associated with adaptation. Adaptive mesh refinement shows promise for the test cases presented here. It can be considerably faster than using conventional grids and provides accurate results. The procedures for adapting the grid are light-weight enough to not require significant computational time and yield significant reductions in grid size.

Efficient workflows for 3D building full-color model reconstruction using LIDAR long-range laser and image-based modeling techniques

NASA Astrophysics Data System (ADS)

Shih, Chihhsiong

2005-01-01

Two efficient workflow are developed for the reconstruction of a 3D full color building model. One uses a point wise sensing device to sample an unknown object densely and attach color textures from a digital camera separately. The other uses an image based approach to reconstruct the model with color texture automatically attached. The point wise sensing device reconstructs the CAD model using a modified best view algorithm that collects the maximum number of construction faces in one view. The partial views of the point clouds data are then glued together using a common face between two consecutive views. Typical overlapping mesh removal and coarsening procedures are adapted to generate a unified 3D mesh shell structure. A post processing step is then taken to combine the digital image content from a separate camera with the 3D mesh shell surfaces. An indirect uv mapping procedure first divide the model faces into groups within which every face share the same normal direction. The corresponding images of these faces in a group is then adjusted using the uv map as a guidance. The final assembled image is then glued back to the 3D mesh to present a full colored building model. The result is a virtual building that can reflect the true dimension and surface material conditions of a real world campus building. The image based modeling procedure uses a commercial photogrammetry package to reconstruct the 3D model. A novel view planning algorithm is developed to guide the photos taking procedure. This algorithm successfully generate a minimum set of view angles. The set of pictures taken at these view angles can guarantee that each model face shows up at least in two of the pictures set and no more than three. The 3D model can then be reconstructed with minimum amount of labor spent in correlating picture pairs. The finished model is compared with the original object in both the topological and dimensional aspects. All the test cases show exact same topology and reasonably low dimension error ratio. Again proving the applicability of the algorithm.

Staggered Mesh Ewald: An extension of the Smooth Particle-Mesh Ewald method adding great versatility

PubMed Central

Cerutti, David S.; Duke, Robert E.; Darden, Thomas A.; Lybrand, Terry P.

2009-01-01

We draw on an old technique for improving the accuracy of mesh-based field calculations to extend the popular Smooth Particle Mesh Ewald (SPME) algorithm as the Staggered Mesh Ewald (StME) algorithm. StME improves the accuracy of computed forces by up to 1.2 orders of magnitude and also reduces the drift in system momentum inherent in the SPME method by averaging the results of two separate reciprocal space calculations. StME can use charge mesh spacings roughly 1.5× larger than SPME to obtain comparable levels of accuracy; the one mesh in an SPME calculation can therefore be replaced with two separate meshes, each less than one third of the original size. Coarsening the charge mesh can be balanced with reductions in the direct space cutoff to optimize performance: the efficiency of StME rivals or exceeds that of SPME calculations with similarly optimized parameters. StME may also offer advantages for parallel molecular dynamics simulations because it permits the use of coarser meshes without requiring higher orders of charge interpolation and also because the two reciprocal space calculations can be run independently if that is most suitable for the machine architecture. We are planning other improvements to the standard SPME algorithm, and anticipate that StME will work synergistically will all of them to dramatically improve the efficiency and parallel scaling of molecular simulations. PMID:20174456

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION

PubMed Central

HOLST, MICHAEL; MCCAMMON, JAMES ANDREW; YU, ZEYUN; ZHOU, YOUNGCHENG; ZHU, YUNRONG

2011-01-01

We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L∞ estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme are demonstrated with FETK through comparisons with the original regularization approach for a model problem. The convergence and accuracy of the overall AFEM algorithm is also illustrated by numerical approximation of electrostatic solvation energy for an insulin protein. PMID:21949541

Surface sampling techniques for 3D object inspection

NASA Astrophysics Data System (ADS)

Shih, Chihhsiong S.; Gerhardt, Lester A.

1995-03-01

While the uniform sampling method is quite popular for pointwise measurement of manufactured parts, this paper proposes three novel sampling strategies which emphasize 3D non-uniform inspection capability. They are: (a) the adaptive sampling, (b) the local adjustment sampling, and (c) the finite element centroid sampling techniques. The adaptive sampling strategy is based on a recursive surface subdivision process. Two different approaches are described for this adaptive sampling strategy. One uses triangle patches while the other uses rectangle patches. Several real world objects were tested using these two algorithms. Preliminary results show that sample points are distributed more closely around edges, corners, and vertices as desired for many classes of objects. Adaptive sampling using triangle patches is shown to generally perform better than both uniform and adaptive sampling using rectangle patches. The local adjustment sampling strategy uses a set of predefined starting points and then finds the local optimum position of each nodal point. This method approximates the object by moving the points toward object edges and corners. In a hybrid approach, uniform points sets and non-uniform points sets, first preprocessed by the adaptive sampling algorithm on a real world object were then tested using the local adjustment sampling method. The results show that the initial point sets when preprocessed by adaptive sampling using triangle patches, are moved the least amount of distance by the subsequently applied local adjustment method, again showing the superiority of this method. The finite element sampling technique samples the centroids of the surface triangle meshes produced from the finite element method. The performance of this algorithm was compared to that of the adaptive sampling using triangular patches. The adaptive sampling with triangular patches was once again shown to be better on different classes of objects.

An optimization-based framework for anisotropic simplex mesh adaptation

NASA Astrophysics Data System (ADS)

Yano, Masayuki; Darmofal, David L.

2012-09-01

We present a general framework for anisotropic h-adaptation of simplex meshes. Given a discretization and any element-wise, localizable error estimate, our adaptive method iterates toward a mesh that minimizes error for a given degrees of freedom. Utilizing mesh-metric duality, we consider a continuous optimization problem of the Riemannian metric tensor field that provides an anisotropic description of element sizes. First, our method performs a series of local solves to survey the behavior of the local error function. This information is then synthesized using an affine-invariant tensor manipulation framework to reconstruct an approximate gradient of the error function with respect to the metric tensor field. Finally, we perform gradient descent in the metric space to drive the mesh toward optimality. The method is first demonstrated to produce optimal anisotropic meshes minimizing the L2 projection error for a pair of canonical problems containing a singularity and a singular perturbation. The effectiveness of the framework is then demonstrated in the context of output-based adaptation for the advection-diffusion equation using a high-order discontinuous Galerkin discretization and the dual-weighted residual (DWR) error estimate. The method presented provides a unified framework for optimizing both the element size and anisotropy distribution using an a posteriori error estimate and enables efficient adaptation of anisotropic simplex meshes for high-order discretizations.

Free Mesh Method: fundamental conception, algorithms and accuracy study

PubMed Central

YAGAWA, Genki

2011-01-01

The finite element method (FEM) has been commonly employed in a variety of fields as a computer simulation method to solve such problems as solid, fluid, electro-magnetic phenomena and so on. However, creation of a quality mesh for the problem domain is a prerequisite when using FEM, which becomes a major part of the cost of a simulation. It is natural that the concept of meshless method has evolved. The free mesh method (FMM) is among the typical meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, especially on parallel processors. FMM is an efficient node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm for the finite element calculations. In this paper, FMM and its variation are reviewed focusing on their fundamental conception, algorithms and accuracy. PMID:21558752

Load Balancing Unstructured Adaptive Grids for CFD Problems

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Oliker, Leonid

1996-01-01

Mesh adaption is a powerful tool for efficient unstructured-grid computations but causes load imbalance among processors on a parallel machine. A dynamic load balancing method is presented that balances the workload across all processors with a global view. After each parallel tetrahedral mesh adaption, the method first determines if the new mesh is sufficiently unbalanced to warrant a repartitioning. If so, the adapted mesh is repartitioned, with new partitions assigned to processors so that the redistribution cost is minimized. The new partitions are accepted only if the remapping cost is compensated by the improved load balance. Results indicate that this strategy is effective for large-scale scientific computations on distributed-memory multiprocessors.

An Automatic Networking and Routing Algorithm for Mesh Network in PLC System

NASA Astrophysics Data System (ADS)

Liu, Xiaosheng; Liu, Hao; Liu, Jiasheng; Xu, Dianguo

2017-05-01

Power line communication (PLC) is considered to be one of the best communication technologies in smart grid. However, the topology of low voltage distribution network is complex, meanwhile power line channel has characteristics of time varying and attenuation, which lead to the unreliability of power line communication. In this paper, an automatic networking and routing algorithm is introduced which can be adapted to the "blind state" topology. The results of simulation and test show that the scheme is feasible, the routing overhead is small, and the load balance performance is good, which can achieve the establishment and maintenance of network quickly and effectively. The scheme is of great significance to improve the reliability of PLC.

Accurate Grid-based Clustering Algorithm with Diagonal Grid Searching and Merging

NASA Astrophysics Data System (ADS)

Liu, Feng; Ye, Chengcheng; Zhu, Erzhou

2017-09-01

Due to the advent of big data, data mining technology has attracted more and more attentions. As an important data analysis method, grid clustering algorithm is fast but with relatively lower accuracy. This paper presents an improved clustering algorithm combined with grid and density parameters. The algorithm first divides the data space into the valid meshes and invalid meshes through grid parameters. Secondly, from the starting point located at the first point of the diagonal of the grids, the algorithm takes the direction of “horizontal right, vertical down” to merge the valid meshes. Furthermore, by the boundary grid processing, the invalid grids are searched and merged when the adjacent left, above, and diagonal-direction grids are all the valid ones. By doing this, the accuracy of clustering is improved. The experimental results have shown that the proposed algorithm is accuracy and relatively faster when compared with some popularly used algorithms.

Parallel, Gradient-Based Anisotropic Mesh Adaptation for Re-entry Vehicle Configurations

NASA Technical Reports Server (NTRS)

Bibb, Karen L.; Gnoffo, Peter A.; Park, Michael A.; Jones, William T.

2006-01-01

Two gradient-based adaptation methodologies have been implemented into the Fun3d refine GridEx infrastructure. A spring-analogy adaptation which provides for nodal movement to cluster mesh nodes in the vicinity of strong shocks has been extended for general use within Fun3d, and is demonstrated for a 70 sphere cone at Mach 2. A more general feature-based adaptation metric has been developed for use with the adaptation mechanics available in Fun3d, and is applicable to any unstructured, tetrahedral, flow solver. The basic functionality of general adaptation is explored through a case of flow over the forebody of a 70 sphere cone at Mach 6. A practical application of Mach 10 flow over an Apollo capsule, computed with the Felisa flow solver, is given to compare the adaptive mesh refinement with uniform mesh refinement. The examples of the paper demonstrate that the gradient-based adaptation capability as implemented can give an improvement in solution quality.

Robust estimation of adaptive tensors of curvature by tensor voting.

PubMed

Tong, Wai-Shun; Tang, Chi-Keung

2005-03-01

Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.

A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

DOE PAGES

Guzik, Stephen M.; Gao, Xinfeng; Owen, Landon D.; ...

2015-12-20

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution ofmore » a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.« less

Hexahedral mesh generation via the dual arrangement of surfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mitchell, S.A.; Tautges, T.J.

1997-12-31

Given a general three-dimensional geometry with a prescribed quadrilateral surface mesh, the authors consider the problem of constructing a hexahedral mesh of the geometry whose boundary is exactly the prescribed surface mesh. Due to the specialized topology of hexahedra, this problem is more difficult than the analogous one for tetrahedra. Folklore has maintained that a surface mesh must have a constrained structure in order for there to exist a compatible hexahedral mesh. However, they have proof that a surface mesh need only satisfy mild parity conditions, depending on the topology of the three-dimensional geometry, for there to exist a compatiblemore » hexahedral mesh. The proof is based on the realization that a hexahedral mesh is dual to an arrangement of surfaces, and the quadrilateral surface mesh is dual to the arrangement of curves bounding these surfaces. The proof is constructive and they are currently developing an algorithm called Whisker Weaving (WW) that mirrors the proof steps. Given the bounding curves, WW builds the topological structure of an arrangement of surfaces having those curves as its boundary. WW progresses in an advancing front manner. Certain local rules are applied to avoid structures that lead to poor mesh quality. Also, after the arrangement is constructed, additional surfaces are inserted to separate features, so e.g., no two hexahedra share more than one quadrilateral face. The algorithm has generated meshes for certain non-trivial problems, but is currently unreliable. The authors are exploring strategies for consistently selecting which portion of the surface arrangement to advance based on the existence proof. This should lead us to a robust algorithm for arbitrary geometries and surface meshes.« less

Using Adaptive Mesh Refinment to Simulate Storm Surge

NASA Astrophysics Data System (ADS)

Mandli, K. T.; Dawson, C.

2012-12-01

Coastal hazards related to strong storms such as hurricanes and typhoons are one of the most frequently recurring and wide spread hazards to coastal communities. Storm surges are among the most devastating effects of these storms, and their prediction and mitigation through numerical simulations is of great interest to coastal communities that need to plan for the subsequent rise in sea level during these storms. Unfortunately these simulations require a large amount of resolution in regions of interest to capture relevant effects resulting in a computational cost that may be intractable. This problem is exacerbated in situations where a large number of similar runs is needed such as in design of infrastructure or forecasting with ensembles of probable storms. One solution to address the problem of computational cost is to employ adaptive mesh refinement (AMR) algorithms. AMR functions by decomposing the computational domain into regions which may vary in resolution as time proceeds. Decomposing the domain as the flow evolves makes this class of methods effective at ensuring that computational effort is spent only where it is needed. AMR also allows for placement of computational resolution independent of user interaction and expectation of the dynamics of the flow as well as particular regions of interest such as harbors. The simulation of many different applications have only been made possible by using AMR-type algorithms, which have allowed otherwise impractical simulations to be performed for much less computational expense. Our work involves studying how storm surge simulations can be improved with AMR algorithms. We have implemented relevant storm surge physics in the GeoClaw package and tested how Hurricane Ike's surge into Galveston Bay and up the Houston Ship Channel compares to available tide gauge data. We will also discuss issues dealing with refinement criteria, optimal resolution and refinement ratios, and inundation.

Conservative multizonal interface algorithm for the 3-D Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Molvik, G. A.

1991-01-01

A conservative zonal interface algorithm using features of both structured and unstructured mesh CFD technology is presented. The flow solver within each of the zones is based on structured mesh CFD technology. The interface algorithm was implemented into two three-dimensional Navier-Stokes finite volume codes and was found to yield good results.

Parallel Adaptive Mesh Refinement Library

NASA Technical Reports Server (NTRS)

Mac-Neice, Peter; Olson, Kevin

2005-01-01

Parallel Adaptive Mesh Refinement Library (PARAMESH) is a package of Fortran 90 subroutines designed to provide a computer programmer with an easy route to extension of (1) a previously written serial code that uses a logically Cartesian structured mesh into (2) a parallel code with adaptive mesh refinement (AMR). Alternatively, in its simplest use, and with minimal effort, PARAMESH can operate as a domain-decomposition tool for users who want to parallelize their serial codes but who do not wish to utilize adaptivity. The package builds a hierarchy of sub-grids to cover the computational domain of a given application program, with spatial resolution varying to satisfy the demands of the application. The sub-grid blocks form the nodes of a tree data structure (a quad-tree in two or an oct-tree in three dimensions). Each grid block has a logically Cartesian mesh. The package supports one-, two- and three-dimensional models.

H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows

NASA Technical Reports Server (NTRS)

Chang, H. J.; Bass, J. M.; Tworzydlo, W.; Oden, J. T.

1993-01-01

The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).

Towards Adaptive Grids for Atmospheric Boundary-Layer Simulations

NASA Astrophysics Data System (ADS)

van Hooft, J. Antoon; Popinet, Stéphane; van Heerwaarden, Chiel C.; van der Linden, Steven J. A.; de Roode, Stephan R.; van de Wiel, Bas J. H.

2018-02-01

We present a proof-of-concept for the adaptive mesh refinement method applied to atmospheric boundary-layer simulations. Such a method may form an attractive alternative to static grids for studies on atmospheric flows that have a high degree of scale separation in space and/or time. Examples include the diurnal cycle and a convective boundary layer capped by a strong inversion. For such cases, large-eddy simulations using regular grids often have to rely on a subgrid-scale closure for the most challenging regions in the spatial and/or temporal domain. Here we analyze a flow configuration that describes the growth and subsequent decay of a convective boundary layer using direct numerical simulation (DNS). We validate the obtained results and benchmark the performance of the adaptive solver against two runs using fixed regular grids. It appears that the adaptive-mesh algorithm is able to coarsen and refine the grid dynamically whilst maintaining an accurate solution. In particular, during the initial growth of the convective boundary layer a high resolution is required compared to the subsequent stage of decaying turbulence. More specifically, the number of grid cells varies by two orders of magnitude over the course of the simulation. For this specific DNS case, the adaptive solver was not yet more efficient than the more traditional solver that is dedicated to these types of flows. However, the overall analysis shows that the method has a clear potential for numerical investigations of the most challenging atmospheric cases.

Towards Adaptive Grids for Atmospheric Boundary-Layer Simulations

NASA Astrophysics Data System (ADS)

van Hooft, J. Antoon; Popinet, Stéphane; van Heerwaarden, Chiel C.; van der Linden, Steven J. A.; de Roode, Stephan R.; van de Wiel, Bas J. H.

2018-06-01

We present a proof-of-concept for the adaptive mesh refinement method applied to atmospheric boundary-layer simulations. Such a method may form an attractive alternative to static grids for studies on atmospheric flows that have a high degree of scale separation in space and/or time. Examples include the diurnal cycle and a convective boundary layer capped by a strong inversion. For such cases, large-eddy simulations using regular grids often have to rely on a subgrid-scale closure for the most challenging regions in the spatial and/or temporal domain. Here we analyze a flow configuration that describes the growth and subsequent decay of a convective boundary layer using direct numerical simulation (DNS). We validate the obtained results and benchmark the performance of the adaptive solver against two runs using fixed regular grids. It appears that the adaptive-mesh algorithm is able to coarsen and refine the grid dynamically whilst maintaining an accurate solution. In particular, during the initial growth of the convective boundary layer a high resolution is required compared to the subsequent stage of decaying turbulence. More specifically, the number of grid cells varies by two orders of magnitude over the course of the simulation. For this specific DNS case, the adaptive solver was not yet more efficient than the more traditional solver that is dedicated to these types of flows. However, the overall analysis shows that the method has a clear potential for numerical investigations of the most challenging atmospheric cases.

Anisotropic adaptive mesh generation in two dimensions for CFD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Borouchaki, H.; Castro-Diaz, M.J.; George, P.L.

This paper describes the extension of the classical Delaunay method in the case where anisotropic meshes are required such as in CFD when the modelized physic is strongly directional. The way in which such a mesh generation method can be incorporated in an adaptative loop of CFD as well as the case of multicriterium adaptation are discussed. Several concrete application examples are provided to illustrate the capabilities of the proposed method.

Performance Evaluation of Various STL File Mesh Refining Algorithms Applied for FDM-RP Process

NASA Astrophysics Data System (ADS)

Ledalla, Siva Rama Krishna; Tirupathi, Balaji; Sriram, Venkatesh

2018-06-01

Layered manufacturing machines use the stereolithography (STL) file to build parts. When a curved surface is converted from a computer aided design (CAD) file to STL, it results in a geometrical distortion and chordal error. Parts manufactured with this file, might not satisfy geometric dimensioning and tolerance requirements due to approximated geometry. Current algorithms built in CAD packages have export options to globally reduce this distortion, which leads to an increase in the file size and pre-processing time. In this work, different mesh subdivision algorithms are applied on STL file of a complex geometric features using MeshLab software. The mesh subdivision algorithms considered in this work are modified butterfly subdivision technique, loops sub division technique and general triangular midpoint sub division technique. A comparative study is made with respect to volume and the build time using the above techniques. It is found that triangular midpoint sub division algorithm is more suitable for the geometry under consideration. Only the wheel cap part is then manufactured on Stratasys MOJO FDM machine. The surface roughness of the part is measured on Talysurf surface roughness tester.

Adaptive Mesh Refinement for Microelectronic Device Design

NASA Technical Reports Server (NTRS)

Cwik, Tom; Lou, John; Norton, Charles

1999-01-01

Finite element and finite volume methods are used in a variety of design simulations when it is necessary to compute fields throughout regions that contain varying materials or geometry. Convergence of the simulation can be assessed by uniformly increasing the mesh density until an observable quantity stabilizes. Depending on the electrical size of the problem, uniform refinement of the mesh may be computationally infeasible due to memory limitations. Similarly, depending on the geometric complexity of the object being modeled, uniform refinement can be inefficient since regions that do not need refinement add to the computational expense. In either case, convergence to the correct (measured) solution is not guaranteed. Adaptive mesh refinement methods attempt to selectively refine the region of the mesh that is estimated to contain proportionally higher solution errors. The refinement may be obtained by decreasing the element size (h-refinement), by increasing the order of the element (p-refinement) or by a combination of the two (h-p refinement). A successful adaptive strategy refines the mesh to produce an accurate solution measured against the correct fields without undue computational expense. This is accomplished by the use of a) reliable a posteriori error estimates, b) hierarchal elements, and c) automatic adaptive mesh generation. Adaptive methods are also useful when problems with multi-scale field variations are encountered. These occur in active electronic devices that have thin doped layers and also when mixed physics is used in the calculation. The mesh needs to be fine at and near the thin layer to capture rapid field or charge variations, but can coarsen away from these layers where field variations smoothen and charge densities are uniform. This poster will present an adaptive mesh refinement package that runs on parallel computers and is applied to specific microelectronic device simulations. Passive sensors that operate in the infrared portion of the spectrum as well as active device simulations that model charge transport and Maxwell's equations will be presented.

Failure of Anisotropic Unstructured Mesh Adaption Based on Multidimensional Residual Minimization

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

2003-01-01

An automated anisotropic unstructured mesh adaptation strategy is proposed, implemented, and assessed for the discretization of viscous flows. The adaption criteria is based upon the minimization of the residual fluctuations of a multidimensional upwind viscous flow solver. For scalar advection, this adaption strategy has been shown to use fewer grid points than gradient based adaption, naturally aligning mesh edges with discontinuities and characteristic lines. The adaption utilizes a compact stencil and is local in scope, with four fundamental operations: point insertion, point deletion, edge swapping, and nodal displacement. Evaluation of the solution-adaptive strategy is performed for a two-dimensional blunt body laminar wind tunnel case at Mach 10. The results demonstrate that the strategy suffers from a lack of robustness, particularly with regard to alignment of the bow shock in the vicinity of the stagnation streamline. In general, constraining the adaption to such a degree as to maintain robustness results in negligible improvement to the solution. Because the present method fails to consistently or significantly improve the flow solution, it is rejected in favor of simple uniform mesh refinement.

An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography

NASA Astrophysics Data System (ADS)

Zhou, Feng; Chen, Guoxian; Huang, Yuefei; Yang, Jerry Zhijian; Feng, Hui

2013-04-01

A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving position-fixed meshes, the iteration process of the AFMV scheme moves a fewer number of the meshes adaptively in response to flow variables calculated in prior solutions and then simulates their posterior values on the new meshes. At each time step of the simulation, the AMFV scheme consists of three parts: an adaptive mesh movement to shift the vertices position, a geometrical conservative interpolation to remap the flow variables by summing the total mass over old meshes to avoid the generation of spurious waves, and a partial differential equations(PDEs) discretization to update the flow variables for a new time step. Five different test cases are presented to verify the computational advantages of the proposed scheme over nonadaptive methods. The results reveal three attractive features: (i) the AMFV scheme could preserve still water equilibrium and positivity of water depth within both mesh movement and PDE discretization steps; (ii) it improved the shock-capturing capability for handling topographic source terms and wet-dry interfaces by moving triangular meshes to approximate the spatial distribution of time-variant flood processes; (iii) it was able to solve the shallow water equations with a relatively higher accuracy and spatial-resolution with a lower computational cost.

Towards a large-scale scalable adaptive heart model using shallow tree meshes

NASA Astrophysics Data System (ADS)

Krause, Dorian; Dickopf, Thomas; Potse, Mark; Krause, Rolf

2015-10-01

Electrophysiological heart models are sophisticated computational tools that place high demands on the computing hardware due to the high spatial resolution required to capture the steep depolarization front. To address this challenge, we present a novel adaptive scheme for resolving the deporalization front accurately using adaptivity in space. Our adaptive scheme is based on locally structured meshes. These tensor meshes in space are organized in a parallel forest of trees, which allows us to resolve complicated geometries and to realize high variations in the local mesh sizes with a minimal memory footprint in the adaptive scheme. We discuss both a non-conforming mortar element approximation and a conforming finite element space and present an efficient technique for the assembly of the respective stiffness matrices using matrix representations of the inclusion operators into the product space on the so-called shallow tree meshes. We analyzed the parallel performance and scalability for a two-dimensional ventricle slice as well as for a full large-scale heart model. Our results demonstrate that the method has good performance and high accuracy.

Improved algorithm of ray tracing in ICF cryogenic targets

NASA Astrophysics Data System (ADS)

Zhang, Rui; Yang, Yongying; Ling, Tong; Jiang, Jiabin

2016-10-01

The high precision ray tracing inside inertial confinement fusion (ICF) cryogenic targets plays an important role in the reconstruction of the three-dimensional density distribution by algebraic reconstruction technique (ART) algorithm. The traditional Runge-Kutta methods, which is restricted by the precision of the grid division and the step size of ray tracing, cannot make an accurate calculation in the case of refractive index saltation. In this paper, we propose an improved algorithm of ray tracing based on the Runge-Kutta methods and Snell's law of refraction to achieve high tracing precision. On the boundary of refractive index, we apply Snell's law of refraction and contact point search algorithm to ensure accuracy of the simulation. Inside the cryogenic target, the combination of the Runge-Kutta methods and self-adaptive step algorithm are employed for computation. The original refractive index data, which is used to mesh the target, can be obtained by experimental measurement or priori refractive index distribution function. A finite differential method is performed to calculate the refractive index gradient of mesh nodes, and the distance weighted average interpolation methods is utilized to obtain refractive index and gradient of each point in space. In the simulation, we take ideal ICF target, Luneberg lens and Graded index rod as simulation model to calculate the spot diagram and wavefront map. Compared the simulation results to Zemax, it manifests that the improved algorithm of ray tracing based on the fourth-order Runge-Kutta methods and Snell's law of refraction exhibits high accuracy. The relative error of the spot diagram is 0.2%, and the peak-to-valley (PV) error and the root-mean-square (RMS) error of the wavefront map is less than λ/35 and λ/100, correspondingly.

Parallel implementation of an adaptive scheme for 3D unstructured grids on the SP2

NASA Technical Reports Server (NTRS)

Strawn, Roger C.; Oliker, Leonid; Biswas, Rupak

1996-01-01

Dynamic mesh adaption on unstructured grids is a powerful tool for computing unsteady flows that require local grid modifications to efficiently resolve solution features. For this work, we consider an edge-based adaption scheme that has shown good single-processor performance on the C90. We report on our experience parallelizing this code for the SP2. Results show a 47.0X speedup on 64 processors when 10 percent of the mesh is randomly refined. Performance deteriorates to 7.7X when the same number of edges are refined in a highly-localized region. This is because almost all the mesh adaption is confined to a single processor. However, this problem can be remedied by repartitioning the mesh immediately after targeting edges for refinement but before the actual adaption takes place. With this change, the speedup improves dramatically to 43.6X.

Parallel Implementation of an Adaptive Scheme for 3D Unstructured Grids on the SP2

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Biswas, Rupak; Strawn, Roger C.

1996-01-01

Dynamic mesh adaption on unstructured grids is a powerful tool for computing unsteady flows that require local grid modifications to efficiently resolve solution features. For this work, we consider an edge-based adaption scheme that has shown good single-processor performance on the C90. We report on our experience parallelizing this code for the SP2. Results show a 47.OX speedup on 64 processors when 10% of the mesh is randomly refined. Performance deteriorates to 7.7X when the same number of edges are refined in a highly-localized region. This is because almost all mesh adaption is confined to a single processor. However, this problem can be remedied by repartitioning the mesh immediately after targeting edges for refinement but before the actual adaption takes place. With this change, the speedup improves dramatically to 43.6X.

Application of Quaternions for Mesh Deformation

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2002-01-01

A new three-dimensional mesh deformation algorithm, based on quaternion algebra, is introduced. A brief overview of quaternion algebra is provided, along with some preliminary results for two-dimensional structured and unstructured viscous mesh deformation.

Application of Quaternions for Mesh

NASA Technical Reports Server (NTRS)

Samareh, Jamshid A.

2002-01-01

A new three dimensional mesh deformation algorithm, based on quaternion algebra, is introduced. A brief overview of quaternion algebra is provided, along with some preliminary results for two-dimensional structured and unstructured viscous mesh deformation.

Gaussian curvature analysis allows for automatic block placement in multi-block hexahedral meshing.

PubMed

Ramme, Austin J; Shivanna, Kiran H; Magnotta, Vincent A; Grosland, Nicole M

2011-10-01

Musculoskeletal finite element analysis (FEA) has been essential to research in orthopaedic biomechanics. The generation of a volumetric mesh is often the most challenging step in a FEA. Hexahedral meshing tools that are based on a multi-block approach rely on the manual placement of building blocks for their mesh generation scheme. We hypothesise that Gaussian curvature analysis could be used to automatically develop a building block structure for multi-block hexahedral mesh generation. The Automated Building Block Algorithm incorporates principles from differential geometry, combinatorics, statistical analysis and computer science to automatically generate a building block structure to represent a given surface without prior information. We have applied this algorithm to 29 bones of varying geometries and successfully generated a usable mesh in all cases. This work represents a significant advancement in automating the definition of building blocks.

Comparison and combination of several MeSH indexing approaches

PubMed Central

Yepes, Antonio Jose Jimeno; Mork, James G.; Demner-Fushman, Dina; Aronson, Alan R.

2013-01-01

MeSH indexing of MEDLINE is becoming a more difficult task for the group of highly qualified indexing staff at the US National Library of Medicine, due to the large yearly growth of MEDLINE and the increasing size of MeSH. Since 2002, this task has been assisted by the Medical Text Indexer or MTI program. We extend previous machine learning analysis by adding a more diverse set of MeSH headings targeting examples where MTI has been shown to perform poorly. Machine learning algorithms exceed MTI’s performance on MeSH headings that are used very frequently and headings for which the indexing frequency is very low. We find that when we combine the MTI suggestions and the prediction of the learning algorithms, the performance improves compared to any single method for most of the evaluated MeSH headings. PMID:24551371

Comparison and combination of several MeSH indexing approaches.

PubMed

Yepes, Antonio Jose Jimeno; Mork, James G; Demner-Fushman, Dina; Aronson, Alan R

2013-01-01

MeSH indexing of MEDLINE is becoming a more difficult task for the group of highly qualified indexing staff at the US National Library of Medicine, due to the large yearly growth of MEDLINE and the increasing size of MeSH. Since 2002, this task has been assisted by the Medical Text Indexer or MTI program. We extend previous machine learning analysis by adding a more diverse set of MeSH headings targeting examples where MTI has been shown to perform poorly. Machine learning algorithms exceed MTI's performance on MeSH headings that are used very frequently and headings for which the indexing frequency is very low. We find that when we combine the MTI suggestions and the prediction of the learning algorithms, the performance improves compared to any single method for most of the evaluated MeSH headings.

Computations of Aerodynamic Performance Databases Using Output-Based Refinement

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2009-01-01

Objectives: Handle complex geometry problems; Control discretization errors via solution-adaptive mesh refinement; Focus on aerodynamic databases of parametric and optimization studies: 1. Accuracy: satisfy prescribed error bounds 2. Robustness and speed: may require over 105 mesh generations 3. Automation: avoid user supervision Obtain "expert meshes" independent of user skill; and Run every case adaptively in production settings.

Quadrilateral/hexahedral finite element mesh coarsening

DOEpatents

Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E

2012-10-16

A technique for coarsening a finite element mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.

Multigrid solution of internal flows using unstructured solution adaptive meshes

NASA Technical Reports Server (NTRS)

Smith, Wayne A.; Blake, Kenneth R.

1992-01-01

This is the final report of the NASA Lewis SBIR Phase 2 Contract Number NAS3-25785, Multigrid Solution of Internal Flows Using Unstructured Solution Adaptive Meshes. The objective of this project, as described in the Statement of Work, is to develop and deliver to NASA a general three-dimensional Navier-Stokes code using unstructured solution-adaptive meshes for accuracy and multigrid techniques for convergence acceleration. The code will primarily be applied, but not necessarily limited, to high speed internal flows in turbomachinery.

Balancing Contention and Synchronization on the Intel Paragon

NASA Technical Reports Server (NTRS)

Bokhari, Shahid H.; Nicol, David M.

1996-01-01

The Intel Paragon is a mesh-connected distributed memory parallel computer. It uses an oblivious and deterministic message routing algorithm: this permits us to develop highly optimized schedules for frequently needed communication patterns. The complete exchange is one such pattern. Several approaches are available for carrying it out on the mesh. We study an algorithm developed by Scott. This algorithm assumes that a communication link can carry one message at a time and that a node can only transmit one message at a time. It requires global synchronization to enforce a schedule of transmissions. Unfortunately global synchronization has substantial overhead on the Paragon. At the same time the powerful interconnection mechanism of this machine permits 2 or 3 messages to share a communication link with minor overhead. It can also overlap multiple message transmission from the same node to some extent. We develop a generalization of Scott's algorithm that executes complete exchange with a prescribed contention. Schedules that incur greater contention require fewer synchronization steps. This permits us to tradeoff contention against synchronization overhead. We describe the performance of this algorithm and compare it with Scott's original algorithm as well as with a naive algorithm that does not take interconnection structure into account. The Bounded contention algorithm is always better than Scott's algorithm and outperforms the naive algorithm for all but the smallest message sizes. The naive algorithm fails to work on meshes larger than 12 x 12. These results show that due consideration of processor interconnect and machine performance parameters is necessary to obtain peak performance from the Paragon and its successor mesh machines.

A FAST ITERATIVE METHOD FOR SOLVING THE EIKONAL EQUATION ON TETRAHEDRAL DOMAINS

PubMed Central

Fu, Zhisong; Kirby, Robert M.; Whitaker, Ross T.

2014-01-01

Generating numerical solutions to the eikonal equation and its many variations has a broad range of applications in both the natural and computational sciences. Efficient solvers on cutting-edge, parallel architectures require new algorithms that may not be theoretically optimal, but that are designed to allow asynchronous solution updates and have limited memory access patterns. This paper presents a parallel algorithm for solving the eikonal equation on fully unstructured tetrahedral meshes. The method is appropriate for the type of fine-grained parallelism found on modern massively-SIMD architectures such as graphics processors and takes into account the particular constraints and capabilities of these computing platforms. This work builds on previous work for solving these equations on triangle meshes; in this paper we adapt and extend previous two-dimensional strategies to accommodate three-dimensional, unstructured, tetrahedralized domains. These new developments include a local update strategy with data compaction for tetrahedral meshes that provides solutions on both serial and parallel architectures, with a generalization to inhomogeneous, anisotropic speed functions. We also propose two new update schemes, specialized to mitigate the natural data increase observed when moving to three dimensions, and the data structures necessary for efficiently mapping data to parallel SIMD processors in a way that maintains computational density. Finally, we present descriptions of the implementations for a single CPU, as well as multicore CPUs with shared memory and SIMD architectures, with comparative results against state-of-the-art eikonal solvers. PMID:25221418

Grid adaption using Chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1993-01-01

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

Grid adaptation using chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1994-01-01

The objective of this paper is to perform grid adaptation using composite overlapping meshes in regions of large gradient to accurately capture the salient features during computation. The chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using trilinear interpolation. Application to the Euler equations for shock reflections and to shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well-resolved.

Grid adaptation using Chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1993-01-01

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

High accuracy mantle convection simulation through modern numerical methods - II: realistic models and problems

NASA Astrophysics Data System (ADS)

Heister, Timo; Dannberg, Juliane; Gassmöller, Rene; Bangerth, Wolfgang

2017-08-01

Computations have helped elucidate the dynamics of Earth's mantle for several decades already. The numerical methods that underlie these simulations have greatly evolved within this time span, and today include dynamically changing and adaptively refined meshes, sophisticated and efficient solvers, and parallelization to large clusters of computers. At the same time, many of the methods - discussed in detail in a previous paper in this series - were developed and tested primarily using model problems that lack many of the complexities that are common to the realistic models our community wants to solve today. With several years of experience solving complex and realistic models, we here revisit some of the algorithm designs of the earlier paper and discuss the incorporation of more complex physics. In particular, we re-consider time stepping and mesh refinement algorithms, evaluate approaches to incorporate compressibility, and discuss dealing with strongly varying material coefficients, latent heat, and how to track chemical compositions and heterogeneities. Taken together and implemented in a high-performance, massively parallel code, the techniques discussed in this paper then allow for high resolution, 3-D, compressible, global mantle convection simulations with phase transitions, strongly temperature dependent viscosity and realistic material properties based on mineral physics data.

Matrix multiplication on the Intel Touchstone Delta

DOE Office of Scientific and Technical Information (OSTI.GOV)

Huss-Lederman, S.; Jacobson, E.M.; Tsao, A.

1993-12-31

Matrix multiplication is a key primitive in block matrix algorithms such as those found in LAPACK. We present results from our study of matrix multiplication algorithms on the Intel Touchstone Delta, a distributed memory message-passing architecture with a two-dimensional mesh topology. We obtain an implementation that uses communication primitives highly suited to the Delta and exploits the single node assembly-coded matrix multiplication. Our algorithm is completely general, able to deal with arbitrary mesh aspect ratios and matrix dimensions, and has achieved parallel efficiency of 86% with overall peak performance in excess of 8 Gflops on 256 nodes for an 8800more » {times} 8800 matrix. We describe our algorithm design and implementation, and present performance results that demonstrate scalability and robust behavior over varying mesh topologies.« less

Evolutionary and biological metaphors for engineering design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jakiela, M.

1994-12-31

Since computing became generally available, there has been strong interest in using computers to assist and automate engineering design processes. Specifically, for design optimization and automation, nonlinear programming and artificial intelligence techniques have been extensively studied. New computational techniques, based upon the natural processes of evolution, adaptation, and learing, are showing promise because of their generality and robustness. This presentation will describe the use of two such techniques, genetic algorithms and classifier systems, for a variety of engineering design problems. Structural topology optimization, meshing, and general engineering optimization are shown as example applications.

Simulation of a pulsatile total artificial heart: Development of a partitioned Fluid Structure Interaction model

NASA Astrophysics Data System (ADS)

Sonntag, Simon J.; Kaufmann, Tim A. S.; Büsen, Martin R.; Laumen, Marco; Linde, Torsten; Schmitz-Rode, Thomas; Steinseifer, Ulrich

2013-04-01

Heart disease is one of the leading causes of death in the world. Due to a shortage in donor organs artificial hearts can be a bridge to transplantation or even serve as a destination therapy for patients with terminal heart insufficiency. A pusher plate driven pulsatile membrane pump, the Total Artificial Heart (TAH) ReinHeart, is currently under development at the Institute of Applied Medical Engineering of RWTH Aachen University.This paper presents the methodology of a fully coupled three-dimensional time-dependent Fluid Structure Interaction (FSI) simulation of the TAH using a commercial partitioned block-Gauss-Seidel coupling package. Partitioned coupling of the incompressible fluid with the slender flexible membrane as well as a high fluid/structure density ratio of about unity led inherently to a deterioration of the stability (‘artificial added mass instability’). The objective was to conduct a stable simulation with high accuracy of the pumping process. In order to achieve stability, a combined resistance and pressure outlet boundary condition as well as the interface artificial compressibility method was applied. An analysis of the contact algorithm and turbulence condition is presented. Independence tests are performed for the structural and the fluid mesh, the time step size and the number of pulse cycles. Because of the large deformation of the fluid domain, a variable mesh stiffness depending on certain mesh properties was specified for the fluid elements. Adaptive remeshing was avoided. Different approaches for the mesh stiffness function are compared with respect to convergence, preservation of mesh topology and mesh quality. The resulting mesh aspect ratios, mesh expansion factors and mesh orthogonalities are evaluated in detail. The membrane motion and flow distribution of the coupled simulations are compared with a top-view recording and stereo Particle Image Velocimetry (PIV) measurements, respectively, of the actual pump.

Filament capturing with the multimaterial moment-of-fluid method*

DOE PAGES

Jemison, Matthew; Sussman, Mark; Shashkov, Mikhail

2015-01-15

A novel method for capturing two-dimensional, thin, under-resolved material configurations, known as “filaments,” is presented in the context of interface reconstruction. This technique uses a partitioning procedure to detect disconnected regions of material in the advective preimage of a cell (indicative of a filament) and makes use of the existing functionality of the Multimaterial Moment-of-Fluid interface reconstruction method to accurately capture the under-resolved feature, while exactly conserving volume. An algorithm for Adaptive Mesh Refinement in the presence of filaments is developed so that refinement is introduced only near the tips of filaments and where the Moment-of-Fluid reconstruction error is stillmore » large. Comparison to the standard Moment-of-Fluid method is made. As a result, it is demonstrated that using filament capturing at a given resolution yields gains in accuracy comparable to introducing an additional level of mesh refinement at significantly lower cost.« less

Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations

NASA Astrophysics Data System (ADS)

Loseille, A.; Dervieux, A.; Alauzet, F.

2010-04-01

This paper studies the coupling between anisotropic mesh adaptation and goal-oriented error estimate. The former is very well suited to the control of the interpolation error. It is generally interpreted as a local geometric error estimate. On the contrary, the latter is preferred when studying approximation errors for PDEs. It generally involves non local error contributions. Consequently, a full and strong coupling between both is hard to achieve due to this apparent incompatibility. This paper shows how to achieve this coupling in three steps. First, a new a priori error estimate is proved in a formal framework adapted to goal-oriented mesh adaptation for output functionals. This estimate is based on a careful analysis of the contributions of the implicit error and of the interpolation error. Second, the error estimate is applied to the set of steady compressible Euler equations which are solved by a stabilized Galerkin finite element discretization. A goal-oriented error estimation is derived. It involves the interpolation error of the Euler fluxes weighted by the gradient of the adjoint state associated with the observed functional. Third, rewritten in the continuous mesh framework, the previous estimate is minimized on the set of continuous meshes thanks to a calculus of variations. The optimal continuous mesh is then derived analytically. Thus, it can be used as a metric tensor field to drive the mesh adaptation. From a numerical point of view, this method is completely automatic, intrinsically anisotropic, and does not depend on any a priori choice of variables to perform the adaptation. 3D examples of steady flows around supersonic and transsonic jets are presented to validate the current approach and to demonstrate its efficiency.

LayTracks3D: A new approach for meshing general solids using medial axis transform

DOE PAGES

Quadros, William Roshan

2015-08-22

This study presents an extension of the all-quad meshing algorithm called LayTracks to generate high quality hex-dominant meshes of general solids. LayTracks3D uses the mapping between the Medial Axis (MA) and the boundary of the 3D domain to decompose complex 3D domains into simpler domains called Tracks. Tracks in 3D have no branches and are symmetric, non-intersecting, orthogonal to the boundary, and the shortest path from the MA to the boundary. These properties of tracks result in desired meshes with near cube shape elements at the boundary, structured mesh along the boundary normal with any irregular nodes restricted to themore » MA, and sharp boundary feature preservation. The algorithm has been tested on a few industrial CAD models and hex-dominant meshes are shown in the Results section. Work is underway to extend LayTracks3D to generate all-hex meshes.« less

Exploring Discretization Error in Simulation-Based Aerodynamic Databases

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J.; Nemec, Marian

2010-01-01

This work examines the level of discretization error in simulation-based aerodynamic databases and introduces strategies for error control. Simulations are performed using a parallel, multi-level Euler solver on embedded-boundary Cartesian meshes. Discretization errors in user-selected outputs are estimated using the method of adjoint-weighted residuals and we use adaptive mesh refinement to reduce these errors to specified tolerances. Using this framework, we examine the behavior of discretization error throughout a token database computed for a NACA 0012 airfoil consisting of 120 cases. We compare the cost and accuracy of two approaches for aerodynamic database generation. In the first approach, mesh adaptation is used to compute all cases in the database to a prescribed level of accuracy. The second approach conducts all simulations using the same computational mesh without adaptation. We quantitatively assess the error landscape and computational costs in both databases. This investigation highlights sensitivities of the database under a variety of conditions. The presence of transonic shocks or the stiffness in the governing equations near the incompressible limit are shown to dramatically increase discretization error requiring additional mesh resolution to control. Results show that such pathologies lead to error levels that vary by over factor of 40 when using a fixed mesh throughout the database. Alternatively, controlling this sensitivity through mesh adaptation leads to mesh sizes which span two orders of magnitude. We propose strategies to minimize simulation cost in sensitive regions and discuss the role of error-estimation in database quality.

Reaction rates for a generalized reaction-diffusion master equation

DOE PAGES

Hellander, Stefan; Petzold, Linda

2016-01-19

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show inmore » two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules.« less

Reaction rates for a generalized reaction-diffusion master equation

PubMed Central

Hellander, Stefan; Petzold, Linda

2016-01-01

It has been established that there is an inherent limit to the accuracy of the reaction-diffusion master equation. Specifically, there exists a fundamental lower bound on the mesh size, below which the accuracy deteriorates as the mesh is refined further. In this paper we extend the standard reaction-diffusion master equation to allow molecules occupying neighboring voxels to react, in contrast to the traditional approach in which molecules react only when occupying the same voxel. We derive reaction rates, in two dimensions as well as three dimensions, to obtain an optimal match to the more fine-grained Smoluchowski model, and show in two numerical examples that the extended algorithm is accurate for a wide range of mesh sizes, allowing us to simulate systems that are intractable with the standard reaction-diffusion master equation. In addition, we show that for mesh sizes above the fundamental lower limit of the standard algorithm, the generalized algorithm reduces to the standard algorithm. We derive a lower limit for the generalized algorithm which, in both two dimensions and three dimensions, is on the order of the reaction radius of a reacting pair of molecules. PMID:26871190

Tartarus: A relativistic Green's function quantum average atom code

DOE PAGES

Gill, Nathanael Matthew; Starrett, Charles Edward

2017-06-28

A relativistic Green’s Function quantum average atom model is implemented in the Tartarus code for the calculation of equation of state data in dense plasmas. We first present the relativistic extension of the quantum Green’s Function average atom model described by Starrett [1]. The Green’s Function approach addresses the numerical challenges arising from resonances in the continuum density of states without the need for resonance tracking algorithms or adaptive meshes, though there are still numerical challenges inherent to this algorithm. We discuss how these challenges are addressed in the Tartarus algorithm. The outputs of the calculation are shown in comparisonmore » to PIMC/DFT-MD simulations of the Principal Shock Hugoniot in Silicon. Finally, we also present the calculation of the Hugoniot for Silver coming from both the relativistic and nonrelativistic modes of the Tartarus code.« less

Tartarus: A relativistic Green's function quantum average atom code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gill, Nathanael Matthew; Starrett, Charles Edward

A relativistic Green’s Function quantum average atom model is implemented in the Tartarus code for the calculation of equation of state data in dense plasmas. We first present the relativistic extension of the quantum Green’s Function average atom model described by Starrett [1]. The Green’s Function approach addresses the numerical challenges arising from resonances in the continuum density of states without the need for resonance tracking algorithms or adaptive meshes, though there are still numerical challenges inherent to this algorithm. We discuss how these challenges are addressed in the Tartarus algorithm. The outputs of the calculation are shown in comparisonmore » to PIMC/DFT-MD simulations of the Principal Shock Hugoniot in Silicon. Finally, we also present the calculation of the Hugoniot for Silver coming from both the relativistic and nonrelativistic modes of the Tartarus code.« less

Adapting to life: ocean biogeochemical modelling and adaptive remeshing

NASA Astrophysics Data System (ADS)

Hill, J.; Popova, E. E.; Ham, D. A.; Piggott, M. D.; Srokosz, M.

2013-11-01

An outstanding problem in biogeochemical modelling of the ocean is that many of the key processes occur intermittently at small scales, such as the sub-mesoscale, that are not well represented in global ocean models. As an example, state-of-the-art models give values of primary production approximately two orders of magnitude lower than those observed in the ocean's oligotrophic gyres, which cover a third of the Earth's surface. This is partly due to their failure to resolve sub-mesoscale phenomena, which play a significant role in nutrient supply. Simply increasing the resolution of the models may be an inefficient computational solution to this problem. An approach based on recent advances in adaptive mesh computational techniques may offer an alternative. Here the first steps in such an approach are described, using the example of a~simple vertical column (quasi 1-D) ocean biogeochemical model. We present a novel method of simulating ocean biogeochemical behaviour on a vertically adaptive computational mesh, where the mesh changes in response to the biogeochemical and physical state of the system throughout the simulation. We show that the model reproduces the general physical and biological behaviour at three ocean stations (India, Papa and Bermuda) as compared to a high-resolution fixed mesh simulation and to observations. The simulations capture both the seasonal and inter-annual variations. The use of an adaptive mesh does not increase the computational error, but reduces the number of mesh elements by a factor of 2-3, so reducing computational overhead. We then show the potential of this method in two case studies where we change the metric used to determine the varying mesh sizes in order to capture the dynamics of chlorophyll at Bermuda and sinking detritus at Papa. We therefore demonstrate adaptive meshes may provide a~suitable numerical technique for simulating seasonal or transient biogeochemical behaviour at high spatial resolution whilst minimising computational cost.

Assigning categorical information to Japanese medical terms using MeSH and MEDLINE.

PubMed

Onogi, Yuzo

2007-01-01

This paper reports on the assigning of MeSH (Medical Subject Headings) categories to Japanese terms in an English-Japanese dictionary using the titles and abstracts of articles indexed in MEDLINE. In a previous study, 30,000 of 80,000 terms in the dictionary were mapped to MeSH terms by normalized comparison. It was reasoned that if the remaining dictionary terms appeared in MEDLINE-indexed articles that are indexed using MeSH terms, then relevancies between the dictionary terms and MeSH terms could be calculated, and thus MeSH categories assigned. This study compares two approaches for calculating the weight matrix. One is the TF*IDF method and the other uses the inner product of two weight matrices. About 20,000 additional dictionary terms were identified in MEDLINE-indexed articles published between 2000 and 2004. The precision and recall of these algorithms were evaluated separately for MeSH terms and non-MeSH terms. Unfortunately, the precision and recall of the algorithms was not good, but this method will help with manual assignment of MeSH categories to dictionary terms.

Performance evaluation of GPU parallelization, space-time adaptive algorithms, and their combination for simulating cardiac electrophysiology.

PubMed

Sachetto Oliveira, Rafael; Martins Rocha, Bernardo; Burgarelli, Denise; Meira, Wagner; Constantinides, Christakis; Weber Dos Santos, Rodrigo

2018-02-01

The use of computer models as a tool for the study and understanding of the complex phenomena of cardiac electrophysiology has attained increased importance nowadays. At the same time, the increased complexity of the biophysical processes translates into complex computational and mathematical models. To speed up cardiac simulations and to allow more precise and realistic uses, 2 different techniques have been traditionally exploited: parallel computing and sophisticated numerical methods. In this work, we combine a modern parallel computing technique based on multicore and graphics processing units (GPUs) and a sophisticated numerical method based on a new space-time adaptive algorithm. We evaluate each technique alone and in different combinations: multicore and GPU, multicore and GPU and space adaptivity, multicore and GPU and space adaptivity and time adaptivity. All the techniques and combinations were evaluated under different scenarios: 3D simulations on slabs, 3D simulations on a ventricular mouse mesh, ie, complex geometry, sinus-rhythm, and arrhythmic conditions. Our results suggest that multicore and GPU accelerate the simulations by an approximate factor of 33×, whereas the speedups attained by the space-time adaptive algorithms were approximately 48. Nevertheless, by combining all the techniques, we obtained speedups that ranged between 165 and 498. The tested methods were able to reduce the execution time of a simulation by more than 498× for a complex cellular model in a slab geometry and by 165× in a realistic heart geometry simulating spiral waves. The proposed methods will allow faster and more realistic simulations in a feasible time with no significant loss of accuracy. Copyright © 2017 John Wiley & Sons, Ltd.

Adaptive CFD schemes for aerospace propulsion

NASA Astrophysics Data System (ADS)

Ferrero, A.; Larocca, F.

2017-05-01

The flow fields which can be observed inside several components of aerospace propulsion systems are characterised by the presence of very localised phenomena (boundary layers, shock waves,...) which can deeply influence the performances of the system. In order to accurately evaluate these effects by means of Computational Fluid Dynamics (CFD) simulations, it is necessary to locally refine the computational mesh. In this way the degrees of freedom related to the discretisation are focused in the most interesting regions and the computational cost of the simulation remains acceptable. In the present work, a discontinuous Galerkin (DG) discretisation is used to numerically solve the equations which describe the flow field. The local nature of the DG reconstruction makes it possible to efficiently exploit several adaptive schemes in which the size of the elements (h-adaptivity) and the order of reconstruction (p-adaptivity) are locally changed. After a review of the main adaptation criteria, some examples related to compressible flows in turbomachinery are presented. An hybrid hp-adaptive algorithm is also proposed and compared with a standard h-adaptive scheme in terms of computational efficiency.

A weakly-compressible Cartesian grid approach for hydrodynamic flows

NASA Astrophysics Data System (ADS)

Bigay, P.; Oger, G.; Guilcher, P.-M.; Le Touzé, D.

2017-11-01

The present article aims at proposing an original strategy to solve hydrodynamic flows. In introduction, the motivations for this strategy are developed. It aims at modeling viscous and turbulent flows including complex moving geometries, while avoiding meshing constraints. The proposed approach relies on a weakly-compressible formulation of the Navier-Stokes equations. Unlike most hydrodynamic CFD (Computational Fluid Dynamics) solvers usually based on implicit incompressible formulations, a fully-explicit temporal scheme is used. A purely Cartesian grid is adopted for numerical accuracy and algorithmic simplicity purposes. This characteristic allows an easy use of Adaptive Mesh Refinement (AMR) methods embedded within a massively parallel framework. Geometries are automatically immersed within the Cartesian grid with an AMR compatible treatment. The method proposed uses an Immersed Boundary Method (IBM) adapted to the weakly-compressible formalism and imposed smoothly through a regularization function, which stands as another originality of this work. All these features have been implemented within an in-house solver based on this WCCH (Weakly-Compressible Cartesian Hydrodynamic) method which meets the above requirements whilst allowing the use of high-order (> 3) spatial schemes rarely used in existing hydrodynamic solvers. The details of this WCCH method are presented and validated in this article.

Taylor bubbles at high viscosity ratios: experiments and numerical simulations

NASA Astrophysics Data System (ADS)

Hewakandamby, Buddhika; Hasan, Abbas; Azzopardi, Barry; Xie, Zhihua; Pain, Chris; Matar, Omar

2015-11-01

The Taylor bubble is a single long bubble which nearly fills the entire cross section of a liquid-filled circular tube, often occurring in gas-liquid slug flows in many industrial applications, particularly oil and gas production. The objective of this study is to investigate the fluid dynamics of three-dimensional Taylor bubble rising in highly viscous silicone oil in a vertical pipe. An adaptive unstructured mesh modelling framework is adopted here which can modify and adapt anisotropic unstructured meshes to better represent the underlying physics of bubble rising and reduce computational effort without sacrificing accuracy. The numerical framework consists of a mixed control volume and finite element formulation, a `volume of fluid'-type method for the interface-capturing based on a compressive control volume advection method, and a force-balanced algorithm for the surface tension implementation. Experimental results for the Taylor bubble shape and rise velocity are presented, together with numerical results for the dynamics of the bubbles. A comparison of the simulation predictions with experimental data available in the literature is also presented to demonstrate the capabilities of our numerical method. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.

An adaptive extended finite element method for the analysis of agglomeration of colloidal particles in a flowing fluid

DOE Office of Scientific and Technical Information (OSTI.GOV)

Choi, Young Joon; Jorshari, Razzi Movassaghi; Djilali, Ned

2015-03-10

Direct numerical simulations of the flow-nanoparticle interaction in a colloidal suspension are presented using an extended finite element method (XFEM) in which the dynamics of the nanoparticles is solved in a fully-coupled manner with the flow. The method is capable of accurately describing solid-fluid interfaces without the need of boundary-fitted meshes to investigate the dynamics of particles in complex flows. In order to accurately compute the high interparticle shear stresses and pressures while minimizing computing costs, an adaptive meshing technique is incorporated with the fluid-structure interaction algorithm. The particle-particle interaction at the microscopic level is modeled using the Lennard-Jones (LJ)more » potential and the corresponding potential parameters are determined by a scaling procedure. The study is relevant to the preparation of inks used in the fabrication of catalyst layers for fuel cells. In this paper, we are particularly interested in investigating agglomeration of the nanoparticles under external shear flow in a sliding bi-periodic Lees-Edwards frame. The results indicate that the external shear has a crucial impact on the structure formation of colloidal particles in a suspension.« less

Tangle-Free Finite Element Mesh Motion for Ablation Problems

NASA Technical Reports Server (NTRS)

Droba, Justin

2016-01-01

In numerical simulations involving boundaries that evolve in time, the primary challenge is updating the computational mesh to reflect the physical changes in the domain. In particular, the fundamental objective for any such \\mesh motion" scheme is to maintain mesh quality and suppress unphysical geometric anamolies and artifacts. External to a physical process of interest, mesh motion is an added component that determines the specifics of how to move the mesh given certain limited information from the main system. This paper develops a set of boundary conditions designed to eliminate tangling and internal collision within the context of PDE-based mesh motion (linear elasticity). These boundary conditions are developed for two- and three-dimensional meshes. The paper presents detailed algorithms for commonly occuring topological scenarios and explains how to apply them appropriately. Notably, the techniques discussed herein make use of none of the specifics of any particular formulation of mesh motion and thus are more broadly applicable. The two-dimensional algorithms are validated by an extensive verification procedure. Finally, many examples of diverse geometries in both two- and three-dimensions are shown to showcase the capabilities of the tangle-free boundary conditions.

First benchmark of the Unstructured Grid Adaptation Working Group

NASA Technical Reports Server (NTRS)

Ibanez, Daniel; Barral, Nicolas; Krakos, Joshua; Loseille, Adrien; Michal, Todd; Park, Mike

2017-01-01

Unstructured grid adaptation is a technology that holds the potential to improve the automation and accuracy of computational fluid dynamics and other computational disciplines. Difficulty producing the highly anisotropic elements necessary for simulation on complex curved geometries that satisfies a resolution request has limited this technology's widespread adoption. The Unstructured Grid Adaptation Working Group is an open gathering of researchers working on adapting simplicial meshes to conform to a metric field. Current members span a wide range of institutions including academia, industry, and national laboratories. The purpose of this group is to create a common basis for understanding and improving mesh adaptation. We present our first major contribution: a common set of benchmark cases, including input meshes and analytic metric specifications, that are publicly available to be used for evaluating any mesh adaptation code. We also present the results of several existing codes on these benchmark cases, to illustrate their utility in identifying key challenges common to all codes and important differences between available codes. Future directions are defined to expand this benchmark to mature the technology necessary to impact practical simulation workflows.

A priori mesh grading for the numerical calculation of the head-related transfer functions

PubMed Central

Ziegelwanger, Harald; Kreuzer, Wolfgang; Majdak, Piotr

2017-01-01

Head-related transfer functions (HRTFs) describe the directional filtering of the incoming sound caused by the morphology of a listener’s head and pinnae. When an accurate model of a listener’s morphology exists, HRTFs can be calculated numerically with the boundary element method (BEM). However, the general recommendation to model the head and pinnae with at least six elements per wavelength renders the BEM as a time-consuming procedure when calculating HRTFs for the full audible frequency range. In this study, a mesh preprocessing algorithm is proposed, viz., a priori mesh grading, which reduces the computational costs in the HRTF calculation process significantly. The mesh grading algorithm deliberately violates the recommendation of at least six elements per wavelength in certain regions of the head and pinnae and varies the size of elements gradually according to an a priori defined grading function. The evaluation of the algorithm involved HRTFs calculated for various geometric objects including meshes of three human listeners and various grading functions. The numerical accuracy and the predicted sound-localization performance of calculated HRTFs were analyzed. A-priori mesh grading appeared to be suitable for the numerical calculation of HRTFs in the full audible frequency range and outperformed uniform meshes in terms of numerical errors, perception based predictions of sound-localization performance, and computational costs. PMID:28239186

A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates

NASA Astrophysics Data System (ADS)

Huang, Weizhang; Kamenski, Lennard; Lang, Jens

2010-03-01

A new anisotropic mesh adaptation strategy for finite element solution of elliptic differential equations is presented. It generates anisotropic adaptive meshes as quasi-uniform ones in some metric space, with the metric tensor being computed based on hierarchical a posteriori error estimates. A global hierarchical error estimate is employed in this study to obtain reliable directional information of the solution. Instead of solving the global error problem exactly, which is costly in general, we solve it iteratively using the symmetric Gauß-Seidel method. Numerical results show that a few GS iterations are sufficient for obtaining a reasonably good approximation to the error for use in anisotropic mesh adaptation. The new method is compared with several strategies using local error estimators or recovered Hessians. Numerical results are presented for a selection of test examples and a mathematical model for heat conduction in a thermal battery with large orthotropic jumps in the material coefficients.

Spatially adaptive bases in wavelet-based coding of semi-regular meshes

NASA Astrophysics Data System (ADS)

Denis, Leon; Florea, Ruxandra; Munteanu, Adrian; Schelkens, Peter

2010-05-01

In this paper we present a wavelet-based coding approach for semi-regular meshes, which spatially adapts the employed wavelet basis in the wavelet transformation of the mesh. The spatially-adaptive nature of the transform requires additional information to be stored in the bit-stream in order to allow the reconstruction of the transformed mesh at the decoder side. In order to limit this overhead, the mesh is first segmented into regions of approximately equal size. For each spatial region, a predictor is selected in a rate-distortion optimal manner by using a Lagrangian rate-distortion optimization technique. When compared against the classical wavelet transform employing the butterfly subdivision filter, experiments reveal that the proposed spatially-adaptive wavelet transform significantly decreases the energy of the wavelet coefficients for all subbands. Preliminary results show also that employing the proposed transform for the lowest-resolution subband systematically yields improved compression performance at low-to-medium bit-rates. For the Venus and Rabbit test models the compression improvements add up to 1.47 dB and 0.95 dB, respectively.

CRASH: A BLOCK-ADAPTIVE-MESH CODE FOR RADIATIVE SHOCK HYDRODYNAMICS-IMPLEMENTATION AND VERIFICATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van der Holst, B.; Toth, G.; Sokolov, I. V.

We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1)more » an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.« less

Gas flow calculation method of a ramjet engine

NASA Astrophysics Data System (ADS)

Kostyushin, Kirill; Kagenov, Anuar; Eremin, Ivan; Zhiltsov, Konstantin; Shuvarikov, Vladimir

2017-11-01

At the present study calculation methodology of gas dynamics equations in ramjet engine is presented. The algorithm is based on Godunov`s scheme. For realization of calculation algorithm, the system of data storage is offered, the system does not depend on mesh topology, and it allows using the computational meshes with arbitrary number of cell faces. The algorithm of building a block-structured grid is given. Calculation algorithm in the software package "FlashFlow" is implemented. Software package is verified on the calculations of simple configurations of air intakes and scramjet models.

Adaptive moving mesh methods for simulating one-dimensional groundwater problems with sharp moving fronts

USGS Publications Warehouse

Huang, W.; Zheng, Lingyun; Zhan, X.

2002-01-01

Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright ?? 2002 John Wiley and Sons, Ltd.

Adaptive unstructured triangular mesh generation and flow solvers for the Navier-Stokes equations at high Reynolds number

NASA Technical Reports Server (NTRS)

Ashford, Gregory A.; Powell, Kenneth G.

1995-01-01

A method for generating high quality unstructured triangular grids for high Reynolds number Navier-Stokes calculations about complex geometries is described. Careful attention is paid in the mesh generation process to resolving efficiently the disparate length scales which arise in these flows. First the surface mesh is constructed in a way which ensures that the geometry is faithfully represented. The volume mesh generation then proceeds in two phases thus allowing the viscous and inviscid regions of the flow to be meshed optimally. A solution-adaptive remeshing procedure which allows the mesh to adapt itself to flow features is also described. The procedure for tracking wakes and refinement criteria appropriate for shock detection are described. Although at present it has only been implemented in two dimensions, the grid generation process has been designed with the extension to three dimensions in mind. An implicit, higher-order, upwind method is also presented for computing compressible turbulent flows on these meshes. Two recently developed one-equation turbulence models have been implemented to simulate the effects of the fluid turbulence. Results for flow about a RAE 2822 airfoil and a Douglas three-element airfoil are presented which clearly show the improved resolution obtainable.

A Parallel Implementation of Multilevel Recursive Spectral Bisection for Application to Adaptive Unstructured Meshes. Chapter 1

NASA Technical Reports Server (NTRS)

Barnard, Stephen T.; Simon, Horst; Lasinski, T. A. (Technical Monitor)

1994-01-01

The design of a parallel implementation of multilevel recursive spectral bisection is described. The goal is to implement a code that is fast enough to enable dynamic repartitioning of adaptive meshes.

High Performance Fortran for Aerospace Applications

NASA Technical Reports Server (NTRS)

Mehrotra, Piyush; Zima, Hans; Bushnell, Dennis M. (Technical Monitor)

2000-01-01

This paper focuses on the use of High Performance Fortran (HPF) for important classes of algorithms employed in aerospace applications. HPF is a set of Fortran extensions designed to provide users with a high-level interface for programming data parallel scientific applications, while delegating to the compiler/runtime system the task of generating explicitly parallel message-passing programs. We begin by providing a short overview of the HPF language. This is followed by a detailed discussion of the efficient use of HPF for applications involving multiple structured grids such as multiblock and adaptive mesh refinement (AMR) codes as well as unstructured grid codes. We focus on the data structures and computational structures used in these codes and on the high-level strategies that can be expressed in HPF to optimally exploit the parallelism in these algorithms.

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Legat, Vincent; Vallaeys, Valentin; Naithani, Jaya; Thiery, Wim; Remacle, Jean-François; Deleersnijder, Eric

2018-03-01

The discontinuous Galerkin (DG) finite element method is well suited for the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces. The mesh vertical movement is determined by means of a conservative arbitrary Lagrangian-Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level. The vertically adaptive mesh approach is implemented in the three-dimensional version of the geophysical and environmental flow Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM 3D; www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA

NASA Technical Reports Server (NTRS)

Djomehri, M. Jahed; Erickson, Larry L.

1994-01-01

A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.

Cosmology on a Mesh

NASA Astrophysics Data System (ADS)

Gill, Stuart P. D.; Knebe, Alexander; Gibson, Brad K.; Flynn, Chris; Ibata, Rodrigo A.; Lewis, Geraint F.

2003-04-01

An adaptive multi grid approach to simulating the formation of structure from collisionless dark matter is described. MLAPM (Multi-Level Adaptive Particle Mesh) is one of the most efficient serial codes available on the cosmological "market" today. As part of Swinburne University's role in the development of the Square Kilometer Array, we are implementing hydrodynamics, feedback, and radiative transfer within the MLAPM adaptive mesh, in order to simulate baryonic processes relevant to the interstellar and intergalactic media at high redshift. We will outline our progress to date in applying the existing MLAPM to a study of the decay of satellite galaxies within massive host potentials.

A universal algorithm for an improved finite element mesh generation Mesh quality assessment in comparison to former automated mesh-generators and an analytic model.

PubMed

Kaminsky, Jan; Rodt, Thomas; Gharabaghi, Alireza; Forster, Jan; Brand, Gerd; Samii, Madjid

2005-06-01

The FE-modeling of complex anatomical structures is not solved satisfyingly so far. Voxel-based as opposed to contour-based algorithms allow an automated mesh generation based on the image data. Nonetheless their geometric precision is limited. We developed an automated mesh-generator that combines the advantages of voxel-based generation with improved representation of the geometry by displacement of nodes on the object-surface. Models of an artificial 3D-pipe-section and a skullbase were generated with different mesh-densities using the newly developed geometric, unsmoothed and smoothed voxel generators. Compared to the analytic calculation of the 3D-pipe-section model the normalized RMS error of the surface stress was 0.173-0.647 for the unsmoothed voxel models, 0.111-0.616 for the smoothed voxel models with small volume error and 0.126-0.273 for the geometric models. The highest element-energy error as a criterion for the mesh quality was 2.61x10(-2) N mm, 2.46x10(-2) N mm and 1.81x10(-2) N mm for unsmoothed, smoothed and geometric voxel models, respectively. The geometric model of the 3D-skullbase resulted in the lowest element-energy error and volume error. This algorithm also allowed the best representation of anatomical details. The presented geometric mesh-generator is universally applicable and allows an automated and accurate modeling by combining the advantages of the voxel-technique and of improved surface-modeling.

Massive parallel 3D PIC simulation of negative ion extraction

NASA Astrophysics Data System (ADS)

Revel, Adrien; Mochalskyy, Serhiy; Montellano, Ivar Mauricio; Wünderlich, Dirk; Fantz, Ursel; Minea, Tiberiu

2017-09-01

The 3D PIC-MCC code ONIX is dedicated to modeling Negative hydrogen/deuterium Ion (NI) extraction and co-extraction of electrons from radio-frequency driven, low pressure plasma sources. It provides valuable insight on the complex phenomena involved in the extraction process. In previous calculations, a mesh size larger than the Debye length was used, implying numerical electron heating. Important steps have been achieved in terms of computation performance and parallelization efficiency allowing successful massive parallel calculations (4096 cores), imperative to resolve the Debye length. In addition, the numerical algorithms have been improved in terms of grid treatment, i.e., the electric field near the complex geometry boundaries (plasma grid) is calculated more accurately. The revised model preserves the full 3D treatment, but can take advantage of a highly refined mesh. ONIX was used to investigate the role of the mesh size, the re-injection scheme for lost particles (extracted or wall absorbed), and the electron thermalization process on the calculated extracted current and plasma characteristics. It is demonstrated that all numerical schemes give the same NI current distribution for extracted ions. Concerning the electrons, the pair-injection technique is found well-adapted to simulate the sheath in front of the plasma grid.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann

1993-01-01

A general solution adaptive scheme-based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

Development of an unstructured solution adaptive method for the quasi-three-dimensional Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Jiang, Yi-Tsann; Usab, William J., Jr.

1993-01-01

A general solution adaptive scheme based on a remeshing technique is developed for solving the two-dimensional and quasi-three-dimensional Euler and Favre-averaged Navier-Stokes equations. The numerical scheme is formulated on an unstructured triangular mesh utilizing an edge-based pointer system which defines the edge connectivity of the mesh structure. Jameson's four-stage hybrid Runge-Kutta scheme is used to march the solution in time. The convergence rate is enhanced through the use of local time stepping and implicit residual averaging. As the solution evolves, the mesh is regenerated adaptively using flow field information. Mesh adaptation parameters are evaluated such that an estimated local numerical error is equally distributed over the whole domain. For inviscid flows, the present approach generates a complete unstructured triangular mesh using the advancing front method. For turbulent flows, the approach combines a local highly stretched structured triangular mesh in the boundary layer region with an unstructured mesh in the remaining regions to efficiently resolve the important flow features. One-equation and two-equation turbulence models are incorporated into the present unstructured approach. Results are presented for a wide range of flow problems including two-dimensional multi-element airfoils, two-dimensional cascades, and quasi-three-dimensional cascades. This approach is shown to gain flow resolution in the refined regions while achieving a great reduction in the computational effort and storage requirements since solution points are not wasted in regions where they are not required.

NeuroTessMesh: A Tool for the Generation and Visualization of Neuron Meshes and Adaptive On-the-Fly Refinement.

PubMed

Garcia-Cantero, Juan J; Brito, Juan P; Mata, Susana; Bayona, Sofia; Pastor, Luis

2017-01-01

Gaining a better understanding of the human brain continues to be one of the greatest challenges for science, largely because of the overwhelming complexity of the brain and the difficulty of analyzing the features and behavior of dense neural networks. Regarding analysis, 3D visualization has proven to be a useful tool for the evaluation of complex systems. However, the large number of neurons in non-trivial circuits, together with their intricate geometry, makes the visualization of a neuronal scenario an extremely challenging computational problem. Previous work in this area dealt with the generation of 3D polygonal meshes that approximated the cells' overall anatomy but did not attempt to deal with the extremely high storage and computational cost required to manage a complex scene. This paper presents NeuroTessMesh, a tool specifically designed to cope with many of the problems associated with the visualization of neural circuits that are comprised of large numbers of cells. In addition, this method facilitates the recovery and visualization of the 3D geometry of cells included in databases, such as NeuroMorpho, and provides the tools needed to approximate missing information such as the soma's morphology. This method takes as its only input the available compact, yet incomplete, morphological tracings of the cells as acquired by neuroscientists. It uses a multiresolution approach that combines an initial, coarse mesh generation with subsequent on-the-fly adaptive mesh refinement stages using tessellation shaders. For the coarse mesh generation, a novel approach, based on the Finite Element Method, allows approximation of the 3D shape of the soma from its incomplete description. Subsequently, the adaptive refinement process performed in the graphic card generates meshes that provide good visual quality geometries at a reasonable computational cost, both in terms of memory and rendering time. All the described techniques have been integrated into NeuroTessMesh, available to the scientific community, to generate, visualize, and save the adaptive resolution meshes.

On Reducing Delay in Mesh-Based P2P Streaming: A Mesh-Push Approach

NASA Astrophysics Data System (ADS)

Liu, Zheng; Xue, Kaiping; Hong, Peilin

The peer-assisted streaming paradigm has been widely employed to distribute live video data on the internet recently. In general, the mesh-based pull approach is more robust and efficient than the tree-based push approach. However, pull protocol brings about longer streaming delay, which is caused by the handshaking process of advertising buffer map message, sending request message and scheduling of the data block. In this paper, we propose a new approach, mesh-push, to address this issue. Different from the traditional pull approach, mesh-push implements block scheduling algorithm at sender side, where the block transmission is initiated by the sender rather than by the receiver. We first formulate the optimal upload bandwidth utilization problem, then present the mesh-push approach, in which a token protocol is designed to avoid block redundancy; a min-cost flow model is employed to derive the optimal scheduling for the push peer; and a push peer selection algorithm is introduced to reduce control overhead. Finally, we evaluate mesh-push through simulation, the results of which show mesh-push outperforms the pull scheduling in streaming delay, and achieves comparable delivery ratio at the same time.

Accelerating Large Data Analysis By Exploiting Regularities

NASA Technical Reports Server (NTRS)

Moran, Patrick J.; Ellsworth, David

2003-01-01

We present techniques for discovering and exploiting regularity in large curvilinear data sets. The data can be based on a single mesh or a mesh composed of multiple submeshes (also known as zones). Multi-zone data are typical to Computational Fluid Dynamics (CFD) simulations. Regularities include axis-aligned rectilinear and cylindrical meshes as well as cases where one zone is equivalent to a rigid-body transformation of another. Our algorithms can also discover rigid-body motion of meshes in time-series data. Next, we describe a data model where we can utilize the results from the discovery process in order to accelerate large data visualizations. Where possible, we replace general curvilinear zones with rectilinear or cylindrical zones. In rigid-body motion cases we replace a time-series of meshes with a transformed mesh object where a reference mesh is dynamically transformed based on a given time value in order to satisfy geometry requests, on demand. The data model enables us to make these substitutions and dynamic transformations transparently with respect to the visualization algorithms. We present results with large data sets where we combine our mesh replacement and transformation techniques with out-of-core paging in order to achieve significant speed-ups in analysis.

Valiant load-balanced robust routing under hose model for WDM mesh networks

NASA Astrophysics Data System (ADS)

Zhang, Xiaoning; Li, Lemin; Wang, Sheng

2006-09-01

In this paper, we propose Valiant Load-Balanced robust routing scheme for WDM mesh networks under the model of polyhedral uncertainty (i.e., hose model), and the proposed routing scheme is implemented with traffic grooming approach. Our Objective is to maximize the hose model throughput. A mathematic formulation of Valiant Load-Balanced robust routing is presented and three fast heuristic algorithms are also proposed. When implementing Valiant Load-Balanced robust routing scheme to WDM mesh networks, a novel traffic-grooming algorithm called MHF (minimizing hop first) is proposed. We compare the three heuristic algorithms with the VPN tree under the hose model. Finally we demonstrate in the simulation results that MHF with Valiant Load-Balanced robust routing scheme outperforms the traditional traffic-grooming algorithm in terms of the throughput for the uniform/non-uniform traffic matrix under the hose model.

2D automatic body-fitted structured mesh generation using advancing extraction method

NASA Astrophysics Data System (ADS)

Zhang, Yaoxin; Jia, Yafei

2018-01-01

This paper presents an automatic mesh generation algorithm for body-fitted structured meshes in Computational Fluids Dynamics (CFD) analysis using the Advancing Extraction Method (AEM). The method is applicable to two-dimensional domains with complex geometries, which have the hierarchical tree-like topography with extrusion-like structures (i.e., branches or tributaries) and intrusion-like structures (i.e., peninsula or dikes). With the AEM, the hierarchical levels of sub-domains can be identified, and the block boundary of each sub-domain in convex polygon shape in each level can be extracted in an advancing scheme. In this paper, several examples were used to illustrate the effectiveness and applicability of the proposed algorithm for automatic structured mesh generation, and the implementation of the method.

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J.; Berger, Marsha J.; Murman, Scott M.

2003-01-01

The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.

Compatible, total energy conserving and symmetry preserving arbitrary Lagrangian-Eulerian hydrodynamics in 2D rz - Cylindrical coordinates

NASA Astrophysics Data System (ADS)

Kenamond, Mack; Bement, Matthew; Shashkov, Mikhail

2014-07-01

We present a new discretization for 2D arbitrary Lagrangian-Eulerian hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, total energy conserving and symmetry preserving. In the first part of the paper, we describe the discretization of the basic Lagrangian hydrodynamics equations in axisymmetric 2D rz geometry on general polygonal meshes. It exactly preserves planar, cylindrical and spherical symmetry of the flow on meshes aligned with the flow. In particular, spherical symmetry is preserved on polar equiangular meshes. The discretization conserves total energy exactly up to machine round-off on any mesh. It has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude. The method for discretization of the Lagrangian equations is based on ideas presented in [2,3,7], where the authors use a special procedure to distribute zonal mass to corners of the zone (subzonal masses). The momentum equation is discretized in its “Cartesian” form with a special definition of “planar” masses (area-weighted). The principal contributions of this part of the paper are as follows: a definition of “planar” subzonal mass for nodes on the z axis (r=0) that does not require a special procedure for movement of these nodes; proof of conservation of the total energy; formulated for general polygonal meshes. We present numerical examples that demonstrate the robustness of the new method for Lagrangian equations on a variety of grids and test problems including polygonal meshes. In particular, we demonstrate the importance of conservation of total energy for correctly modeling shock waves. In the second part of the paper we describe the remapping stage of the arbitrary Lagrangian-Eulerian algorithm. The general idea is based on the following papers [25-28], where it was described for Cartesian coordinates. We describe a distribution-based algorithm for the definition of remapped subzonal densities and a local constrained-optimization-based approach for each zone to find the subzonal mass fluxes. In this paper we give a systematic and complete description of the algorithm for the axisymmetric case and provide justification for our approach. The ALE algorithm conserves total energy on arbitrary meshes and preserves symmetry when remapping from one equiangular polar mesh to another. The principal contributions of this part of the paper are the extension of this algorithm to general polygonal meshes and 2D rz geometry with requirement of symmetry preservation on special meshes. We present numerical examples that demonstrate the robustness of the new ALE method on a variety of grids and test problems including polygonal meshes and some realistic experiments. We confirm the importance of conservation of total energy for correctly modeling shock waves.

A hybrid multiview stereo algorithm for modeling urban scenes.

PubMed

Lafarge, Florent; Keriven, Renaud; Brédif, Mathieu; Vu, Hoang-Hiep

2013-01-01

We present an original multiview stereo reconstruction algorithm which allows the 3D-modeling of urban scenes as a combination of meshes and geometric primitives. The method provides a compact model while preserving details: Irregular elements such as statues and ornaments are described by meshes, whereas regular structures such as columns and walls are described by primitives (planes, spheres, cylinders, cones, and tori). We adopt a two-step strategy consisting first in segmenting the initial meshbased surface using a multilabel Markov Random Field-based model and second in sampling primitive and mesh components simultaneously on the obtained partition by a Jump-Diffusion process. The quality of a reconstruction is measured by a multi-object energy model which takes into account both photo-consistency and semantic considerations (i.e., geometry and shape layout). The segmentation and sampling steps are embedded into an iterative refinement procedure which provides an increasingly accurate hybrid representation. Experimental results on complex urban structures and large scenes are presented and compared to state-of-the-art multiview stereo meshing algorithms.

M-Adapting Low Order Mimetic Finite Differences for Dielectric Interface Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

McGregor, Duncan A.; Gyrya, Vitaliy; Manzini, Gianmarco

2016-03-07

We consider a problem of reducing numerical dispersion for electromagnetic wave in the domain with two materials separated by a at interface in 2D with a factor of two di erence in wave speed. The computational mesh in the homogeneous parts of the domain away from the interface consists of square elements. Here the method construction is based on m-adaptation construction in homogeneous domain that leads to fourth-order numerical dispersion (vs. second order in non-optimized method). The size of the elements in two domains also di ers by a factor of two, so as to preserve the same value ofmore » Courant number in each. Near the interface where two meshes merge the mesh with larger elements consists of degenerate pentagons. We demonstrate that prior to m-adaptation the accuracy of the method falls from second to rst due to breaking of symmetry in the mesh. Next we develop m-adaptation framework for the interface region and devise an optimization criteria. We prove that for the interface problem m-adaptation cannot produce increase in method accuracy. This is in contrast to homogeneous medium where m-adaptation can increase accuracy by two orders.« less

2D Automatic body-fitted structured mesh generation using advancing extraction method

USDA-ARS?s Scientific Manuscript database

This paper presents an automatic mesh generation algorithm for body-fitted structured meshes in Computational Fluids Dynamics (CFD) analysis using the Advancing Extraction Method (AEM). The method is applicable to two-dimensional domains with complex geometries, which have the hierarchical tree-like...

2D automatic body-fitted structured mesh generation using advancing extraction method

USDA-ARS?s Scientific Manuscript database

This paper presents an automatic mesh generation algorithm for body-fitted structured meshes in Computational Fluids Dynamics (CFD) analysis using the Advancing Extraction Method (AEM). The method is applicable to two-dimensional domains with complex geometries, which have the hierarchical tree-like...

Astrophysical Computation in Research, the Classroom and Beyond

NASA Astrophysics Data System (ADS)

Frank, Adam

2009-03-01

In this talk I review progress in the use of simulations as a tool for astronomical research, for education and public outreach. The talk will include the basic elements of numerical simulations as well as advances in algorithms which have led to recent dramatic progress such as the use of Adaptive Mesh Refinement methods. The scientific focus of the talk will be star formation jets and outflows while the educational emphasis will be on the use of advanced platforms for simulation based learning in lecture and integrated homework. Learning modules for science outreach websites such as DISCOVER magazine will also be highlighted.

Algorithm for protecting light-trees in survivable mesh wavelength-division-multiplexing networks

NASA Astrophysics Data System (ADS)

Luo, Hongbin; Li, Lemin; Yu, Hongfang

2006-12-01

Wavelength-division-multiplexing (WDM) technology is expected to facilitate bandwidth-intensive multicast applications such as high-definition television. A single fiber cut in a WDM mesh network, however, can disrupt the dissemination of information to several destinations on a light-tree based multicast session. Thus it is imperative to protect multicast sessions by reserving redundant resources. We propose a novel and efficient algorithm for protecting light-trees in survivable WDM mesh networks. The algorithm is called segment-based protection with sister node first (SSNF), whose basic idea is to protect a light-tree using a set of backup segments with a higher priority to protect the segments from a branch point to its children (sister nodes). The SSNF algorithm differs from the segment protection scheme proposed in the literature in how the segments are identified and protected. Our objective is to minimize the network resources used for protecting each primary light-tree such that the blocking probability can be minimized. To verify the effectiveness of the SSNF algorithm, we conduct extensive simulation experiments. The simulation results demonstrate that the SSNF algorithm outperforms existing algorithms for the same problem.

Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes

DOE PAGES

Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

2016-08-18

In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used tomore » project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.« less

Finite element meshing approached as a global minimization process

DOE Office of Scientific and Technical Information (OSTI.GOV)

WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R.

2000-03-01

The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within amore » charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested before this project ended. The primary complexity in the extension was in the connectivity problem formulation. Defining all of the interparticle interactions that occur in three-dimensions and expressing them in mathematical relationships is very difficult.« less

Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kikinzon, Evgeny; Kuznetsov, Yuri; Lipnikov, Konstatin

In this study, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. Finally, we suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.

Approximate static condensation algorithm for solving multi-material diffusion problems on meshes non-aligned with material interfaces

DOE PAGES

Kikinzon, Evgeny; Kuznetsov, Yuri; Lipnikov, Konstatin; ...

2017-07-08

In this study, we describe a new algorithm for solving multi-material diffusion problem when material interfaces are not aligned with the mesh. In this case interface reconstruction methods are used to construct approximate representation of interfaces between materials. They produce so-called multi-material cells, in which materials are represented by material polygons that contain only one material. The reconstructed interface is not continuous between cells. Finally, we suggest the new method for solving multi-material diffusion problems on such meshes and compare its performance with known homogenization methods.

Adaptive mesh refinement techniques for the immersed interface method applied to flow problems

PubMed Central

Li, Zhilin; Song, Peng

2013-01-01

In this paper, we develop an adaptive mesh refinement strategy of the Immersed Interface Method for flow problems with a moving interface. The work is built on the AMR method developed for two-dimensional elliptic interface problems in the paper [12] (CiCP, 12(2012), 515–527). The interface is captured by the zero level set of a Lipschitz continuous function φ(x, y, t). Our adaptive mesh refinement is built within a small band of |φ(x, y, t)| ≤ δ with finer Cartesian meshes. The AMR-IIM is validated for Stokes and Navier-Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. A new simple area preserving strategy is also proposed in this paper for the level set method. PMID:23794763

Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes

NASA Technical Reports Server (NTRS)

Feng, Huiyu; Mavriplis, Catherine; VanderWijngaart, Rob; Biswas, Rupak

2004-01-01

High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel Benchmarks (NPB). In this paper, we present some interesting performance results of ow OpenMP parallel implementation on different architectures such as the SGI Origin2000, SGI Altix, and Cray MTA-2.

Anisotropic norm-oriented mesh adaptation for a Poisson problem

NASA Astrophysics Data System (ADS)

Brèthes, Gautier; Dervieux, Alain

2016-10-01

We present a novel formulation for the mesh adaptation of the approximation of a Partial Differential Equation (PDE). The discussion is restricted to a Poisson problem. The proposed norm-oriented formulation extends the goal-oriented formulation since it is equation-based and uses an adjoint. At the same time, the norm-oriented formulation somewhat supersedes the goal-oriented one since it is basically a solution-convergent method. Indeed, goal-oriented methods rely on the reduction of the error in evaluating a chosen scalar output with the consequence that, as mesh size is increased (more degrees of freedom), only this output is proven to tend to its continuous analog while the solution field itself may not converge. A remarkable quality of goal-oriented metric-based adaptation is the mathematical formulation of the mesh adaptation problem under the form of the optimization, in the well-identified set of metrics, of a well-defined functional. In the new proposed formulation, we amplify this advantage. We search, in the same well-identified set of metrics, the minimum of a norm of the approximation error. The norm is prescribed by the user and the method allows addressing the case of multi-objective adaptation like, for example in aerodynamics, adaptating the mesh for drag, lift and moment in one shot. In this work, we consider the basic linear finite-element approximation and restrict our study to L2 norm in order to enjoy second-order convergence. Numerical examples for the Poisson problem are computed.

Bas-relief generation using adaptive histogram equalization.

PubMed

Sun, Xianfang; Rosin, Paul L; Martin, Ralph R; Langbein, Frank C

2009-01-01

An algorithm is presented to automatically generate bas-reliefs based on adaptive histogram equalization (AHE), starting from an input height field. A mesh model may alternatively be provided, in which case a height field is first created via orthogonal or perspective projection. The height field is regularly gridded and treated as an image, enabling a modified AHE method to be used to generate a bas-relief with a user-chosen height range. We modify the original image-contrast-enhancement AHE method to use gradient weights also to enhance the shape features of the bas-relief. To effectively compress the height field, we limit the height-dependent scaling factors used to compute relative height variations in the output from height variations in the input; this prevents any height differences from having too great effect. Results of AHE over different neighborhood sizes are averaged to preserve information at different scales in the resulting bas-relief. Compared to previous approaches, the proposed algorithm is simple and yet largely preserves original shape features. Experiments show that our results are, in general, comparable to and in some cases better than the best previously published methods.

Using Multi-threading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes

NASA Technical Reports Server (NTRS)

Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Saini, Subhash (Technical Monitor)

1998-01-01

In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the adaption phase of FE applications oil triangular meshes and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments oil EARTH-SP2, on implementation of EARTH on the IBM SP2 with different load balancing strategies that are built into the runtime system.

Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers

NASA Technical Reports Server (NTRS)

Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

2014-01-01

This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.

Evaluation of optical data gained by ARAMIS-measurement of abdominal wall movements for an anisotropic pattern design of stress-adapted hernia meshes produced by embroidery technology

NASA Astrophysics Data System (ADS)

Breier, A.; Bittrich, L.; Hahn, J.; Spickenheuer, A.

2017-10-01

For the sustainable repair of abdominal wall hernia the application of hernia meshes is required. One reason for the relapse of hernia after surgery is seen in an inadequate adaption of the mechanical properties of the mesh to the movements of the abdominal wall. Differences in the stiffness of the mesh and the abdominal tissue cause tension, friction and stress resulting in a deficient tissue response and subsequently in a recurrence of a hernia, preferentially in the marginal area of the mesh. Embroidery technology enables a targeted influence on the mechanical properties of the generated textile structure by a directed thread deposition. Textile parameters like stitch density, alignment and angle can be changed easily and locally in the embroidery pattern to generate a space-resolved mesh with mechanical properties adapted to the requirement of the surrounding tissue. To determine those requirements the movements of the abdominal wall and the resulting distortions need to be known. This study was conducted to gain optical data of the abdominal wall movements by non-invasive ARAMIS-measurement on 39 test persons to estimate direction and value of the major strains.

Practical implementation of tetrahedral mesh reconstruction in emission tomography

PubMed Central

Boutchko, R.; Sitek, A.; Gullberg, G. T.

2014-01-01

This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. Image intensities are defined at the mesh nodes and linearly interpolated inside each tetrahedron. For the given mesh geometry, the intensities can be computed directly from tomographic projections using iterative reconstruction algorithms with a system matrix calculated using an exact analytical formula. The mesh geometry is optimized for a specific patient using a two stage process. First, a noisy image is reconstructed on a finely-spaced uniform cloud. Then, the geometry of the representation is adaptively transformed through boundary-preserving node motion and elimination. Nodes are removed in constant intensity regions, merged along the boundaries, and moved in the direction of the mean local intensity gradient in order to provide higher node density in the boundary regions. Attenuation correction and detector geometric response are included in the system matrix. Once the mesh geometry is optimized, it is used to generate the final system matrix for ML-EM reconstruction of node intensities and for visualization of the reconstructed images. In dynamic PET or SPECT imaging, the system matrix generation procedure is performed using a quasi-static sinogram, generated by summing projection data from multiple time frames. This system matrix is then used to reconstruct the individual time frame projections. Performance of the new method is evaluated by reconstructing simulated projections of the NCAT phantom and the method is then applied to dynamic SPECT phantom and patient studies and to a dynamic microPET rat study. Tetrahedral mesh-based images are compared to the standard voxel-based reconstruction for both high and low signal-to-noise ratio projection datasets. The results demonstrate that the reconstructed images represented as tetrahedral meshes based on point clouds offer image quality comparable to that achievable using a standard voxel grid while allowing substantial reduction in the number of unknown intensities to be reconstructed and reducing the noise. PMID:23588373

Practical implementation of tetrahedral mesh reconstruction in emission tomography

NASA Astrophysics Data System (ADS)

Boutchko, R.; Sitek, A.; Gullberg, G. T.

2013-05-01

This paper presents a practical implementation of image reconstruction on tetrahedral meshes optimized for emission computed tomography with parallel beam geometry. Tetrahedral mesh built on a point cloud is a convenient image representation method, intrinsically three-dimensional and with a multi-level resolution property. Image intensities are defined at the mesh nodes and linearly interpolated inside each tetrahedron. For the given mesh geometry, the intensities can be computed directly from tomographic projections using iterative reconstruction algorithms with a system matrix calculated using an exact analytical formula. The mesh geometry is optimized for a specific patient using a two stage process. First, a noisy image is reconstructed on a finely-spaced uniform cloud. Then, the geometry of the representation is adaptively transformed through boundary-preserving node motion and elimination. Nodes are removed in constant intensity regions, merged along the boundaries, and moved in the direction of the mean local intensity gradient in order to provide higher node density in the boundary regions. Attenuation correction and detector geometric response are included in the system matrix. Once the mesh geometry is optimized, it is used to generate the final system matrix for ML-EM reconstruction of node intensities and for visualization of the reconstructed images. In dynamic PET or SPECT imaging, the system matrix generation procedure is performed using a quasi-static sinogram, generated by summing projection data from multiple time frames. This system matrix is then used to reconstruct the individual time frame projections. Performance of the new method is evaluated by reconstructing simulated projections of the NCAT phantom and the method is then applied to dynamic SPECT phantom and patient studies and to a dynamic microPET rat study. Tetrahedral mesh-based images are compared to the standard voxel-based reconstruction for both high and low signal-to-noise ratio projection datasets. The results demonstrate that the reconstructed images represented as tetrahedral meshes based on point clouds offer image quality comparable to that achievable using a standard voxel grid while allowing substantial reduction in the number of unknown intensities to be reconstructed and reducing the noise.

Comparing AMR and SPH Cosmological Simulations. I. Dark Matter and Adiabatic Simulations

NASA Astrophysics Data System (ADS)

O'Shea, Brian W.; Nagamine, Kentaro; Springel, Volker; Hernquist, Lars; Norman, Michael L.

2005-09-01

We compare two cosmological hydrodynamic simulation codes in the context of hierarchical galaxy formation: the Lagrangian smoothed particle hydrodynamics (SPH) code GADGET, and the Eulerian adaptive mesh refinement (AMR) code Enzo. Both codes represent dark matter with the N-body method but use different gravity solvers and fundamentally different approaches for baryonic hydrodynamics. The SPH method in GADGET uses a recently developed ``entropy conserving'' formulation of SPH, while for the mesh-based Enzo two different formulations of Eulerian hydrodynamics are employed: the piecewise parabolic method (PPM) extended with a dual energy formulation for cosmology, and the artificial viscosity-based scheme used in the magnetohydrodynamics code ZEUS. In this paper we focus on a comparison of cosmological simulations that follow either only dark matter, or also a nonradiative (``adiabatic'') hydrodynamic gaseous component. We perform multiple simulations using both codes with varying spatial and mass resolution with identical initial conditions. The dark matter-only runs agree generally quite well provided Enzo is run with a comparatively fine root grid and a low overdensity threshold for mesh refinement, otherwise the abundance of low-mass halos is suppressed. This can be readily understood as a consequence of the hierarchical particle-mesh algorithm used by Enzo to compute gravitational forces, which tends to deliver lower force resolution than the tree-algorithm of GADGET at early times before any adaptive mesh refinement takes place. At comparable force resolution we find that the latter offers substantially better performance and lower memory consumption than the present gravity solver in Enzo. In simulations that include adiabatic gasdynamics we find general agreement in the distribution functions of temperature, entropy, and density for gas of moderate to high overdensity, as found inside dark matter halos. However, there are also some significant differences in the same quantities for gas of lower overdensity. For example, at z=3 the fraction of cosmic gas that has temperature logT>0.5 is ~80% for both Enzo ZEUS and GADGET, while it is 40%-60% for Enzo PPM. We argue that these discrepancies are due to differences in the shock-capturing abilities of the different methods. In particular, we find that the ZEUS implementation of artificial viscosity in Enzo leads to some unphysical heating at early times in preshock regions. While this is apparently a significantly weaker effect in GADGET, its use of an artificial viscosity technique may also make it prone to some excess generation of entropy that should be absent in Enzo PPM. Overall, the hydrodynamical results for GADGET are bracketed by those for Enzo ZEUS and Enzo PPM but are closer to Enzo ZEUS.

Multigrid solution strategies for adaptive meshing problems

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1995-01-01

This paper discusses the issues which arise when combining multigrid strategies with adaptive meshing techniques for solving steady-state problems on unstructured meshes. A basic strategy is described, and demonstrated by solving several inviscid and viscous flow cases. Potential inefficiencies in this basic strategy are exposed, and various alternate approaches are discussed, some of which are demonstrated with an example. Although each particular approach exhibits certain advantages, all methods have particular drawbacks, and the formulation of a completely optimal strategy is considered to be an open problem.

A finite element method to correct deformable image registration errors in low-contrast regions

NASA Astrophysics Data System (ADS)

Zhong, Hualiang; Kim, Jinkoo; Li, Haisen; Nurushev, Teamour; Movsas, Benjamin; Chetty, Indrin J.

2012-06-01

Image-guided adaptive radiotherapy requires deformable image registration to map radiation dose back and forth between images. The purpose of this study is to develop a novel method to improve the accuracy of an intensity-based image registration algorithm in low-contrast regions. A computational framework has been developed in this study to improve the quality of the ‘demons’ registration. For each voxel in the registration's target image, the standard deviation of image intensity in a neighborhood of this voxel was calculated. A mask for high-contrast regions was generated based on their standard deviations. In the masked regions, a tetrahedral mesh was refined recursively so that a sufficient number of tetrahedral nodes in these regions can be selected as driving nodes. An elastic system driven by the displacements of the selected nodes was formulated using a finite element method (FEM) and implemented on the refined mesh. The displacements of these driving nodes were generated with the ‘demons’ algorithm. The solution of the system was derived using a conjugated gradient method, and interpolated to generate a displacement vector field for the registered images. The FEM correction method was compared with the ‘demons’ algorithm on the computed tomography (CT) images of lung and prostate patients. The performance of the FEM correction relating to the ‘demons’ registration was analyzed based on the physical property of their deformation maps, and quantitatively evaluated through a benchmark model developed specifically for this study. Compared to the benchmark model, the ‘demons’ registration has the maximum error of 1.2 cm, which can be corrected by the FEM to 0.4 cm, and the average error of the ‘demons’ registration is reduced from 0.17 to 0.11 cm. For the CT images of lung and prostate patients, the deformation maps generated by the ‘demons’ algorithm were found unrealistic at several places. In these places, the displacement differences between the ‘demons’ registrations and their FEM corrections were found in the range of 0.4 and 1.1 cm. The mesh refinement and FEM simulation were implemented in a single thread application which requires about 45 min of computation time on a 2.6 GHz computer. This study has demonstrated that the FEM can be integrated with intensity-based image registration algorithms to improve their registration accuracy, especially in low-contrast regions.

Computing Normal Shock-Isotropic Turbulence Interaction With Tetrahedral Meshes and the Space-Time CESE Method

NASA Astrophysics Data System (ADS)

Venkatachari, Balaji Shankar; Chang, Chau-Lyan

2016-11-01

The focus of this study is scale-resolving simulations of the canonical normal shock- isotropic turbulence interaction using unstructured tetrahedral meshes and the space-time conservation element solution element (CESE) method. Despite decades of development in unstructured mesh methods and its potential benefits of ease of mesh generation around complex geometries and mesh adaptation, direct numerical or large-eddy simulations of turbulent flows are predominantly carried out using structured hexahedral meshes. This is due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for unstructured meshes that can resolve multiple physical scales and flow discontinuities simultaneously. The CESE method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to accurately simulate turbulent flows using tetrahedral meshes. As part of the study, various regimes of the shock-turbulence interaction (wrinkled and broken shock regimes) will be investigated along with a study on how adaptive refinement of tetrahedral meshes benefits this problem. The research funding for this paper has been provided by Revolutionary Computational Aerosciences (RCA) subproject under the NASA Transformative Aeronautics Concepts Program (TACP).

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Murman, S. M.; Berger, M. J.

2003-01-01

This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.

Impact of Load Balancing on Unstructured Adaptive Grid Computations for Distributed-Memory Multiprocessors

NASA Technical Reports Server (NTRS)

Sohn, Andrew; Biswas, Rupak; Simon, Horst D.

1996-01-01

The computational requirements for an adaptive solution of unsteady problems change as the simulation progresses. This causes workload imbalance among processors on a parallel machine which, in turn, requires significant data movement at runtime. We present a new dynamic load-balancing framework, called JOVE, that balances the workload across all processors with a global view. Whenever the computational mesh is adapted, JOVE is activated to eliminate the load imbalance. JOVE has been implemented on an IBM SP2 distributed-memory machine in MPI for portability. Experimental results for two model meshes demonstrate that mesh adaption with load balancing gives more than a sixfold improvement over one without load balancing. We also show that JOVE gives a 24-fold speedup on 64 processors compared to sequential execution.

Efficient Load Balancing and Data Remapping for Adaptive Grid Calculations

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Biswas, Rupak

1997-01-01

Mesh adaption is a powerful tool for efficient unstructured- grid computations but causes load imbalance among processors on a parallel machine. We present a novel method to dynamically balance the processor workloads with a global view. This paper presents, for the first time, the implementation and integration of all major components within our dynamic load balancing strategy for adaptive grid calculations. Mesh adaption, repartitioning, processor assignment, and remapping are critical components of the framework that must be accomplished rapidly and efficiently so as not to cause a significant overhead to the numerical simulation. Previous results indicated that mesh repartitioning and data remapping are potential bottlenecks for performing large-scale scientific calculations. We resolve these issues and demonstrate that our framework remains viable on a large number of processors.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.

1990-01-01

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

A Parallel, Multi-Scale Watershed-Hydrologic-Inundation Model with Adaptively Switching Mesh for Capturing Flooding and Lake Dynamics

NASA Astrophysics Data System (ADS)

Ji, X.; Shen, C.

2017-12-01

Flood inundation presents substantial societal hazards and also changes biogeochemistry for systems like the Amazon. It is often expensive to simulate high-resolution flood inundation and propagation in a long-term watershed-scale model. Due to the Courant-Friedrichs-Lewy (CFL) restriction, high resolution and large local flow velocity both demand prohibitively small time steps even for parallel codes. Here we develop a parallel surface-subsurface process-based model enhanced by multi-resolution meshes that are adaptively switched on or off. The high-resolution overland flow meshes are enabled only when the flood wave invades to floodplains. This model applies semi-implicit, semi-Lagrangian (SISL) scheme in solving dynamic wave equations, and with the assistant of the multi-mesh method, it also adaptively chooses the dynamic wave equation only in the area of deep inundation. Therefore, the model achieves a balance between accuracy and computational cost.

Efficient parallel resolution of the simplified transport equations in mixed-dual formulation

NASA Astrophysics Data System (ADS)

Barrault, M.; Lathuilière, B.; Ramet, P.; Roman, J.

2011-03-01

A reactivity computation consists of computing the highest eigenvalue of a generalized eigenvalue problem, for which an inverse power algorithm is commonly used. Very fine modelizations are difficult to treat for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time. A first implementation of a Lagrangian based domain decomposition method brings to a poor parallel efficiency because of an increase in the power iterations [1]. In order to obtain a high parallel efficiency, we improve the parallelization scheme by changing the location of the loop over the subdomains in the overall algorithm and by benefiting from the characteristics of the Raviart-Thomas finite element. The new parallel algorithm still allows us to locally adapt the numerical scheme (mesh, finite element order). However, it can be significantly optimized for the matching grid case. The good behavior of the new parallelization scheme is demonstrated for the matching grid case on several hundreds of nodes for computations based on a pin-by-pin discretization.

Adaptive Multilinear Tensor Product Wavelets

DOE PAGES

Weiss, Kenneth; Lindstrom, Peter

2015-08-12

Many foundational visualization techniques including isosurfacing, direct volume rendering and texture mapping rely on piecewise multilinear interpolation over the cells of a mesh. However, there has not been much focus within the visualization community on techniques that efficiently generate and encode globally continuous functions defined by the union of multilinear cells. Wavelets provide a rich context for analyzing and processing complicated datasets. In this paper, we exploit adaptive regular refinement as a means of representing and evaluating functions described by a subset of their nonzero wavelet coefficients. We analyze the dependencies involved in the wavelet transform and describe how tomore » generate and represent the coarsest adaptive mesh with nodal function values such that the inverse wavelet transform is exactly reproduced via simple interpolation (subdivision) over the mesh elements. This allows for an adaptive, sparse representation of the function with on-demand evaluation at any point in the domain. In conclusion, we focus on the popular wavelets formed by tensor products of linear B-splines, resulting in an adaptive, nonconforming but crack-free quadtree (2D) or octree (3D) mesh that allows reproducing globally continuous functions via multilinear interpolation over its cells.« less

NeuroTessMesh: A Tool for the Generation and Visualization of Neuron Meshes and Adaptive On-the-Fly Refinement

PubMed Central

Garcia-Cantero, Juan J.; Brito, Juan P.; Mata, Susana; Bayona, Sofia; Pastor, Luis

2017-01-01

Gaining a better understanding of the human brain continues to be one of the greatest challenges for science, largely because of the overwhelming complexity of the brain and the difficulty of analyzing the features and behavior of dense neural networks. Regarding analysis, 3D visualization has proven to be a useful tool for the evaluation of complex systems. However, the large number of neurons in non-trivial circuits, together with their intricate geometry, makes the visualization of a neuronal scenario an extremely challenging computational problem. Previous work in this area dealt with the generation of 3D polygonal meshes that approximated the cells’ overall anatomy but did not attempt to deal with the extremely high storage and computational cost required to manage a complex scene. This paper presents NeuroTessMesh, a tool specifically designed to cope with many of the problems associated with the visualization of neural circuits that are comprised of large numbers of cells. In addition, this method facilitates the recovery and visualization of the 3D geometry of cells included in databases, such as NeuroMorpho, and provides the tools needed to approximate missing information such as the soma’s morphology. This method takes as its only input the available compact, yet incomplete, morphological tracings of the cells as acquired by neuroscientists. It uses a multiresolution approach that combines an initial, coarse mesh generation with subsequent on-the-fly adaptive mesh refinement stages using tessellation shaders. For the coarse mesh generation, a novel approach, based on the Finite Element Method, allows approximation of the 3D shape of the soma from its incomplete description. Subsequently, the adaptive refinement process performed in the graphic card generates meshes that provide good visual quality geometries at a reasonable computational cost, both in terms of memory and rendering time. All the described techniques have been integrated into NeuroTessMesh, available to the scientific community, to generate, visualize, and save the adaptive resolution meshes. PMID:28690511

A second-order 3D electromagnetics algorithm for curved interfaces between anisotropic dielectrics on a Yee mesh

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bauer, Carl A., E-mail: bauerca@colorado.ed; Werner, Gregory R.; Cary, John R.

A new frequency-domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a Yee mesh with second-order error in resonant frequencies. The algorithm is systematically derived using the finite integration formulation of Maxwell's equations on the Yee mesh. Second-order convergence of the error in resonant frequencies is achieved by guaranteeing first-order error on dielectric boundaries and second-order error in bulk (possibly anisotropic) regions. Convergence studies, conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant, both show second-order convergence of frequency error; the convergence is sufficiently smooth that Richardsonmore » extrapolation yields roughly third-order convergence. The convergence of electric fields near the dielectric interface for the analytic problem is also presented.« less

A novel method of the image processing on irregular triangular meshes

NASA Astrophysics Data System (ADS)

Vishnyakov, Sergey; Pekhterev, Vitaliy; Sokolova, Elizaveta

2018-04-01

The paper describes a novel method of the image processing based on irregular triangular meshes implementation. The triangular mesh is adaptive to the image content, least mean square linear approximation is proposed for the basic interpolation within the triangle. It is proposed to use triangular numbers to simplify using of the local (barycentric) coordinates for the further analysis - triangular element of the initial irregular mesh is to be represented through the set of the four equilateral triangles. This allows to use fast and simple pixels indexing in local coordinates, e.g. "for" or "while" loops for access to the pixels. Moreover, representation proposed allows to use discrete cosine transform of the simple "rectangular" symmetric form without additional pixels reordering (as it is used for shape-adaptive DCT forms). Furthermore, this approach leads to the simple form of the wavelet transform on triangular mesh. The results of the method application are presented. It is shown that advantage of the method proposed is a combination of the flexibility of the image-adaptive irregular meshes with the simple form of the pixel indexing in local triangular coordinates and the using of the common forms of the discrete transforms for triangular meshes. Method described is proposed for the image compression, pattern recognition, image quality improvement, image search and indexing. It also may be used as a part of video coding (intra-frame or inter-frame coding, motion detection).

Direction-aware Slope Limiter for 3D Cubic Grids with Adaptive Mesh Refinement

DOE PAGES

Velechovsky, Jan; Francois, Marianne M.; Masser, Thomas

2018-06-07

In the context of finite volume methods for hyperbolic systems of conservation laws, slope limiters are an effective way to suppress creation of unphysical local extrema and/or oscillations near discontinuities. We investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three-dimensional simulations. In particular, we are interested in linear reconstructions on Cartesian adaptively refined meshes, where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity. We design a new slope limiter, which combines the robustness of a minmod limiter with the accuracy ofmore » a van Leer limiter. The limiter is called Direction-Aware Limiter (DAL), because the combination is based on a principal flow direction. In particular, DAL is useful in situations where the Barth–Jespersen limiter for general meshes fails to maintain global linear functions, such as on cubic computational meshes with stencils including only faceneighboring cells. Here, we verify the new slope limiter on a suite of standard hydrodynamic test problems on Cartesian adaptively refined meshes. Lastly, we demonstrate reduced mesh imprinting; for radially symmetric problems such as the Sedov blast wave or the Noh implosion test cases, the results with DAL show better preservation of radial symmetry compared to the other standard methods on Cartesian meshes.« less

A propagation method with adaptive mesh grid based on wave characteristics for wave optics simulation

NASA Astrophysics Data System (ADS)

Tang, Qiuyan; Wang, Jing; Lv, Pin; Sun, Quan

2015-10-01

Propagation simulation method and choosing mesh grid are both very important to get the correct propagation results in wave optics simulation. A new angular spectrum propagation method with alterable mesh grid based on the traditional angular spectrum method and the direct FFT method is introduced. With this method, the sampling space after propagation is not limited to propagation methods no more, but freely alterable. However, choosing mesh grid on target board influences the validity of simulation results directly. So an adaptive mesh choosing method based on wave characteristics is proposed with the introduced propagation method. We can calculate appropriate mesh grids on target board to get satisfying results. And for complex initial wave field or propagation through inhomogeneous media, we can also calculate and set the mesh grid rationally according to above method. Finally, though comparing with theoretical results, it's shown that the simulation result with the proposed method coinciding with theory. And by comparing with the traditional angular spectrum method and the direct FFT method, it's known that the proposed method is able to adapt to a wider range of Fresnel number conditions. That is to say, the method can simulate propagation results efficiently and correctly with propagation distance of almost zero to infinity. So it can provide better support for more wave propagation applications such as atmospheric optics, laser propagation and so on.

Direction-aware Slope Limiter for 3D Cubic Grids with Adaptive Mesh Refinement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Velechovsky, Jan; Francois, Marianne M.; Masser, Thomas

In the context of finite volume methods for hyperbolic systems of conservation laws, slope limiters are an effective way to suppress creation of unphysical local extrema and/or oscillations near discontinuities. We investigate properties of these limiters as applied to piecewise linear reconstructions of conservative fluid quantities in three-dimensional simulations. In particular, we are interested in linear reconstructions on Cartesian adaptively refined meshes, where a reconstructed fluid quantity at a face center depends on more than a single gradient component of the quantity. We design a new slope limiter, which combines the robustness of a minmod limiter with the accuracy ofmore » a van Leer limiter. The limiter is called Direction-Aware Limiter (DAL), because the combination is based on a principal flow direction. In particular, DAL is useful in situations where the Barth–Jespersen limiter for general meshes fails to maintain global linear functions, such as on cubic computational meshes with stencils including only faceneighboring cells. Here, we verify the new slope limiter on a suite of standard hydrodynamic test problems on Cartesian adaptively refined meshes. Lastly, we demonstrate reduced mesh imprinting; for radially symmetric problems such as the Sedov blast wave or the Noh implosion test cases, the results with DAL show better preservation of radial symmetry compared to the other standard methods on Cartesian meshes.« less

Formulation of boundary conditions for the multigrid acceleration of the Euler and Navier Stokes equations

NASA Technical Reports Server (NTRS)

Jentink, Thomas Neil; Usab, William J., Jr.

1990-01-01

An explicit, Multigrid algorithm was written to solve the Euler and Navier-Stokes equations with special consideration given to the coarse mesh boundary conditions. These are formulated in a manner consistent with the interior solution, utilizing forcing terms to prevent coarse-mesh truncation error from affecting the fine-mesh solution. A 4-Stage Hybrid Runge-Kutta Scheme is used to advance the solution in time, and Multigrid convergence is further enhanced by using local time-stepping and implicit residual smoothing. Details of the algorithm are presented along with a description of Jameson's standard Multigrid method and a new approach to formulating the Multigrid equations.

Emerging CFD technologies and aerospace vehicle design

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J.

1995-01-01

With the recent focus on the needs of design and applications CFD, research groups have begun to address the traditional bottlenecks of grid generation and surface modeling. Now, a host of emerging technologies promise to shortcut or dramatically simplify the simulation process. This paper discusses the current status of these emerging technologies. It will argue that some tools are already available which can have positive impact on portions of the design cycle. However, in most cases, these tools need to be integrated into specific engineering systems and process cycles to be used effectively. The rapidly maturing status of unstructured and Cartesian approaches for inviscid simulations makes suggests the possibility of highly automated Euler-boundary layer simulations with application to loads estimation and even preliminary design. Similarly, technology is available to link block structured mesh generation algorithms with topology libraries to avoid tedious re-meshing of topologically similar configurations. Work in algorithmic based auto-blocking suggests that domain decomposition and point placement operations in multi-block mesh generation may be properly posed as problems in Computational Geometry, and following this approach may lead to robust algorithmic processes for automatic mesh generation.

Spectral turning bands for efficient Gaussian random fields generation on GPUs and accelerators

NASA Astrophysics Data System (ADS)

Hunger, L.; Cosenza, B.; Kimeswenger, S.; Fahringer, T.

2015-11-01

A random field (RF) is a set of correlated random variables associated with different spatial locations. RF generation algorithms are of crucial importance for many scientific areas, such as astrophysics, geostatistics, computer graphics, and many others. Current approaches commonly make use of 3D fast Fourier transform (FFT), which does not scale well for RF bigger than the available memory; they are also limited to regular rectilinear meshes. We introduce random field generation with the turning band method (RAFT), an RF generation algorithm based on the turning band method that is optimized for massively parallel hardware such as GPUs and accelerators. Our algorithm replaces the 3D FFT with a lower-order, one-dimensional FFT followed by a projection step and is further optimized with loop unrolling and blocking. RAFT can easily generate RF on non-regular (non-uniform) meshes and efficiently produce fields with mesh sizes bigger than the available device memory by using a streaming, out-of-core approach. Our algorithm generates RF with the correct statistical behavior and is tested on a variety of modern hardware, such as NVIDIA Tesla, AMD FirePro and Intel Phi. RAFT is faster than the traditional methods on regular meshes and has been successfully applied to two real case scenarios: planetary nebulae and cosmological simulations.

Numerical simulation of immiscible viscous fingering using adaptive unstructured meshes

NASA Astrophysics Data System (ADS)

Adam, A.; Salinas, P.; Percival, J. R.; Pavlidis, D.; Pain, C.; Muggeridge, A. H.; Jackson, M.

2015-12-01

Displacement of one fluid by another in porous media occurs in various settings including hydrocarbon recovery, CO2 storage and water purification. When the invading fluid is of lower viscosity than the resident fluid, the displacement front is subject to a Saffman-Taylor instability and is unstable to transverse perturbations. These instabilities can grow, leading to fingering of the invading fluid. Numerical simulation of viscous fingering is challenging. The physics is controlled by a complex interplay of viscous and diffusive forces and it is necessary to ensure physical diffusion dominates numerical diffusion to obtain converged solutions. This typically requires the use of high mesh resolution and high order numerical methods. This is computationally expensive. We demonstrate here the use of a novel control volume - finite element (CVFE) method along with dynamic unstructured mesh adaptivity to simulate viscous fingering with higher accuracy and lower computational cost than conventional methods. Our CVFE method employs a discontinuous representation for both pressure and velocity, allowing the use of smaller control volumes (CVs). This yields higher resolution of the saturation field which is represented CV-wise. Moreover, dynamic mesh adaptivity allows high mesh resolution to be employed where it is required to resolve the fingers and lower resolution elsewhere. We use our results to re-examine the existing criteria that have been proposed to govern the onset of instability.Mesh adaptivity requires the mapping of data from one mesh to another. Conventional methods such as consistent interpolation do not readily generalise to discontinuous fields and are non-conservative. We further contribute a general framework for interpolation of CV fields by Galerkin projection. The method is conservative, higher order and yields improved results, particularly with higher order or discontinuous elements where existing approaches are often excessively diffusive.

Multiphase flow modelling of volcanic ash particle settling in water using adaptive unstructured meshes

NASA Astrophysics Data System (ADS)

Jacobs, C. T.; Collins, G. S.; Piggott, M. D.; Kramer, S. C.; Wilson, C. R. G.

2013-02-01

Small-scale experiments of volcanic ash particle settling in water have demonstrated that ash particles can either settle slowly and individually, or rapidly and collectively as a gravitationally unstable ash-laden plume. This has important implications for the emplacement of tephra deposits on the seabed. Numerical modelling has the potential to extend the results of laboratory experiments to larger scales and explore the conditions under which plumes may form and persist, but many existing models are computationally restricted by the fixed mesh approaches that they employ. In contrast, this paper presents a new multiphase flow model that uses an adaptive unstructured mesh approach. As a simulation progresses, the mesh is optimized to focus numerical resolution in areas important to the dynamics and decrease it where it is not needed, thereby potentially reducing computational requirements. Model verification is performed using the method of manufactured solutions, which shows the correct solution convergence rates. Model validation and application considers 2-D simulations of plume formation in a water tank which replicate published laboratory experiments. The numerically predicted settling velocities for both individual particles and plumes, as well as instability behaviour, agree well with experimental data and observations. Plume settling is clearly hindered by the presence of a salinity gradient, and its influence must therefore be taken into account when considering particles in bodies of saline water. Furthermore, individual particles settle in the laminar flow regime while plume settling is shown (by plume Reynolds numbers greater than unity) to be in the turbulent flow regime, which has a significant impact on entrainment and settling rates. Mesh adaptivity maintains solution accuracy while providing a substantial reduction in computational requirements when compared to the same simulation performed using a fixed mesh, highlighting the benefits of an adaptive unstructured mesh approach.

Grid generation for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.; Erlebacher, Gordon

1989-01-01

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

Grid generation for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.; Erlebacher, Gordon

1987-01-01

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

High-fidelity meshes from tissue samples for diffusion MRI simulations.

PubMed

Panagiotaki, Eleftheria; Hall, Matt G; Zhang, Hui; Siow, Bernard; Lythgoe, Mark F; Alexander, Daniel C

2010-01-01

This paper presents a method for constructing detailed geometric models of tissue microstructure for synthesizing realistic diffusion MRI data. We construct three-dimensional mesh models from confocal microscopy image stacks using the marching cubes algorithm. Random-walk simulations within the resulting meshes provide synthetic diffusion MRI measurements. Experiments optimise simulation parameters and complexity of the meshes to achieve accuracy and reproducibility while minimizing computation time. Finally we assess the quality of the synthesized data from the mesh models by comparison with scanner data as well as synthetic data from simple geometric models and simplified meshes that vary only in two dimensions. The results support the extra complexity of the three-dimensional mesh compared to simpler models although sensitivity to the mesh resolution is quite robust.

Adaptive and dynamic meshing methods for numerical simulations

NASA Astrophysics Data System (ADS)

Acikgoz, Nazmiye

For the numerical simulation of many problems of engineering interest, it is desirable to have an automated mesh adaption tool capable of producing high quality meshes with an affordably low number of mesh points. This is important especially for problems, which are characterized by anisotropic features of the solution and require mesh clustering in the direction of high gradients. Another significant issue in meshing emerges in the area of unsteady simulations with moving boundaries or interfaces, where the motion of the boundary has to be accommodated by deforming the computational grid. Similarly, there exist problems where current mesh needs to be adapted to get more accurate solutions because either the high gradient regions are initially predicted inaccurately or they change location throughout the simulation. To solve these problems, we propose three novel procedures. For this purpose, in the first part of this work, we present an optimization procedure for three-dimensional anisotropic tetrahedral grids based on metric-driven h-adaptation. The desired anisotropy in the grid is dictated by a metric that defines the size, shape, and orientation of the grid elements throughout the computational domain. Through the use of topological and geometrical operators, the mesh is iteratively adapted until the final mesh minimizes a given objective function. In this work, the objective function measures the distance between the metric of each simplex and a target metric, which can be either user-defined (a-priori) or the result of a-posteriori error analysis. During the adaptation process, one tries to decrease the metric-based objective function until the final mesh is compliant with the target within a given tolerance. However, in regions such as corners and complex face intersections, the compliance condition was found to be very difficult or sometimes impossible to satisfy. In order to address this issue, we propose an optimization process based on an ad-hoc application of the simulated annealing technique, which improves the likelihood of removing poor elements from the grid. Moreover, a local implementation of the simulated annealing is proposed to reduce the computational cost. Many challenging multi-physics and multi-field problems that are unsteady in nature are characterized by moving boundaries and/or interfaces. When the boundary displacements are large, which typically occurs when implicit time marching procedures are used, degenerate elements are easily formed in the grid such that frequent remeshing is required. To deal with this problem, in the second part of this work, we propose a new r-adaptation methodology. The new technique is valid for both simplicial (e.g., triangular, tet) and non-simplicial (e.g., quadrilateral, hex) deforming grids that undergo large imposed displacements at their boundaries. A two- or three-dimensional grid is deformed using a network of linear springs composed of edge springs and a set of virtual springs. The virtual springs are constructed in such a way as to oppose element collapsing. This is accomplished by confining each vertex to its ball through springs that are attached to the vertex and its projection on the ball entities. The resulting linear problem is solved using a preconditioned conjugate gradient method. The new method is compared with the classical spring analogy technique in two- and three-dimensional examples, highlighting the performance improvements achieved by the new method. Meshes are an important part of numerical simulations. Depending on the geometry and flow conditions, the most suitable mesh for each particular problem is different. Meshes are usually generated by either using a suitable software package or solving a PDE. In both cases, engineering intuition plays a significant role in deciding where clusterings should take place. In addition, for unsteady problems, the gradients vary for each time step, which requires frequent remeshing during simulations. Therefore, in order to minimize user intervention and prevent frequent remeshings, we conclude this work by defining a novel mesh adaptation technique that integrates metric based target mesh definitions with the ball-vertex mesh deformation method. In this new approach, the entire mesh is deformed based on either an a-priori or an a-posteriori error estimator. In other words, nodal points are repositioned upon application of a force field in order to comply with the target mesh or to get more accurate solutions. The method has been tested for two-dimensional problems of a-priori metric definitions as well as for oblique shock clusterings.

Determination of the optimal mesh parameters for Iguassu centrifuge flow and separation calculations

NASA Astrophysics Data System (ADS)

Romanihin, S. M.; Tronin, I. V.

2016-09-01

We present the method and the results of the determination for optimal computational mesh parameters for axisymmetric modeling of flow and separation in the Iguasu gas centrifuge. The aim of this work was to determine the mesh parameters which provide relatively low computational cost whithout loss of accuracy. We use direct search optimization algorithm to calculate optimal mesh parameters. Obtained parameters were tested by the calculation of the optimal working regime of the Iguasu GC. Separative power calculated using the optimal mesh parameters differs less than 0.5% from the result obtained on the detailed mesh. Presented method can be used to determine optimal mesh parameters of the Iguasu GC with different rotor speeds.

Reconfigurable Model Execution in the OpenMDAO Framework

NASA Technical Reports Server (NTRS)

Hwang, John T.

2017-01-01

NASA's OpenMDAO framework facilitates constructing complex models and computing their derivatives for multidisciplinary design optimization. Decomposing a model into components that follow a prescribed interface enables OpenMDAO to assemble multidisciplinary derivatives from the component derivatives using what amounts to the adjoint method, direct method, chain rule, global sensitivity equations, or any combination thereof, using the MAUD architecture. OpenMDAO also handles the distribution of processors among the disciplines by hierarchically grouping the components, and it automates the data transfer between components that are on different processors. These features have made OpenMDAO useful for applications in aircraft design, satellite design, wind turbine design, and aircraft engine design, among others. This paper presents new algorithms for OpenMDAO that enable reconfigurable model execution. This concept refers to dynamically changing, during execution, one or more of: the variable sizes, solution algorithm, parallel load balancing, or set of variables-i.e., adding and removing components, perhaps to switch to a higher-fidelity sub-model. Any component can reconfigure at any point, even when running in parallel with other components, and the reconfiguration algorithm presented here performs the synchronized updates to all other components that are affected. A reconfigurable software framework for multidisciplinary design optimization enables new adaptive solvers, adaptive parallelization, and new applications such as gradient-based optimization with overset flow solvers and adaptive mesh refinement. Benchmarking results demonstrate the time savings for reconfiguration compared to setting up the model again from scratch, which can be significant in large-scale problems. Additionally, the new reconfigurability feature is applied to a mission profile optimization problem for commercial aircraft where both the parametrization of the mission profile and the time discretization are adaptively refined, resulting in computational savings of roughly 10% and the elimination of oscillations in the optimized altitude profile.

Cart3D Simulations for the Second AIAA Sonic Boom Prediction Workshop

NASA Technical Reports Server (NTRS)

Anderson, George R.; Aftosmis, Michael J.; Nemec, Marian

2017-01-01

Simulation results are presented for all test cases prescribed in the Second AIAA Sonic Boom Prediction Workshop. For each of the four nearfield test cases, we compute pressure signatures at specified distances and off-track angles, using an inviscid, embedded-boundary Cartesian-mesh flow solver with output-based mesh adaptation. The cases range in complexity from an axisymmetric body to a full low-boom aircraft configuration with a powered nacelle. For efficiency, boom carpets are decomposed into sets of independent meshes and computed in parallel. This also facilitates the use of more effective meshing strategies - each off-track angle is computed on a mesh with good azimuthal alignment, higher aspect ratio cells, and more tailored adaptation. The nearfield signatures generally exhibit good convergence with mesh refinement. We introduce a local error estimation procedure to highlight regions of the signatures most sensitive to mesh refinement. Results are also presented for the two propagation test cases, which investigate the effects of atmospheric profiles on ground noise. Propagation is handled with an augmented Burgers' equation method (NASA's sBOOM), and ground noise metrics are computed with LCASB.

Terrain-driven unstructured mesh development through semi-automatic vertical feature extraction

NASA Astrophysics Data System (ADS)

Bilskie, Matthew V.; Coggin, David; Hagen, Scott C.; Medeiros, Stephen C.

2015-12-01

A semi-automated vertical feature terrain extraction algorithm is described and applied to a two-dimensional, depth-integrated, shallow water equation inundation model. The extracted features describe what are commonly sub-mesh scale elevation details (ridge and valleys), which may be ignored in standard practice because adequate mesh resolution cannot be afforded. The extraction algorithm is semi-automated, requires minimal human intervention, and is reproducible. A lidar-derived digital elevation model (DEM) of coastal Mississippi and Alabama serves as the source data for the vertical feature extraction. Unstructured mesh nodes and element edges are aligned to the vertical features and an interpolation algorithm aimed at minimizing topographic elevation error assigns elevations to mesh nodes via the DEM. The end result is a mesh that accurately represents the bare earth surface as derived from lidar with element resolution in the floodplain ranging from 15 m to 200 m. To examine the influence of the inclusion of vertical features on overland flooding, two additional meshes were developed, one without crest elevations of the features and another with vertical features withheld. All three meshes were incorporated into a SWAN+ADCIRC model simulation of Hurricane Katrina. Each of the three models resulted in similar validation statistics when compared to observed time-series water levels at gages and post-storm collected high water marks. Simulated water level peaks yielded an R2 of 0.97 and upper and lower 95% confidence interval of ∼ ± 0.60 m. From the validation at the gages and HWM locations, it was not clear which of the three model experiments performed best in terms of accuracy. Examination of inundation extent among the three model results were compared to debris lines derived from NOAA post-event aerial imagery, and the mesh including vertical features showed higher accuracy. The comparison of model results to debris lines demonstrates that additional validation techniques are necessary for state-of-the-art flood inundation models. In addition, the semi-automated, unstructured mesh generation process presented herein increases the overall accuracy of simulated storm surge across the floodplain without reliance on hand digitization or sacrificing computational cost.

Efficient numerical method for solving Cauchy problem for the Gamma equation

NASA Astrophysics Data System (ADS)

Koleva, Miglena N.

2011-12-01

In this work we consider Cauchy problem for the so called Gamma equation, derived by transforming the fully nonlinear Black-Scholes equation for option price into a quasilinear parabolic equation for the second derivative (Greek) Γ = VSS of the option price V. We develop an efficient numerical method for solving the model problem concerning different volatility terms. Using suitable change of variables the problem is transformed on finite interval, keeping original behavior of the solution at the infinity. Then we construct Picard-Newton algorithm with adaptive mesh step in time, which can be applied also in the case of non-differentiable functions. Results of numerical simulations are given.

Adaptive mesh refinement and adjoint methods in geophysics simulations

NASA Astrophysics Data System (ADS)

Burstedde, Carsten

2013-04-01

It is an ongoing challenge to increase the resolution that can be achieved by numerical geophysics simulations. This applies to considering sub-kilometer mesh spacings in global-scale mantle convection simulations as well as to using frequencies up to 1 Hz in seismic wave propagation simulations. One central issue is the numerical cost, since for three-dimensional space discretizations, possibly combined with time stepping schemes, a doubling of resolution can lead to an increase in storage requirements and run time by factors between 8 and 16. A related challenge lies in the fact that an increase in resolution also increases the dimensionality of the model space that is needed to fully parametrize the physical properties of the simulated object (a.k.a. earth). Systems that exhibit a multiscale structure in space are candidates for employing adaptive mesh refinement, which varies the resolution locally. An example that we found well suited is the mantle, where plate boundaries and fault zones require a resolution on the km scale, while deeper area can be treated with 50 or 100 km mesh spacings. This approach effectively reduces the number of computational variables by several orders of magnitude. While in this case it is possible to derive the local adaptation pattern from known physical parameters, it is often unclear what are the most suitable criteria for adaptation. We will present the goal-oriented error estimation procedure, where such criteria are derived from an objective functional that represents the observables to be computed most accurately. Even though this approach is well studied, it is rarely used in the geophysics community. A related strategy to make finer resolution manageable is to design methods that automate the inference of model parameters. Tweaking more than a handful of numbers and judging the quality of the simulation by adhoc comparisons to known facts and observations is a tedious task and fundamentally limited by the turnaround times required by human intervention and analysis. Specifying an objective functional that quantifies the misfit between the simulation outcome and known constraints and then minimizing it through numerical optimization can serve as an automated technique for parameter identification. As suggested by the similarity in formulation, the numerical algorithm is closely related to the one used for goal-oriented error estimation. One common point is that the so-called adjoint equation needs to be solved numerically. We will outline the derivation and implementation of these methods and discuss some of their pros and cons, supported by numerical results.

Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.

PubMed

Spilker, R L; de Almeida, E S; Donzelli, P S

1992-01-01

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory of mixtures can be used to represent soft hydrated tissues in the human musculoskeletal system as a two-phase continuum consisting of an incompressible solid phase (collagen and proteoglycan) and an incompressible fluid phase (interstitial water). We first consider the finite deformation of soft hydrated tissues in which the solid phase is represented as hyperelastic. A finite element formulation of the governing nonlinear biphasic equations is presented based on a mixed-penalty approach and derived using the weighted residual method. Fluid and solid phase deformation, velocity, and pressure are interpolated within each element, and the pressure variables within each element are eliminated at the element level. A system of nonlinear, first-order differential equations in the fluid and solid phase deformation and velocity is obtained. In order to solve these equations, the contributions of the hyperelastic solid phase are incrementally linearized, a finite difference rule is introduced for temporal discretization, and an iterative scheme is adopted to achieve equilibrium at the end of each time increment. We demonstrate the accuracy and adequacy of the procedure using a six-node, isoparametric axisymmetric element, and we present an example problem for which independent numerical solution is available. Next, we present an automated, adaptive environment for the simulation of soft tissue continua in which the finite element analysis is coupled with automatic mesh generation, error indicators, and projection methods. Mesh generation and updating, including both refinement and coarsening, for the two-dimensional examples examined in this study are performed using the finite quadtree approach. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. To allow the finite difference algorithm to proceed in time using an updated mesh, solution values must be transferred to the new nodal locations. This rezoning is accomplished using a projected field for the primary variables. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using a linear, two-dimensional, axisymmetric problem corresponding to the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients and to produce solutions in good agreement with independent, converged, numerical solutions.

Three-dimensional unstructured grid refinement and optimization using edge-swapping

NASA Technical Reports Server (NTRS)

Gandhi, Amar; Barth, Timothy

1993-01-01

This paper presents a three-dimensional (3-D) 'edge-swapping method based on local transformations. This method extends Lawson's edge-swapping algorithm into 3-D. The 3-D edge-swapping algorithm is employed for the purpose of refining and optimizing unstructured meshes according to arbitrary mesh-quality measures. Several criteria including Delaunay triangulations are examined. Extensions from two to three dimensions of several known properties of Delaunay triangulations are also discussed.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chrisochoides, N.; Sukup, F.

In this paper we present a parallel implementation of the Bowyer-Watson (BW) algorithm using the task-parallel programming model. The BW algorithm constitutes an ideal mesh refinement strategy for implementing a large class of unstructured mesh generation techniques on both sequential and parallel computers, by preventing the need for global mesh refinement. Its implementation on distributed memory multicomputes using the traditional data-parallel model has been proven very inefficient due to excessive synchronization needed among processors. In this paper we demonstrate that with the task-parallel model we can tolerate synchronization costs inherent to data-parallel methods by exploring concurrency in the processor level.more » Our preliminary performance data indicate that the task- parallel approach: (i) is almost four times faster than the existing data-parallel methods, (ii) scales linearly, and (iii) introduces minimum overheads compared to the {open_quotes}best{close_quotes} sequential implementation of the BW algorithm.« less

Solving very large, sparse linear systems on mesh-connected parallel computers

NASA Technical Reports Server (NTRS)

Opsahl, Torstein; Reif, John

1987-01-01

The implementation of Pan and Reif's Parallel Nested Dissection (PND) algorithm on mesh connected parallel computers is described. This is the first known algorithm that allows very large, sparse linear systems of equations to be solved efficiently in polylog time using a small number of processors. How the processor bound of PND can be matched to the number of processors available on a given parallel computer by slowing down the algorithm by constant factors is described. Also, for the important class of problems where G(A) is a grid graph, a unique memory mapping that reduces the inter-processor communication requirements of PND to those that can be executed on mesh connected parallel machines is detailed. A description of an implementation on the Goodyear Massively Parallel Processor (MPP), located at Goddard is given. Also, a detailed discussion of data mappings and performance issues is given.

Effects of adaptive refinement on the inverse EEG solution

NASA Astrophysics Data System (ADS)

Weinstein, David M.; Johnson, Christopher R.; Schmidt, John A.

1995-10-01

One of the fundamental problems in electroencephalography can be characterized by an inverse problem. Given a subset of electrostatic potentials measured on the surface of the scalp and the geometry and conductivity properties within the head, calculate the current vectors and potential fields within the cerebrum. Mathematically the generalized EEG problem can be stated as solving Poisson's equation of electrical conduction for the primary current sources. The resulting problem is mathematically ill-posed i.e., the solution does not depend continuously on the data, such that small errors in the measurement of the voltages on the scalp can yield unbounded errors in the solution, and, for the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions the general treatment of a solution of Poisson's equation, the solution is non-unique. However, if accurate solutions to such problems could be obtained, neurologists would gain noninvasive accesss to patient-specific cortical activity. Access to such data would ultimately increase the number of patients who could be effectively treated for pathological cortical conditions such as temporal lobe epilepsy. In this paper, we present the effects of spatial adaptive refinement on the inverse EEG problem and show that the use of adaptive methods allow for significantly better estimates of electric and potential fileds within the brain through an inverse procedure. To test these methods, we have constructed several finite element head models from magneteic resonance images of a patient. The finite element meshes ranged in size from 2724 nodes and 12,812 elements to 5224 nodes and 29,135 tetrahedral elements, depending on the level of discretization. We show that an adaptive meshing algorithm minimizes the error in the forward problem due to spatial discretization and thus increases the accuracy of the inverse solution.

Molecular surface mesh generation by filtering electron density map.

PubMed

Giard, Joachim; Macq, Benoît

2010-01-01

Bioinformatics applied to macromolecules are now widely spread and in continuous expansion. In this context, representing external molecular surface such as the Van der Waals Surface or the Solvent Excluded Surface can be useful for several applications. We propose a fast and parameterizable algorithm giving good visual quality meshes representing molecular surfaces. It is obtained by isosurfacing a filtered electron density map. The density map is the result of the maximum of Gaussian functions placed around atom centers. This map is filtered by an ideal low-pass filter applied on the Fourier Transform of the density map. Applying the marching cubes algorithm on the inverse transform provides a mesh representation of the molecular surface.

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

Integration of Mesh Optimization with 3D All-Hex Mesh Generation, LDRD Subcase 3504340000, Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

KNUPP,PATRICK; MITCHELL,SCOTT A.

1999-11-01

In an attempt to automatically produce high-quality all-hex meshes, we investigated a mesh improvement strategy: given an initial poor-quality all-hex mesh, we iteratively changed the element connectivity, adding and deleting elements and nodes, and optimized the node positions. We found a set of hex reconnection primitives. We improved the optimization algorithms so they can untangle a negative-Jacobian mesh, even considering Jacobians on the boundary, and subsequently optimize the condition number of elements in an untangled mesh. However, even after applying both the primitives and optimization we were unable to produce high-quality meshes in certain regions. Our experiences suggest that manymore » boundary configurations of quadrilaterals admit no hexahedral mesh with positive Jacobians, although we have no proof of this.« less

Comparison of two non-convex mixed-integer nonlinear programming algorithms applied to autoregressive moving average model structure and parameter estimation

NASA Astrophysics Data System (ADS)

Uilhoorn, F. E.

2016-10-01

In this article, the stochastic modelling approach proposed by Box and Jenkins is treated as a mixed-integer nonlinear programming (MINLP) problem solved with a mesh adaptive direct search and a real-coded genetic class of algorithms. The aim is to estimate the real-valued parameters and non-negative integer, correlated structure of stationary autoregressive moving average (ARMA) processes. The maximum likelihood function of the stationary ARMA process is embedded in Akaike's information criterion and the Bayesian information criterion, whereas the estimation procedure is based on Kalman filter recursions. The constraints imposed on the objective function enforce stability and invertibility. The best ARMA model is regarded as the global minimum of the non-convex MINLP problem. The robustness and computational performance of the MINLP solvers are compared with brute-force enumeration. Numerical experiments are done for existing time series and one new data set.

Computational Aerothermodynamic Simulation Issues on Unstructured Grids

NASA Technical Reports Server (NTRS)

Gnoffo, Peter A.; White, Jeffery A.

2004-01-01

The synthesis of physical models for gas chemistry and turbulence from the structured grid codes LAURA and VULCAN into the unstructured grid code FUN3D is described. A directionally Symmetric, Total Variation Diminishing (STVD) algorithm and an entropy fix (eigenvalue limiter) keyed to local cell Reynolds number are introduced to improve solution quality for hypersonic aeroheating applications. A simple grid-adaptation procedure is incorporated within the flow solver. Simulations of flow over an ellipsoid (perfect gas, inviscid), Shuttle Orbiter (viscous, chemical nonequilibrium) and comparisons to the structured grid solvers LAURA (cylinder, Shuttle Orbiter) and VULCAN (flat plate) are presented to show current capabilities. The quality of heating in 3D stagnation regions is very sensitive to algorithm options in general, high aspect ratio tetrahedral elements complicate the simulation of high Reynolds number, viscous flow as compared to locally structured meshes aligned with the flow.

Array-based Hierarchical Mesh Generation in Parallel

DOE PAGES

Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

2015-11-03

In this paper, we describe an array-based hierarchical mesh generation capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial mesh that can be used for a number of purposes such as multi-level methods to generating large meshes. The capability is developed under the parallel mesh framework “Mesh Oriented dAtaBase” a.k.a MOAB. We describe the underlying data structures and algorithms to generate such hierarchies and present numerical results for computational efficiency and mesh quality. Inmore » conclusion, we also present results to demonstrate the applicability of the developed capability to a multigrid finite-element solver.« less

Towards Improved Finite Element Modelling of the Interaction of Elastic Waves with Complex Defect Geometries

NASA Astrophysics Data System (ADS)

Rajagopal, P.; Drozdz, M.; Lowe, M. J. S.

2009-03-01

A solution to the problem of improving the finite element (FE) modeling of elastic wave-defect interaction is sought by reconsidering the conventional opinion on meshing strategy. The standard approach using uniform square elements imposes severe limitations in representing complex defect outlines but this is thought to improve when the mesh is made finer. Free meshing algorithms available widely in commercial packages of late can cope with difficult features well but they are thought to cause scattering by the irregular mesh itself. This paper examines whether the benefits offered by free meshing in representing defects better outweigh the inaccuracies due to mesh scattering. If using the standard mesh, the questions whether mesh refinement leads to improved results and whether a practical strategy can be constructed are considered.

Fault diagnosis for wind turbine planetary ring gear via a meshing resonance based filtering algorithm.

PubMed

Wang, Tianyang; Chu, Fulei; Han, Qinkai

2017-03-01

Identifying the differences between the spectra or envelope spectra of a faulty signal and a healthy baseline signal is an efficient planetary gearbox local fault detection strategy. However, causes other than local faults can also generate the characteristic frequency of a ring gear fault; this may further affect the detection of a local fault. To address this issue, a new filtering algorithm based on the meshing resonance phenomenon is proposed. In detail, the raw signal is first decomposed into different frequency bands and levels. Then, a new meshing index and an MRgram are constructed to determine which bands belong to the meshing resonance frequency band. Furthermore, an optimal filter band is selected from this MRgram. Finally, the ring gear fault can be detected according to the envelope spectrum of the band-pass filtering result. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Directional Agglomeration Multigrid Techniques for High Reynolds Number Viscous Flow Solvers

NASA Technical Reports Server (NTRS)

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

A Generalized Framework for Constrained Design Optimization of General Supersonic Configurations Using Adjoint Based Sensitivity Derivatives

NASA Technical Reports Server (NTRS)

Karman, Steve L., Jr.

2011-01-01

The Aeronautics Research Mission Directorate (ARMD) sent out an NASA Research Announcement (NRA) for proposals soliciting research and technical development. The proposed research program was aimed at addressing the desired milestones and outcomes of ROA (ROA-2006) Subtopic A.4.1.1 Advanced Computational Methods. The second milestone, SUP.1.06.02 Robust, validated mesh adaptation and error quantification for near field Computational Fluid Dynamics (CFD), was addressed by the proposed research. Additional research utilizing the direct links to geometry through a CAD interface enabled by this work will allow for geometric constraints to be applied and address the final milestone, SUP2.07.06 Constrained low-drag supersonic aerodynamic design capability. The original product of the proposed research program was an integrated system of tools that can be used for the mesh mechanics required for rapid high fidelity analysis and for design of supersonic cruise vehicles. These Euler and Navier-Stokes volume grid manipulation tools were proposed to efficiently use parallel processing. The mesh adaptation provides a systematic approach for achieving demonstrated levels of accuracy in the solutions. NASA chose to fund only the mesh generation/adaptation portion of the proposal. So this report describes the completion of the proposed tasks for mesh creation, manipulation and adaptation as it pertains to sonic boom prediction of supersonic configurations.

Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation

NASA Technical Reports Server (NTRS)

Park, Michael A.

2002-01-01

Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can offer the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solving the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust mesh-adaptation procedure automatically terminates when the simulation is within a user specified error tolerance. This procedure for estimating and adapting to error in a functional is demonstrated for three-dimensional Euler problems. An adaptive mesh procedure that links to a Computer Aided Design (CAD) surface representation is demonstrated for wing, wing-body, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with ten times as many grid points.

PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes. Degree awarded by Colorado Univ.

NASA Technical Reports Server (NTRS)

Oliker, Leonid

1998-01-01

Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. By locally refining and coarsening the mesh to capture physical phenomena of interest, such procedures make standard computational methods more cost effective. Unfortunately, an efficient parallel implementation of these adaptive methods is rather difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. This requires significant communication at runtime, leading to idle processors and adversely affecting the total execution time. Nonetheless, it is generally thought that unstructured adaptive- grid techniques will constitute a significant fraction of future high-performance supercomputing. Various dynamic load balancing methods have been reported to date; however, most of them either lack a global view of loads across processors or do not apply their techniques to realistic large-scale applications.

An adaptive embedded mesh procedure for leading-edge vortex flows

NASA Technical Reports Server (NTRS)

Powell, Kenneth G.; Beer, Michael A.; Law, Glenn W.

1989-01-01

A procedure for solving the conical Euler equations on an adaptively refined mesh is presented, along with a method for determining which cells to refine. The solution procedure is a central-difference cell-vertex scheme. The adaptation procedure is made up of a parameter on which the refinement decision is based, and a method for choosing a threshold value of the parameter. The refinement parameter is a measure of mesh-convergence, constructed by comparison of locally coarse- and fine-grid solutions. The threshold for the refinement parameter is based on the curvature of the curve relating the number of cells flagged for refinement to the value of the refinement threshold. Results for three test cases are presented. The test problem is that of a delta wing at angle of attack in a supersonic free-stream. The resulting vortices and shocks are captured efficiently by the adaptive code.

PLUM: Parallel Load Balancing for Adaptive Unstructured Meshes

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Biswas, Rupak; Saini, Subhash (Technical Monitor)

1998-01-01

Mesh adaption is a powerful tool for efficient unstructured-grid computations but causes load imbalance among processors on a parallel machine. We present a novel method called PLUM to dynamically balance the processor workloads with a global view. This paper presents the implementation and integration of all major components within our dynamic load balancing strategy for adaptive grid calculations. Mesh adaption, repartitioning, processor assignment, and remapping are critical components of the framework that must be accomplished rapidly and efficiently so as not to cause a significant overhead to the numerical simulation. A data redistribution model is also presented that predicts the remapping cost on the SP2. This model is required to determine whether the gain from a balanced workload distribution offsets the cost of data movement. Results presented in this paper demonstrate that PLUM is an effective dynamic load balancing strategy which remains viable on a large number of processors.

Spatial adaptation procedures on tetrahedral meshes for unsteady aerodynamic flow calculations

NASA Technical Reports Server (NTRS)

Rausch, Russ D.; Batina, John T.; Yang, Henry T. Y.

1993-01-01

Spatial adaptation procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaptation procedures were developed and implemented within a three-dimensional, unstructured-grid, upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. A detailed description of the enrichment and coarsening procedures are presented and comparisons with experimental data for an ONERA M6 wing and an exact solution for a shock-tube problem are presented to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady results, obtained using spatial adaptation procedures, are shown to be of high spatial accuracy, primarily in that discontinuities such as shock waves are captured very sharply.

Spatial adaptation procedures on tetrahedral meshes for unsteady aerodynamic flow calculations

NASA Technical Reports Server (NTRS)

Rausch, Russ D.; Batina, John T.; Yang, Henry T. Y.

1993-01-01

Spatial adaptation procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaptation procedures were developed and implemented within a three-dimensional, unstructured-grid, upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. The paper gives a detailed description of the enrichment and coarsening procedures and presents comparisons with experimental data for an ONERA M6 wing and an exact solution for a shock-tube problem to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady results, obtained using spatial adaptation procedures, are shown to be of high spatial accuracy, primarily in that discontinuities such as shock waves are captured very sharply.

Multi-resolution Shape Analysis via Non-Euclidean Wavelets: Applications to Mesh Segmentation and Surface Alignment Problems.

PubMed

Kim, Won Hwa; Chung, Moo K; Singh, Vikas

2013-01-01

The analysis of 3-D shape meshes is a fundamental problem in computer vision, graphics, and medical imaging. Frequently, the needs of the application require that our analysis take a multi-resolution view of the shape's local and global topology, and that the solution is consistent across multiple scales. Unfortunately, the preferred mathematical construct which offers this behavior in classical image/signal processing, Wavelets, is no longer applicable in this general setting (data with non-uniform topology). In particular, the traditional definition does not allow writing out an expansion for graphs that do not correspond to the uniformly sampled lattice (e.g., images). In this paper, we adapt recent results in harmonic analysis, to derive Non-Euclidean Wavelets based algorithms for a range of shape analysis problems in vision and medical imaging. We show how descriptors derived from the dual domain representation offer native multi-resolution behavior for characterizing local/global topology around vertices. With only minor modifications, the framework yields a method for extracting interest/key points from shapes, a surprisingly simple algorithm for 3-D shape segmentation (competitive with state of the art), and a method for surface alignment (without landmarks). We give an extensive set of comparison results on a large shape segmentation benchmark and derive a uniqueness theorem for the surface alignment problem.

An adaptive simplex cut-cell method for high-order discontinuous Galerkin discretizations of elliptic interface problems and conjugate heat transfer problems

NASA Astrophysics Data System (ADS)

Sun, Huafei; Darmofal, David L.

2014-12-01

In this paper we propose a new high-order solution framework for interface problems on non-interface-conforming meshes. The framework consists of a discontinuous Galerkin (DG) discretization, a simplex cut-cell technique, and an output-based adaptive scheme. We first present a DG discretization with a dual-consistent output evaluation for elliptic interface problems on interface-conforming meshes, and then extend the method to handle multi-physics interface problems, in particular conjugate heat transfer (CHT) problems. The method is then applied to non-interface-conforming meshes using a cut-cell technique, where the interface definition is completely separate from the mesh generation process. No assumption is made on the interface shape (other than Lipschitz continuity). We then equip our strategy with an output-based adaptive scheme for an accurate output prediction. Through numerical examples, we demonstrate high-order convergence for elliptic interface problems and CHT problems with both smooth and non-smooth interface shapes.

Data Assimilation Methods on a Non-conservative Adaptive Mesh

NASA Astrophysics Data System (ADS)

Guider, Colin Thomas; Rabatel, Matthias; Carrassi, Alberto; Jones, Christopher K. R. T.

2017-04-01

Adaptive mesh methods are used to model a wide variety of physical phenomena. Some of these models, in particular those of sea ice movement, are particularly interesting in that they use a remeshing process to remove and insert mesh points at various points in their evolution. This presents a challenge in developing compatible data assimilation schemes, as the dimension of the state space we wish to estimate can change over time when these remeshings occur. In this work, we first describe a remeshing scheme for an adaptive mesh in one dimension. We then develop advanced data assimilation methods that are appropriate for such a moving and remeshed grid. We hope to extend these techniques to two-dimensional models, like the Lagrangian sea ice model neXtSIM te{ns}. \\bibitem{ns} P. Rampal, S. Bouillon, E. Ólason, and M. Morlighem. ne{X}t{SIM}: a new {L}agrangian sea ice model. {The Cryosphere}, 10 (3): 1055-1073, 2016.

Improved ALE mesh velocities for complex flows

DOE PAGES

Bakosi, Jozsef; Waltz, Jacob I.; Morgan, Nathaniel Ray

2017-05-31

A key choice in the development of arbitrary Lagrangian-Eulerian solution algorithms is how to move the computational mesh. The most common approaches are smoothing and relaxation techniques, or to compute a mesh velocity field that produces smooth mesh displacements. We present a method in which the mesh velocity is specified by the irrotational component of the fluid velocity as computed from a Helmholtz decomposition, and excess compression of mesh cells is treated through a noniterative, local spring-force model. This approach allows distinct and separate control over rotational and translational modes. In conclusion, the utility of the new mesh motion algorithmmore » is demonstrated on a number of 3D test problems, including problems that involve both shocks and significant amounts of vorticity.« less

Galerkin finite difference Laplacian operators on isolated unstructured triangular meshes by linear combinations

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.

1990-01-01

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formulae in Cartesian coordinates for the Laplacian operator on isolated unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator along with linear combinations of the residual equations are used to develop the algorithm. The algorithm was tested for a wide variety of unstructured meshes and found to give satisfactory results.

Ray tracing through a hexahedral mesh in HADES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henderson, G L; Aufderheide, M B

In this paper we describe a new ray tracing method targeted for inclusion in HADES. The algorithm tracks rays through three-dimensional tetrakis hexahedral mesh objects, like those used by the ARES code to model inertial confinement experiments.

Front tracking based modeling of the solid grain growth on the adaptive control volume grid

NASA Astrophysics Data System (ADS)

Seredyński, Mirosław; Łapka, Piotr

2017-07-01

The paper presents the micro-scale model of unconstrained solidification of the grain immersed in under-cooled liquid, based on the front tracking approach. For this length scale, the interface tracked through the domain is meant as the solid-liquid boundary. To prevent generation of huge meshes the energy transport equation is discretized on the adaptive control volume (c.v.) mesh. The coupling of dynamically changing mesh and moving front position is addressed. Preliminary results of simulation of a test case, the growth of single grain, are presented and discussed.

Laser Ray Tracing in a Parallel Arbitrary Lagrangian-Eulerian Adaptive Mesh Refinement Hydrocode

DOE Office of Scientific and Technical Information (OSTI.GOV)

Masters, N D; Kaiser, T B; Anderson, R W

2009-09-28

ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray-tracing in ALE-AMR. We present the equations of laser ray tracing, our approach to efficient traversal of the adaptive mesh hierarchy in which we propagate computational rays through a virtual composite mesh consisting of the finest resolution representation of the modeled space, and anticipate simulations that will be compared to experiments for code validation.

Time-dependent grid adaptation for meshes of triangles and tetrahedra

NASA Technical Reports Server (NTRS)

Rausch, Russ D.

1993-01-01

This paper presents in viewgraph form a method of optimizing grid generation for unsteady CFD flow calculations that distributes the numerical error evenly throughout the mesh. Adaptive meshing is used to locally enrich in regions of relatively large errors and to locally coarsen in regions of relatively small errors. The enrichment/coarsening procedures are robust for isotropic cells; however, enrichment of high aspect ratio cells may fail near boundary surfaces with relatively large curvature. The enrichment indicator worked well for the cases shown, but in general requires user supervision for a more efficient solution.

Controlling the error on target motion through real-time mesh adaptation: Applications to deep brain stimulation.

PubMed

Bui, Huu Phuoc; Tomar, Satyendra; Courtecuisse, Hadrien; Audette, Michel; Cotin, Stéphane; Bordas, Stéphane P A

2018-05-01

An error-controlled mesh refinement procedure for needle insertion simulations is presented. As an example, the procedure is applied for simulations of electrode implantation for deep brain stimulation. We take into account the brain shift phenomena occurring when a craniotomy is performed. We observe that the error in the computation of the displacement and stress fields is localised around the needle tip and the needle shaft during needle insertion simulation. By suitably and adaptively refining the mesh in this region, our approach enables to control, and thus to reduce, the error whilst maintaining a coarser mesh in other parts of the domain. Through academic and practical examples we demonstrate that our adaptive approach, as compared with a uniform coarse mesh, increases the accuracy of the displacement and stress fields around the needle shaft and, while for a given accuracy, saves computational time with respect to a uniform finer mesh. This facilitates real-time simulations. The proposed methodology has direct implications in increasing the accuracy, and controlling the computational expense of the simulation of percutaneous procedures such as biopsy, brachytherapy, regional anaesthesia, or cryotherapy. Moreover, the proposed approach can be helpful in the development of robotic surgeries because the simulation taking place in the control loop of a robot needs to be accurate, and to occur in real time. Copyright © 2018 John Wiley & Sons, Ltd.

A Structured Grid Based Solution-Adaptive Technique for Complex Separated Flows

NASA Technical Reports Server (NTRS)

Thornburg, Hugh; Soni, Bharat K.; Kishore, Boyalakuntla; Yu, Robert

1996-01-01

The objective of this work was to enhance the predictive capability of widely used computational fluid dynamic (CFD) codes through the use of solution adaptive gridding. Most problems of engineering interest involve multi-block grids and widely disparate length scales. Hence, it is desirable that the adaptive grid feature detection algorithm be developed to recognize flow structures of different type as well as differing intensity, and adequately address scaling and normalization across blocks. In order to study the accuracy and efficiency improvements due to the grid adaptation, it is necessary to quantify grid size and distribution requirements as well as computational times of non-adapted solutions. Flow fields about launch vehicles of practical interest often involve supersonic freestream conditions at angle of attack exhibiting large scale separate vortical flow, vortex-vortex and vortex-surface interactions, separated shear layers and multiple shocks of different intensity. In this work, a weight function and an associated mesh redistribution procedure is presented which detects and resolves these features without user intervention. Particular emphasis has been placed upon accurate resolution of expansion regions and boundary layers. Flow past a wedge at Mach=2.0 is used to illustrate the enhanced detection capabilities of this newly developed weight function.

Meshing of a Spiral Bevel Gearset with 3D Finite Element Analysis

NASA Technical Reports Server (NTRS)

Bibel, George D.; Handschuh, Robert

1996-01-01

Recent advances in spiral bevel gear geometry and finite element technology make it practical to conduct a structural analysis and analytically roll the gearset through mesh. With the advent of user specific programming linked to 3D solid modelers and mesh generators, model generation has become greatly automated. Contact algorithms available in general purpose finite element codes eliminate the need for the use and alignment of gap elements. Once the gearset is placed in mesh, user subroutines attached to the FE code easily roll the gearset through mesh. The method is described in detail. Preliminary results for a gearset segment showing the progression of the contact lineload is given as the gears roll through mesh.

Dynamic Load Balancing for Adaptive Computations on Distributed-Memory Machines

NASA Technical Reports Server (NTRS)

1999-01-01

Dynamic load balancing is central to adaptive mesh-based computations on large-scale parallel computers. The principal investigator has investigated various issues on the dynamic load balancing problem under NASA JOVE and JAG rants. The major accomplishments of the project are two graph partitioning algorithms and a load balancing framework. The S-HARP dynamic graph partitioner is known to be the fastest among the known dynamic graph partitioners to date. It can partition a graph of over 100,000 vertices in 0.25 seconds on a 64- processor Cray T3E distributed-memory multiprocessor while maintaining the scalability of over 16-fold speedup. Other known and widely used dynamic graph partitioners take over a second or two while giving low scalability of a few fold speedup on 64 processors. These results have been published in journals and peer-reviewed flagship conferences.

A charge- and energy-conserving implicit, electrostatic particle-in-cell algorithm on mapped computational meshes

NASA Astrophysics Data System (ADS)

Chacón, L.; Chen, G.; Barnes, D. C.

2013-01-01

We describe the extension of the recent charge- and energy-conserving one-dimensional electrostatic particle-in-cell algorithm in Ref. [G. Chen, L. Chacón, D.C. Barnes, An energy- and charge-conserving, implicit electrostatic particle-in-cell algorithm, Journal of Computational Physics 230 (2011) 7018-7036] to mapped (body-fitted) computational meshes. The approach maintains exact charge and energy conservation properties. Key to the algorithm is a hybrid push, where particle positions are updated in logical space, while velocities are updated in physical space. The effectiveness of the approach is demonstrated with a challenging numerical test case, the ion acoustic shock wave. The generalization of the approach to multiple dimensions is outlined.

Adaptive mesh strategies for the spectral element method

NASA Technical Reports Server (NTRS)

Mavriplis, Catherine

1992-01-01

An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility, and general capabilities for high order spectral methods.

Feature engineering for MEDLINE citation categorization with MeSH.

PubMed

Jimeno Yepes, Antonio Jose; Plaza, Laura; Carrillo-de-Albornoz, Jorge; Mork, James G; Aronson, Alan R

2015-04-08

Research in biomedical text categorization has mostly used the bag-of-words representation. Other more sophisticated representations of text based on syntactic, semantic and argumentative properties have been less studied. In this paper, we evaluate the impact of different text representations of biomedical texts as features for reproducing the MeSH annotations of some of the most frequent MeSH headings. In addition to unigrams and bigrams, these features include noun phrases, citation meta-data, citation structure, and semantic annotation of the citations. Traditional features like unigrams and bigrams exhibit strong performance compared to other feature sets. Little or no improvement is obtained when using meta-data or citation structure. Noun phrases are too sparse and thus have lower performance compared to more traditional features. Conceptual annotation of the texts by MetaMap shows similar performance compared to unigrams, but adding concepts from the UMLS taxonomy does not improve the performance of using only mapped concepts. The combination of all the features performs largely better than any individual feature set considered. In addition, this combination improves the performance of a state-of-the-art MeSH indexer. Concerning the machine learning algorithms, we find that those that are more resilient to class imbalance largely obtain better performance. We conclude that even though traditional features such as unigrams and bigrams have strong performance compared to other features, it is possible to combine them to effectively improve the performance of the bag-of-words representation. We have also found that the combination of the learning algorithm and feature sets has an influence in the overall performance of the system. Moreover, using learning algorithms resilient to class imbalance largely improves performance. However, when using a large set of features, consideration needs to be taken with algorithms due to the risk of over-fitting. Specific combinations of learning algorithms and features for individual MeSH headings could further increase the performance of an indexing system.

Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

NASA Technical Reports Server (NTRS)

Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

2013-01-01

This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

A 3D global-to-local deformable mesh model based registration and anatomy-constrained segmentation method for image guided prostate radiotherapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou Jinghao; Kim, Sung; Jabbour, Salma

2010-03-15

Purpose: In the external beam radiation treatment of prostate cancers, successful implementation of adaptive radiotherapy and conformal radiation dose delivery is highly dependent on precise and expeditious segmentation and registration of the prostate volume between the simulation and the treatment images. The purpose of this study is to develop a novel, fast, and accurate segmentation and registration method to increase the computational efficiency to meet the restricted clinical treatment time requirement in image guided radiotherapy. Methods: The method developed in this study used soft tissues to capture the transformation between the 3D planning CT (pCT) images and 3D cone-beam CTmore » (CBCT) treatment images. The method incorporated a global-to-local deformable mesh model based registration framework as well as an automatic anatomy-constrained robust active shape model (ACRASM) based segmentation algorithm in the 3D CBCT images. The global registration was based on the mutual information method, and the local registration was to minimize the Euclidian distance of the corresponding nodal points from the global transformation of deformable mesh models, which implicitly used the information of the segmented target volume. The method was applied on six data sets of prostate cancer patients. Target volumes delineated by the same radiation oncologist on the pCT and CBCT were chosen as the benchmarks and were compared to the segmented and registered results. The distance-based and the volume-based estimators were used to quantitatively evaluate the results of segmentation and registration. Results: The ACRASM segmentation algorithm was compared to the original active shape model (ASM) algorithm by evaluating the values of the distance-based estimators. With respect to the corresponding benchmarks, the mean distance ranged from -0.85 to 0.84 mm for ACRASM and from -1.44 to 1.17 mm for ASM. The mean absolute distance ranged from 1.77 to 3.07 mm for ACRASM and from 2.45 to 6.54 mm for ASM. The volume overlap ratio ranged from 79% to 91% for ACRASM and from 44% to 80% for ASM. These data demonstrated that the segmentation results of ACRASM were in better agreement with the corresponding benchmarks than those of ASM. The developed registration algorithm was quantitatively evaluated by comparing the registered target volumes from the pCT to the benchmarks on the CBCT. The mean distance and the root mean square error ranged from 0.38 to 2.2 mm and from 0.45 to 2.36 mm, respectively, between the CBCT images and the registered pCT. The mean overlap ratio of the prostate volumes ranged from 85.2% to 95% after registration. The average time of the ACRASM-based segmentation was under 1 min. The average time of the global transformation was from 2 to 4 min on two 3D volumes and the average time of the local transformation was from 20 to 34 s on two deformable superquadrics mesh models. Conclusions: A novel and fast segmentation and deformable registration method was developed to capture the transformation between the planning and treatment images for external beam radiotherapy of prostate cancers. This method increases the computational efficiency and may provide foundation to achieve real time adaptive radiotherapy.« less

Planetary Transmission Diagnostics

NASA Technical Reports Server (NTRS)

Lewicki, David G. (Technical Monitor); Samuel, Paul D.; Conroy, Joseph K.; Pines, Darryll J.

2004-01-01

This report presents a methodology for detecting and diagnosing gear faults in the planetary stage of a helicopter transmission. This diagnostic technique is based on the constrained adaptive lifting algorithm. The lifting scheme, developed by Wim Sweldens of Bell Labs, is a time domain, prediction-error realization of the wavelet transform that allows for greater flexibility in the construction of wavelet bases. Classic lifting analyzes a given signal using wavelets derived from a single fundamental basis function. A number of researchers have proposed techniques for adding adaptivity to the lifting scheme, allowing the transform to choose from a set of fundamental bases the basis that best fits the signal. This characteristic is desirable for gear diagnostics as it allows the technique to tailor itself to a specific transmission by selecting a set of wavelets that best represent vibration signals obtained while the gearbox is operating under healthy-state conditions. However, constraints on certain basis characteristics are necessary to enhance the detection of local wave-form changes caused by certain types of gear damage. The proposed methodology analyzes individual tooth-mesh waveforms from a healthy-state gearbox vibration signal that was generated using the vibration separation (synchronous signal-averaging) algorithm. Each waveform is separated into analysis domains using zeros of its slope and curvature. The bases selected in each analysis domain are chosen to minimize the prediction error, and constrained to have the same-sign local slope and curvature as the original signal. The resulting set of bases is used to analyze future-state vibration signals and the lifting prediction error is inspected. The constraints allow the transform to effectively adapt to global amplitude changes, yielding small prediction errors. However, local wave-form changes associated with certain types of gear damage are poorly adapted, causing a significant change in the prediction error. The constrained adaptive lifting diagnostic algorithm is validated using data collected from the University of Maryland Transmission Test Rig and the results are discussed.

Crack Growth Prediction Methodology for Multi-Site Damage: Layered Analysis and Growth During Plasticity

NASA Technical Reports Server (NTRS)

James, Mark Anthony

1999-01-01

A finite element program has been developed to perform quasi-static, elastic-plastic crack growth simulations. The model provides a general framework for mixed-mode I/II elastic-plastic fracture analysis using small strain assumptions and plane stress, plane strain, and axisymmetric finite elements. Cracks are modeled explicitly in the mesh. As the cracks propagate, automatic remeshing algorithms delete the mesh local to the crack tip, extend the crack, and build a new mesh around the new tip. State variable mapping algorithms transfer stresses and displacements from the old mesh to the new mesh. The von Mises material model is implemented in the context of a non-linear Newton solution scheme. The fracture criterion is the critical crack tip opening displacement, and crack direction is predicted by the maximum tensile stress criterion at the crack tip. The implementation can accommodate multiple curving and interacting cracks. An additional fracture algorithm based on nodal release can be used to simulate fracture along a horizontal plane of symmetry. A core of plane strain elements can be used with the nodal release algorithm to simulate the triaxial state of stress near the crack tip. Verification and validation studies compare analysis results with experimental data and published three-dimensional analysis results. Fracture predictions using nodal release for compact tension, middle-crack tension, and multi-site damage test specimens produced accurate results for residual strength and link-up loads. Curving crack predictions using remeshing/mapping were compared with experimental data for an Arcan mixed-mode specimen. Loading angles from 0 degrees to 90 degrees were analyzed. The maximum tensile stress criterion was able to predict the crack direction and path for all loading angles in which the material failed in tension. Residual strength was also accurately predicted for these cases.

3D level set methods for evolving fronts on tetrahedral meshes with adaptive mesh refinement

DOE PAGES

Morgan, Nathaniel Ray; Waltz, Jacob I.

2017-03-02

The level set method is commonly used to model dynamically evolving fronts and interfaces. In this work, we present new methods for evolving fronts with a specified velocity field or in the surface normal direction on 3D unstructured tetrahedral meshes with adaptive mesh refinement (AMR). The level set field is located at the nodes of the tetrahedral cells and is evolved using new upwind discretizations of Hamilton–Jacobi equations combined with a Runge–Kutta method for temporal integration. The level set field is periodically reinitialized to a signed distance function using an iterative approach with a new upwind gradient. We discuss themore » details of these level set and reinitialization methods. Results from a range of numerical test problems are presented.« less

Continuum Vlasov Simulation in Four Phase-space Dimensions

NASA Astrophysics Data System (ADS)

Cohen, B. I.; Banks, J. W.; Berger, R. L.; Hittinger, J. A.; Brunner, S.

2010-11-01

In the VALHALLA project, we are developing scalable algorithms for the continuum solution of the Vlasov-Maxwell equations in two spatial and two velocity dimensions. We use fourth-order temporal and spatial discretizations of the conservative form of the equations and a finite-volume representation to enable adaptive mesh refinement and nonlinear oscillation control [1]. The code has been implemented with and without adaptive mesh refinement, and with electromagnetic and electrostatic field solvers. A goal is to study the efficacy of continuum Vlasov simulations in four phase-space dimensions for laser-plasma interactions. We have verified the code in examples such as the two-stream instability, the weak beam-plasma instability, Landau damping, electron plasma waves with electron trapping and nonlinear frequency shifts [2]^ extended from 1D to 2D propagation, and light wave propagation.^ We will report progress on code development, computational methods, and physics applications. This work was performed under the auspices of the U.S. DOE by LLNL under contract no. DE-AC52-07NA27344. This work was funded by the Lab. Dir. Res. and Dev. Prog. at LLNL under project tracking code 08-ERD-031. [1] J.W. Banks and J.A.F. Hittinger, to appear in IEEE Trans. Plas. Sci. (Sept., 2010). [2] G.J. Morales and T.M. O'Neil, Phys. Rev. Lett. 28,417 (1972); R. L. Dewar, Phys. Fluids 15,712 (1972).

Adaptive finite volume methods with well-balanced Riemann solvers for modeling floods in rugged terrain: Application to the Malpasset dam-break flood (France, 1959)

USGS Publications Warehouse

George, D.L.

2011-01-01

The simulation of advancing flood waves over rugged topography, by solving the shallow-water equations with well-balanced high-resolution finite volume methods and block-structured dynamic adaptive mesh refinement (AMR), is described and validated in this paper. The efficiency of block-structured AMR makes large-scale problems tractable, and allows the use of accurate and stable methods developed for solving general hyperbolic problems on quadrilateral grids. Features indicative of flooding in rugged terrain, such as advancing wet-dry fronts and non-stationary steady states due to balanced source terms from variable topography, present unique challenges and require modifications such as special Riemann solvers. A well-balanced Riemann solver for inundation and general (non-stationary) flow over topography is tested in this context. The difficulties of modeling floods in rugged terrain, and the rationale for and efficacy of using AMR and well-balanced methods, are presented. The algorithms are validated by simulating the Malpasset dam-break flood (France, 1959), which has served as a benchmark problem previously. Historical field data, laboratory model data and other numerical simulation results (computed on static fitted meshes) are shown for comparison. The methods are implemented in GEOCLAW, a subset of the open-source CLAWPACK software. All the software is freely available at. Published in 2010 by John Wiley & Sons, Ltd.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen, Z; Greskovich, J; Xia, P

Purpose: To generate virtual phantoms with clinically relevant deformation and use them to objectively evaluate geometric and dosimetric uncertainties of deformable image registration (DIR) algorithms. Methods: Ten lung cancer patients undergoing adaptive 3DCRT planning were selected. For each patient, a pair of planning CT (pCT) and replanning CT (rCT) were used as the basis for virtual phantom generation. Manually adjusted meshes were created for selected ROIs (e.g. PTV, lungs, spinal cord, esophagus, and heart) on pCT and rCT. The mesh vertices were input into a thin-plate spline algorithm to generate a reference displacement vector field (DVF). The reference DVF wasmore » used to deform pCT to generate a simulated replanning CT (srCT) that was closely matched to rCT. Three DIR algorithms (Demons, B-Spline, and intensity-based) were applied to these ten virtual phantoms. The images, ROIs, and doses were mapped from pCT to srCT using the DVFs computed by these three DIRs and compared to those mapped using the reference DVF. Results: The average Dice coefficients for selected ROIs were from 0.85 to 0.96 for Demons, from 0.86 to 0.97 for intensity-based, and from 0.76 to 0.95 for B-Spline. The average Hausdorff distances for selected ROIs were from 2.2 to 5.4 mm for Demons, from 2.3 to 6.8 mm for intensity-based, and from 2.4 to 11.4 mm for B-Spline. The average absolute dose errors for selected ROIs were from 0.2 to 0.6 Gy for Demons, from 0.1 to 0.5 Gy for intensity-based, and from 0.5 to 1.5 Gy for B-Spline. Conclusion: Virtual phantoms were modeled after patients with lung cancer and were clinically relevant for adaptive radiotherapy treatment replanning. Virtual phantoms with known DVFs serve as references and can provide a fair comparison when evaluating different DIRs. Demons and intensity-based DIRs were shown to have smaller geometric and dosimetric uncertainties than B-Spline. Z Shen: None; K Bzdusek: an employee of Philips Healthcare; J Greskovich: None; P Xia: received research grants from Philips Healthcare and Siemens Healthcare.« less

Spherical Harmonic Decomposition of Gravitational Waves Across Mesh Refinement Boundaries

NASA Technical Reports Server (NTRS)

Fiske, David R.; Baker, John; vanMeter, James R.; Centrella, Joan M.

2005-01-01

We evolve a linearized (Teukolsky) solution of the Einstein equations with a non-linear Einstein solver. Using this testbed, we are able to show that such gravitational waves, defined by the Weyl scalars in the Newman-Penrose formalism, propagate faithfully across mesh refinement boundaries, and use, for the first time to our knowledge, a novel algorithm due to Misner to compute spherical harmonic components of our waveforms. We show that the algorithm performs extremely well, even when the extraction sphere intersects refinement boundaries.

A discontinuous Galerkin method with a bound preserving limiter for the advection of non-diffusive fields in solid Earth geodynamics

NASA Astrophysics Data System (ADS)

He, Ying; Puckett, Elbridge Gerry; Billen, Magali I.

2017-02-01

Mineral composition has a strong effect on the properties of rocks and is an essentially non-diffusive property in the context of large-scale mantle convection. Due to the non-diffusive nature and the origin of compositionally distinct regions in the Earth the boundaries between distinct regions can be nearly discontinuous. While there are different methods for tracking rock composition in numerical simulations of mantle convection, one must consider trade-offs between computational cost, accuracy or ease of implementation when choosing an appropriate method. Existing methods can be computationally expensive, cause over-/undershoots, smear sharp boundaries, or are not easily adapted to tracking multiple compositional fields. Here we present a Discontinuous Galerkin method with a bound preserving limiter (abbreviated as DG-BP) using a second order Runge-Kutta, strong stability-preserving time discretization method for the advection of non-diffusive fields. First, we show that the method is bound-preserving for a point-wise divergence free flow (e.g., a prescribed circular flow in a box). However, using standard adaptive mesh refinement (AMR) there is an over-shoot error (2%) because the cell average is not preserved during mesh coarsening. The effectiveness of the algorithm for convection-dominated flows is demonstrated using the falling box problem. We find that the DG-BP method maintains sharper compositional boundaries (3-5 elements) as compared to an artificial entropy-viscosity method (6-15 elements), although the over-/undershoot errors are similar. When used with AMR the DG-BP method results in fewer degrees of freedom due to smaller regions of mesh refinement in the neighborhood of the discontinuity. However, using Taylor-Hood elements and a uniform mesh there is an over-/undershoot error on the order of 0.0001%, but this error increases to 0.01-0.10% when using AMR. Therefore, for research problems in which a continuous field method is desired the DG-BP method can provide improved tracking of sharp compositional boundaries. For applications in which strict bound-preserving behavior is desired, use of an element that provides a divergence-free condition on the weak formulation (e.g., Raviart-Thomas) and an improved mesh coarsening scheme for the AMR are required.

Streaming simplification of tetrahedral meshes.

PubMed

Vo, Huy T; Callahan, Steven P; Lindstrom, Peter; Pascucci, Valerio; Silva, Cláudio T

2007-01-01

Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can accomplish real-time visualization necessary for scientific analysis. We propose a two-step approach for streaming simplification of large tetrahedral meshes. Our algorithm arranges the data on disk in a streaming, I/O-efficient format that allows coherent access to the tetrahedral cells. A quadric-based simplification is sequentially performed on small portions of the mesh in-core. Our output is a coherent streaming mesh which facilitates future processing. Our technique is fast, produces high quality approximations, and operates out-of-core to process meshes too large for main memory.

Robust hashing for 3D models

NASA Astrophysics Data System (ADS)

Berchtold, Waldemar; Schäfer, Marcel; Rettig, Michael; Steinebach, Martin

2014-02-01

3D models and applications are of utmost interest in both science and industry. With the increment of their usage, their number and thereby the challenge to correctly identify them increases. Content identification is commonly done by cryptographic hashes. However, they fail as a solution in application scenarios such as computer aided design (CAD), scientific visualization or video games, because even the smallest alteration of the 3D model, e.g. conversion or compression operations, massively changes the cryptographic hash as well. Therefore, this work presents a robust hashing algorithm for 3D mesh data. The algorithm applies several different bit extraction methods. They are built to resist desired alterations of the model as well as malicious attacks intending to prevent correct allocation. The different bit extraction methods are tested against each other and, as far as possible, the hashing algorithm is compared to the state of the art. The parameters tested are robustness, security and runtime performance as well as False Acceptance Rate (FAR) and False Rejection Rate (FRR), also the probability calculation of hash collision is included. The introduced hashing algorithm is kept adaptive e.g. in hash length, to serve as a proper tool for all applications in practice.

A Finite Element Method to Correct Deformable Image Registration Errors in Low-Contrast Regions

PubMed Central

Zhong, Hualiang; Kim, Jinkoo; Li, Haisen; Nurushev, Teamour; Movsas, Benjamin; Chetty, Indrin J.

2012-01-01

Image-guided adaptive radiotherapy requires deformable image registration to map radiation dose back and forth between images. The purpose of this study is to develop a novel method to improve the accuracy of an intensity-based image registration algorithm in low-contrast regions. A computational framework has been developed in this study to improve the quality of the “demons” registration. For each voxel in the registration’s target image, the standard deviation of image intensity in a neighborhood of this voxel was calculated. A mask for high-contrast regions was generated based on their standard deviations. In the masked regions, a tetrahedral mesh was refined recursively so that a sufficient number of tetrahedral nodes in these regions can be selected as driving nodes. An elastic system driven by the displacements of the selected nodes was formulated using a finite element method (FEM) and implemented on the refined mesh. The displacements of these driving nodes were generated with the “demons” algorithm. The solution of the system was derived using a conjugated gradient method, and interpolated to generate a displacement vector field for the registered images. The FEM correction method was compared with the “demons” algorithm on the CT images of lung and prostate patients. The performance of the FEM correction relating to the “demons” registration was analyzed based on the physical property of their deformation maps, and quantitatively evaluated through a benchmark model developed specifically for this study. Compared to the benchmark model, the “demons” registration has the maximum error of 1.2 cm, which can be corrected by the FEM method to 0.4 cm, and the average error of the “demons” registration is reduced from 0.17 cm to 0.11 cm. For the CT images of lung and prostate patients, the deformation maps generated by the “demons” algorithm were found unrealistic at several places. In these places, the displacement differences between the “demons” registrations and their FEM corrections were found in the range of 0.4 cm and 1.1cm. The mesh refinement and FEM simulation were implemented in a single thread application which requires about 45 minutes of computation time on a 2.6 GH computer. This study has demonstrated that the finite element method can be integrated with intensity-based image registration algorithms to improve their registration accuracy, especially in low-contrast regions. PMID:22581269

New Software Developments for Quality Mesh Generation and Optimization from Biomedical Imaging Data

PubMed Central

Yu, Zeyun; Wang, Jun; Gao, Zhanheng; Xu, Ming; Hoshijima, Masahiko

2013-01-01

In this paper we present a new software toolkit for generating and optimizing surface and volumetric meshes from three-dimensional (3D) biomedical imaging data, targeted at image-based finite element analysis of some biomedical activities in a single material domain. Our toolkit includes a series of geometric processing algorithms including surface re-meshing and quality-guaranteed tetrahedral mesh generation and optimization. All methods described have been encapsulated into a user-friendly graphical interface for easy manipulation and informative visualization of biomedical images and mesh models. Numerous examples are presented to demonstrate the effectiveness and efficiency of the described methods and toolkit. PMID:24252469

Method for generating a mesh representation of a region characterized by a trunk and a branch thereon

DOEpatents

Shepherd, Jason [Albuquerque, NM; Mitchell, Scott A [Albuquerque, NM; Jankovich, Steven R [Anaheim, CA; Benzley, Steven E [Provo, UT

2007-05-15

The present invention provides a meshing method, called grafting, that lifts the prior art constraint on abutting surfaces, including surfaces that are linking, source/target, or other types of surfaces of the trunk volume. The grafting method locally modifies the structured mesh of the linking surfaces allowing the mesh to conform to additional surface features. Thus, the grafting method can provide a transition between multiple sweep directions extending sweeping algorithms to 23/4-D solids. The method is also suitable for use with non-sweepable volumes; the method provides a transition between meshes generated by methods other than sweeping as well.

Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

NASA Technical Reports Server (NTRS)

Woodard, Paul R.; Batina, John T.; Yang, Henry T. Y.

1992-01-01

Quality assessment procedures are described for two-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate accuracy of an implicit upwind Euler solution algorithm.

Mesh Generation via Local Bisection Refinement of Triangulated Grids

DTIC Science & Technology

2015-06-01

Science and Technology Organisation DSTO–TR–3095 ABSTRACT This report provides a comprehensive implementation of an unstructured mesh generation method...and Technology Organisation 506 Lorimer St, Fishermans Bend, Victoria 3207, Australia Telephone: 1300 333 362 Facsimile: (03) 9626 7999 c© Commonwealth...their behaviour is critically linked to Maubach’s method and the data structures N and T . The top- level mesh refinement algorithm is also presented

Unstructured mesh methods for CFD

NASA Technical Reports Server (NTRS)

Peraire, J.; Morgan, K.; Peiro, J.

1990-01-01

Mesh generation methods for Computational Fluid Dynamics (CFD) are outlined. Geometric modeling is discussed. An advancing front method is described. Flow past a two engine Falcon aeroplane is studied. An algorithm and associated data structure called the alternating digital tree, which efficiently solves the geometric searching problem is described. The computation of an initial approximation to the steady state solution of a given poblem is described. Mesh generation for transient flows is described.

A grid generation and flow solution method for the Euler equations on unstructured grids

NASA Astrophysics Data System (ADS)

Anderson, W. Kyle

1994-01-01

A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.

A Cartesian cut cell method for rarefied flow simulations around moving obstacles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dechristé, G., E-mail: Guillaume.Dechriste@math.u-bordeaux1.fr; CNRS, IMB, UMR 5251, F-33400 Talence; Mieussens, L., E-mail: Luc.Mieussens@math.u-bordeaux1.fr

2016-06-01

For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian cells and various kinds of cut cells by the same algorithm, with no need to identify the specific shape of each cut cell. This makes the implementation quite simple, and allows a direct extension to 3D problems. Such simulations are also made possible by using an adaptive mesh refinement technique and a hybrid parallel implementation. This is illustrated by several test cases, including amore » 3D unsteady simulation of the Crookes radiometer.« less

ALEGRA -- A massively parallel h-adaptive code for solid dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Summers, R.M.; Wong, M.K.; Boucheron, E.A.

1997-12-31

ALEGRA is a multi-material, arbitrary-Lagrangian-Eulerian (ALE) code for solid dynamics designed to run on massively parallel (MP) computers. It combines the features of modern Eulerian shock codes, such as CTH, with modern Lagrangian structural analysis codes using an unstructured grid. ALEGRA is being developed for use on the teraflop supercomputers to conduct advanced three-dimensional (3D) simulations of shock phenomena important to a variety of systems. ALEGRA was designed with the Single Program Multiple Data (SPMD) paradigm, in which the mesh is decomposed into sub-meshes so that each processor gets a single sub-mesh with approximately the same number of elements. Usingmore » this approach the authors have been able to produce a single code that can scale from one processor to thousands of processors. A current major effort is to develop efficient, high precision simulation capabilities for ALEGRA, without the computational cost of using a global highly resolved mesh, through flexible, robust h-adaptivity of finite elements. H-adaptivity is the dynamic refinement of the mesh by subdividing elements, thus changing the characteristic element size and reducing numerical error. The authors are working on several major technical challenges that must be met to make effective use of HAMMER on MP computers.« less

Unstructured Adaptive Meshes: Bad for Your Memory?

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Feng, Hui-Yu; VanderWijngaart, Rob

2003-01-01

This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.

Using Multithreading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes

NASA Technical Reports Server (NTRS)

Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Bailey, David H. (Technical Monitor)

1998-01-01

In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes. The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the question phase of FE applications on triangular meshes, and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments on EARTH-SP2, an implementation of EARTH on the IBM SP2, with different load balancing strategies that are built into the runtime system.

Mesh refinement and numerical sensitivity analysis for parameter calibration of partial differential equations

NASA Astrophysics Data System (ADS)

Becker, Roland; Vexler, Boris

2005-06-01

We consider the calibration of parameters in physical models described by partial differential equations. This task is formulated as a constrained optimization problem with a cost functional of least squares type using information obtained from measurements. An important issue in the numerical solution of this type of problem is the control of the errors introduced, first, by discretization of the equations describing the physical model, and second, by measurement errors or other perturbations. Our strategy is as follows: we suppose that the user defines an interest functional I, which might depend on both the state variable and the parameters and which represents the goal of the computation. First, we propose an a posteriori error estimator which measures the error with respect to this functional. This error estimator is used in an adaptive algorithm to construct economic meshes by local mesh refinement. The proposed estimator requires the solution of an auxiliary linear equation. Second, we address the question of sensitivity. Applying similar techniques as before, we derive quantities which describe the influence of small changes in the measurements on the value of the interest functional. These numbers, which we call relative condition numbers, give additional information on the problem under consideration. They can be computed by means of the solution of the auxiliary problem determined before. Finally, we demonstrate our approach at hand of a parameter calibration problem for a model flow problem.

An Interpreted Language and System for the Visualization of Unstructured Meshes

NASA Technical Reports Server (NTRS)

Moran, Patrick J.; Gerald-Yamasaki, Michael (Technical Monitor)

1998-01-01

We present an interpreted language and system supporting the visualization of unstructured meshes and the manipulation of shapes defined in terms of mesh subsets. The language features primitives inspired by geometric modeling, mathematical morphology and algebraic topology. The adaptation of the topology ideas to an interpreted environment, along with support for programming constructs such, as user function definition, provide a flexible system for analyzing a mesh and for calculating with shapes defined in terms of the mesh. We present results demonstrating some of the capabilities of the language, based on an implementation called the Shape Calculator, for tetrahedral meshes in R^3.

Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computation

NASA Technical Reports Server (NTRS)

Rausch, Russ D.; Batina, John T.; Yang, Henry T. Y.

1991-01-01

Spatial adaption procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaption procedures were developed and implemented within a two-dimensional unstructured-grid upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in a high gradient region or the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational costs. A detailed description is given of the enrichment and coarsening procedures and comparisons with alternative results and experimental data are presented to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady transonic results, obtained using spatial adaption for the NACA 0012 airfoil, are shown to be of high spatial accuracy, primarily in that the shock waves are very sharply captured. The results were obtained with a computational savings of a factor of approximately fifty-three for a steady case and as much as twenty-five for the unsteady cases.

Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computation

NASA Technical Reports Server (NTRS)

Rausch, Russ D.; Yang, Henry T. Y.; Batina, John T.

1991-01-01

Spatial adaption procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaption procedures were developed and implemented within a two-dimensional unstructured-grid upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. The paper gives a detailed description of the enrichment and coarsening procedures and presents comparisons with alternative results and experimental data to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady transonic results, obtained using spatial adaption for the NACA 0012 airfoil, are shown to be of high spatial accuracy, primarily in that the shock waves are very sharply captured. The results were obtained with a computational savings of a factor of approximately fifty-three for a steady case and as much as twenty-five for the unsteady cases.

Automated hexahedral mesh generation from biomedical image data: applications in limb prosthetics.

PubMed

Zachariah, S G; Sanders, J E; Turkiyyah, G M

1996-06-01

A general method to generate hexahedral meshes for finite element analysis of residual limbs and similar biomedical geometries is presented. The method utilizes skeleton-based subdivision of cross-sectional domains to produce simple subdomains in which structured meshes are easily generated. Application to a below-knee residual limb and external prosthetic socket is described. The residual limb was modeled as consisting of bones, soft tissue, and skin. The prosthetic socket model comprised a socket wall with an inner liner. The geometries of these structures were defined using axial cross-sectional contour data from X-ray computed tomography, optical scanning, and mechanical surface digitization. A tubular surface representation, using B-splines to define the directrix and generator, is shown to be convenient for definition of the structure geometries. Conversion of cross-sectional data to the compact tubular surface representation is direct, and the analytical representation simplifies geometric querying and numerical optimization within the mesh generation algorithms. The element meshes remain geometrically accurate since boundary nodes are constrained to lie on the tubular surfaces. Several element meshes of increasing mesh density were generated for two residual limbs and prosthetic sockets. Convergence testing demonstrated that approximately 19 elements are required along a circumference of the residual limb surface for a simple linear elastic model. A model with the fibula absent compared with the same geometry with the fibula present showed differences suggesting higher distal stresses in the absence of the fibula. Automated hexahedral mesh generation algorithms for sliced data represent an advancement in prosthetic stress analysis since they allow rapid modeling of any given residual limb and optimization of mesh parameters.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Strauss, H.R.

This paper describes the code FEMHD, an adaptive finite element MHD code, which is applied in a number of different manners to model MHD behavior and edge plasma phenomena on a diverted tokamak. The code uses an unstructured triangular mesh in 2D and wedge shaped mesh elements in 3D. The code has been adapted to look at neutral and charged particle dynamics in the plasma scrape off region, and into a full MHD-particle code.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Duchaineau, M.; Wolinsky, M.; Sigeti, D.E.

Real-time terrain rendering for interactive visualization remains a demanding task. We present a novel algorithm with several advantages over previous methods: our method is unusually stingy with polygons yet achieves real-time performance and is scalable to arbitrary regions and resolutions. The method provides a continuous terrain mesh of specified triangle count having provably minimum error in restricted but reasonably general classes of permissible meshes and error metrics. Our method provides an elegant solution to guaranteeing certain elusive types of consistency in scenes produced by multiple scene generators which share a common finest-resolution database but which otherwise operate entirely independently. Thismore » consistency is achieved by exploiting the freedom of choice of error metric allowed by the algorithm to provide, for example, multiple exact lines-of-sight in real-time. Our methods rely on an off-line pre-processing phase to construct a multi-scale data structure consisting of triangular terrain approximations enhanced ({open_quotes}thickened{close_quotes}) with world-space error information. In real time, this error data is efficiently transformed into screen-space where it is used to guide a greedy top-down triangle subdivision algorithm which produces the desired minimal error continuous terrain mesh. Our algorithm has been implemented and it operates at real-time rates.« less

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Barth, Timothy J.

1992-01-01

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology.

Merging Surface Reconstructions of Terrestrial and Airborne LIDAR Range Data

DTIC Science & Technology

2009-05-19

Mangan and R. Whitaker. Partitioning 3D surface meshes using watershed segmentation . IEEE Trans. on Visualization and Computer Graphics, 5(4), pp...Jain, and A. Zakhor. Data Processing Algorithms for Generating Textured 3D Building Facade Meshes from Laser Scans and Camera Images. International...acquired set of overlapping range images into a single mesh [2,9,10]. However, due to the volume of data involved in large scale urban modeling, data

Minimizing finite-volume discretization errors on polyhedral meshes

NASA Astrophysics Data System (ADS)

Mouly, Quentin; Evrard, Fabien; van Wachem, Berend; Denner, Fabian

2017-11-01

Tetrahedral meshes are widely used in CFD to simulate flows in and around complex geometries, as automatic generation tools now allow tetrahedral meshes to represent arbitrary domains in a relatively accessible manner. Polyhedral meshes, however, are an increasingly popular alternative. While tetrahedron have at most four neighbours, the higher number of neighbours per polyhedral cell leads to a more accurate evaluation of gradients, essential for the numerical resolution of PDEs. The use of polyhedral meshes, nonetheless, introduces discretization errors for finite-volume methods: skewness and non-orthogonality, which occur with all sorts of unstructured meshes, as well as errors due to non-planar faces, specific to polygonal faces with more than three vertices. Indeed, polyhedral mesh generation algorithms cannot, in general, guarantee to produce meshes free of non-planar faces. The presented work focuses on the quantification and optimization of discretization errors on polyhedral meshes in the context of finite-volume methods. A quasi-Newton method is employed to optimize the relevant mesh quality measures. Various meshes are optimized and CFD results of cases with known solutions are presented to assess the improvements the optimization approach can provide.

TH-A-BRF-08: Deformable Registration of MRI and CT Images for MRI-Guided Radiation Therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhong, H; Wen, N; Gordon, J

2014-06-15

Purpose: To evaluate the quality of a commercially available MRI-CT image registration algorithm and then develop a method to improve the performance of this algorithm for MRI-guided prostate radiotherapy. Methods: Prostate contours were delineated on ten pairs of MRI and CT images using Eclipse. Each pair of MRI and CT images was registered with an intensity-based B-spline algorithm implemented in Velocity. A rectangular prism that contains the prostate volume was partitioned into a tetrahedral mesh which was aligned to the CT image. A finite element method (FEM) was developed on the mesh with the boundary constraints assigned from the Velocitymore » generated displacement vector field (DVF). The resultant FEM displacements were used to adjust the Velocity DVF within the prism. Point correspondences between the CT and MR images identified within the prism could be used as additional boundary constraints to enforce the model deformation. The FEM deformation field is smooth in the interior of the prism, and equal to the Velocity displacements at the boundary of the prism. To evaluate the Velocity and FEM registration results, three criteria were used: prostate volume conservation and center consistence under contour mapping, and unbalanced energy of their deformation maps. Results: With the DVFs generated by the Velocity and FEM simulations, the prostate contours were warped from MRI to CT images. With the Velocity DVFs, the prostate volumes changed 10.2% on average, in contrast to 1.8% induced by the FEM DVFs. The average of the center deviations was 0.36 and 0.27 cm, and the unbalance energy was 2.65 and 0.38 mJ/cc3 for the Velocity and FEM registrations, respectively. Conclusion: The adaptive FEM method developed can be used to reduce the error of the MIbased registration algorithm implemented in Velocity in the prostate region, and consequently may help improve the quality of MRI-guided radiation therapy.« less

New software developments for quality mesh generation and optimization from biomedical imaging data.

PubMed

Yu, Zeyun; Wang, Jun; Gao, Zhanheng; Xu, Ming; Hoshijima, Masahiko

2014-01-01

In this paper we present a new software toolkit for generating and optimizing surface and volumetric meshes from three-dimensional (3D) biomedical imaging data, targeted at image-based finite element analysis of some biomedical activities in a single material domain. Our toolkit includes a series of geometric processing algorithms including surface re-meshing and quality-guaranteed tetrahedral mesh generation and optimization. All methods described have been encapsulated into a user-friendly graphical interface for easy manipulation and informative visualization of biomedical images and mesh models. Numerous examples are presented to demonstrate the effectiveness and efficiency of the described methods and toolkit. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Adaptive Numerical Algorithms in Space Weather Modeling

NASA Technical Reports Server (NTRS)

Toth, Gabor; vanderHolst, Bart; Sokolov, Igor V.; DeZeeuw, Darren; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Nakib, Dalal; Powell, Kenneth G.;

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1994-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: a gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A Cartesian, cell-based approach for adaptively-refined solutions of the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, N-sided 'cut' cells are created using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded: A gradient-limited, linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The more robust of a series of viscous flux functions is used to provide the viscous fluxes at the cell interfaces. Adaptively-refined solutions of the Navier-Stokes equations using the Cartesian, cell-based approach are obtained and compared to theory, experiment and other accepted computational results for a series of low and moderate Reynolds number flows.

Solution-Adaptive Cartesian Cell Approach for Viscous and Inviscid Flows

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1996-01-01

A Cartesian cell-based approach for adaptively refined solutions of the Euler and Navier-Stokes equations in two dimensions is presented. Grids about geometrically complicated bodies are generated automatically, by the recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal cut cells are created using modified polygon-clipping algorithms. The grid is stored in a binary tree data structure that provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive mesh refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite volume formulation. The convective terms are upwinded: A linear reconstruction of the primitive variables is performed, providing input states to an approximate Riemann solver for computing the fluxes between neighboring cells. The results of a study comparing the accuracy and positivity of two classes of cell-centered, viscous gradient reconstruction procedures is briefly summarized. Adaptively refined solutions of the Navier-Stokes equations are shown using the more robust of these gradient reconstruction procedures, where the results computed by the Cartesian approach are compared to theory, experiment, and other accepted computational results for a series of low and moderate Reynolds number flows.

Diffraction Analysis of Antennas With Mesh Surfaces

NASA Technical Reports Server (NTRS)

Rahmat-Samii, Yahya

1987-01-01

Strip-aperture model replaces wire-grid model. Far-field radiation pattern of antenna with mesh reflector calculated more accurately with new strip-aperture model than with wire-grid model of reflector surface. More adaptable than wire-grid model to variety of practical configurations and decidedly superior for reflectors in which mesh-cell width exceeds mesh thickness. Satisfies reciprocity theorem. Applied where mesh cells are no larger than tenth of wavelength. Small cell size permits use of simplifying approximation that reflector-surface current induced by electromagnetic field is present even in apertures. Approximation useful in calculating far field.

Multigrid techniques for unstructured meshes

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1995-01-01

An overview of current multigrid techniques for unstructured meshes is given. The basic principles of the multigrid approach are first outlined. Application of these principles to unstructured mesh problems is then described, illustrating various different approaches, and giving examples of practical applications. Advanced multigrid topics, such as the use of algebraic multigrid methods, and the combination of multigrid techniques with adaptive meshing strategies are dealt with in subsequent sections. These represent current areas of research, and the unresolved issues are discussed. The presentation is organized in an educational manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.

Robust and efficient overset grid assembly for partitioned unstructured meshes

NASA Astrophysics Data System (ADS)

Roget, Beatrice; Sitaraman, Jayanarayanan

2014-03-01

This paper presents a method to perform efficient and automated Overset Grid Assembly (OGA) on a system of overlapping unstructured meshes in a parallel computing environment where all meshes are partitioned into multiple mesh-blocks and processed on multiple cores. The main task of the overset grid assembler is to identify, in parallel, among all points in the overlapping mesh system, at which points the flow solution should be computed (field points), interpolated (receptor points), or ignored (hole points). Point containment search or donor search, an algorithm to efficiently determine the cell that contains a given point, is the core procedure necessary for accomplishing this task. Donor search is particularly challenging for partitioned unstructured meshes because of the complex irregular boundaries that are often created during partitioning.

Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)

2002-01-01

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Triangle geometry processing for surface modeling and cartesian grid generation

DOEpatents

Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY

2002-09-03

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Fast animation of lightning using an adaptive mesh.

PubMed

Kim, Theodore; Lin, Ming C

2007-01-01

We present a fast method for simulating, animating, and rendering lightning using adaptive grids. The "dielectric breakdown model" is an elegant algorithm for electrical pattern formation that we extend to enable animation of lightning. The simulation can be slow, particularly in 3D, because it involves solving a large Poisson problem. Losasso et al. recently proposed an octree data structure for simulating water and smoke, and we show that this discretization can be applied to the problem of lightning simulation as well. However, implementing the incomplete Cholesky conjugate gradient (ICCG) solver for this problem can be daunting, so we provide an extensive discussion of implementation issues. ICCG solvers can usually be accelerated using "Eisenstat's trick," but the trick cannot be directly applied to the adaptive case. Fortunately, we show that an "almost incomplete Cholesky" factorization can be computed so that Eisenstat's trick can still be used. We then present a fast rendering method based on convolution that is competitive with Monte Carlo ray tracing but orders of magnitude faster, and we also show how to further improve the visual results using jittering.

On the anomaly of velocity-pressure decoupling in collocated mesh solutions

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook; Vanoverbeke, Thomas

1991-01-01

The use of various pressure correction algorithms originally developed for fully staggered meshes can yield a velocity-pressure decoupled solution for collocated meshes. The mechanism that causes velocity-pressure decoupling is identified. It is shown that the use of a partial differential equation for the incremental pressure eliminates such a mechanism and yields a velocity-pressure coupled solution. Example flows considered are a three dimensional lid-driven cavity flow and a laminar flow through a 90 deg bend square duct. Numerical results obtained using the collocated mesh are in good agreement with the measured data and other numerical results.

Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

NASA Technical Reports Server (NTRS)

Woodard, Paul R.; Yang, Henry T. Y.; Batina, John T.

1992-01-01

Quality assessment procedures are described for two-dimensional and three-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate the accuracy of an implicit upwind Euler solution algorithm.

Adaptive mesh refinement for time-domain electromagnetics using vector finite elements :a feasibility study.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis

This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.

Particle systems for adaptive, isotropic meshing of CAD models

PubMed Central

Levine, Joshua A.; Whitaker, Ross T.

2012-01-01

We present a particle-based approach for generating adaptive triangular surface and tetrahedral volume meshes from computer-aided design models. Input shapes are treated as a collection of smooth, parametric surface patches that can meet non-smoothly on boundaries. Our approach uses a hierarchical sampling scheme that places particles on features in order of increasing dimensionality. These particles reach a good distribution by minimizing an energy computed in 3D world space, with movements occurring in the parametric space of each surface patch. Rather than using a pre-computed measure of feature size, our system automatically adapts to both curvature as well as a notion of topological separation. It also enforces a measure of smoothness on these constraints to construct a sizing field that acts as a proxy to piecewise-smooth feature size. We evaluate our technique with comparisons against other popular triangular meshing techniques for this domain. PMID:23162181

Arbitrary Lagrangian-Eulerian Method with Local Structured Adaptive Mesh Refinement for Modeling Shock Hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anderson, R W; Pember, R B; Elliott, N S

2001-10-22

A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid Lagrangian integration method. The novel components of the method are mainly driven by the need to reconcile traditionalmore » AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.« less

Slices: A Scalable Partitioner for Finite Element Meshes

NASA Technical Reports Server (NTRS)

Ding, H. Q.; Ferraro, R. D.

1995-01-01

A parallel partitioner for partitioning unstructured finite element meshes on distributed memory architectures is developed. The element based partitioner can handle mixtures of different element types. All algorithms adopted in the partitioner are scalable, including a communication template for unpredictable incoming messages, as shown in actual timing measurements.

Mesh-free based variational level set evolution for breast region segmentation and abnormality detection using mammograms.

PubMed

Kashyap, Kanchan L; Bajpai, Manish K; Khanna, Pritee; Giakos, George

2018-01-01

Automatic segmentation of abnormal region is a crucial task in computer-aided detection system using mammograms. In this work, an automatic abnormality detection algorithm using mammographic images is proposed. In the preprocessing step, partial differential equation-based variational level set method is used for breast region extraction. The evolution of the level set method is done by applying mesh-free-based radial basis function (RBF). The limitation of mesh-based approach is removed by using mesh-free-based RBF method. The evolution of variational level set function is also done by mesh-based finite difference method for comparison purpose. Unsharp masking and median filtering is used for mammogram enhancement. Suspicious abnormal regions are segmented by applying fuzzy c-means clustering. Texture features are extracted from the segmented suspicious regions by computing local binary pattern and dominated rotated local binary pattern (DRLBP). Finally, suspicious regions are classified as normal or abnormal regions by means of support vector machine with linear, multilayer perceptron, radial basis, and polynomial kernel function. The algorithm is validated on 322 sample mammograms of mammographic image analysis society (MIAS) and 500 mammograms from digital database for screening mammography (DDSM) datasets. Proficiency of the algorithm is quantified by using sensitivity, specificity, and accuracy. The highest sensitivity, specificity, and accuracy of 93.96%, 95.01%, and 94.48%, respectively, are obtained on MIAS dataset using DRLBP feature with RBF kernel function. Whereas, the highest 92.31% sensitivity, 98.45% specificity, and 96.21% accuracy are achieved on DDSM dataset using DRLBP feature with RBF kernel function. Copyright © 2017 John Wiley & Sons, Ltd.

Incremental triangulation by way of edge swapping and local optimization

NASA Technical Reports Server (NTRS)

Wiltberger, N. Lyn

1994-01-01

This document is intended to serve as an installation, usage, and basic theory guide for the two dimensional triangulation software 'HARLEY' written for the Silicon Graphics IRIS workstation. This code consists of an incremental triangulation algorithm based on point insertion and local edge swapping. Using this basic strategy, several types of triangulations can be produced depending on user selected options. For example, local edge swapping criteria can be chosen which minimizes the maximum interior angle (a MinMax triangulation) or which maximizes the minimum interior angle (a MaxMin or Delaunay triangulation). It should be noted that the MinMax triangulation is generally only locally optical (not globally optimal) in this measure. The MaxMin triangulation, however, is both locally and globally optical. In addition, Steiner triangulations can be constructed by inserting new sites at triangle circumcenters followed by edge swapping based on the MaxMin criteria. Incremental insertion of sites also provides flexibility in choosing cell refinement criteria. A dynamic heap structure has been implemented in the code so that once a refinement measure is specified (i.e., maximum aspect ratio or some measure of a solution gradient for the solution adaptive grid generation) the cell with the largest value of this measure is continually removed from the top of the heap and refined. The heap refinement strategy allows the user to specify either the number of cells desired or refine the mesh until all cell refinement measures satisfy a user specified tolerance level. Since the dynamic heap structure is constantly updated, the algorithm always refines the particular cell in the mesh with the largest refinement criteria value. The code allows the user to: triangulate a cloud of prespecified points (sites), triangulate a set of prespecified interior points constrained by prespecified boundary curve(s), Steiner triangulate the interior/exterior of prespecified boundary curve(s), refine existing triangulations based on solution error measures, and partition meshes based on the Cuthill-McKee, spectral, and coordinate bisection strategies.

The optimization of high resolution topographic data for 1D hydrodynamic models

NASA Astrophysics Data System (ADS)

Ales, Ronovsky; Michal, Podhoranyi

2016-06-01

The main focus of our research presented in this paper is to optimize and use high resolution topographical data (HRTD) for hydrological modelling. Optimization of HRTD is done by generating adaptive mesh by measuring distance of coarse mesh and the surface of the dataset and adapting the mesh from the perspective of keeping the geometry as close to initial resolution as possible. Technique described in this paper enables computation of very accurate 1-D hydrodynamic models. In the paper, we use HEC-RAS software as a solver. For comparison, we have chosen the amount of generated cells/grid elements (in whole discretization domain and selected cross sections) with respect to preservation of the accuracy of the computational domain. Generation of the mesh for hydrodynamic modelling is strongly reliant on domain size and domain resolution. Topographical dataset used in this paper was created using LiDAR method and it captures 5.9km long section of a catchment of the river Olše. We studied crucial changes in topography for generated mesh. Assessment was done by commonly used statistical and visualization methods.

Local mesh adaptation technique for front tracking problems

NASA Astrophysics Data System (ADS)

Lock, N.; Jaeger, M.; Medale, M.; Occelli, R.

1998-09-01

A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented in this paper: the broken dam problem and the Rayleigh-Taylor instability. Good agreement has been obtained in the comparison of the numerical results with theory or available experimental data.

The optimization of high resolution topographic data for 1D hydrodynamic models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ales, Ronovsky, E-mail: ales.ronovsky@vsb.cz; Michal, Podhoranyi

2016-06-08

The main focus of our research presented in this paper is to optimize and use high resolution topographical data (HRTD) for hydrological modelling. Optimization of HRTD is done by generating adaptive mesh by measuring distance of coarse mesh and the surface of the dataset and adapting the mesh from the perspective of keeping the geometry as close to initial resolution as possible. Technique described in this paper enables computation of very accurate 1-D hydrodynamic models. In the paper, we use HEC-RAS software as a solver. For comparison, we have chosen the amount of generated cells/grid elements (in whole discretization domainmore » and selected cross sections) with respect to preservation of the accuracy of the computational domain. Generation of the mesh for hydrodynamic modelling is strongly reliant on domain size and domain resolution. Topographical dataset used in this paper was created using LiDAR method and it captures 5.9km long section of a catchment of the river Olše. We studied crucial changes in topography for generated mesh. Assessment was done by commonly used statistical and visualization methods.« less

Advanced positive airway pressure modes: adaptive servo ventilation and volume assured pressure support.

PubMed

Selim, Bernardo; Ramar, Kannan

2016-09-01

Volume assured pressure support (VAPS) and adaptive servo ventilation (ASV) are non-invasive positive airway pressure (PAP) modes with sophisticated negative feedback control systems (servomechanism), having the capability to self-adjust in real time its respiratory controlled variables to patient's respiratory fluctuations. However, the widespread use of VAPS and ASV is limited by scant clinical experience, high costs, and the incomplete understanding of propriety algorithmic differences in devices' response to patient's respiratory changes. Hence, we will review and highlight similarities and differences in technical aspects, control algorithms, and settings of each mode, focusing on the literature search published in this area. One hundred twenty relevant articles were identified by Scopus, PubMed, and Embase databases from January 2010 to 2016, using a combination of MeSH terms and keywords. Articles were further supplemented by pearling. Recommendations were based on the literature review and the authors' expertise in this area. Expert commentary: ASV and VAPS differ in their respiratory targets and response to a respiratory fluctuation. The VAPS mode targets a more consistent minute ventilation, being recommended in the treatment of sleep related hypoventilation disorders, while ASV mode attempts to provide a more steady breathing airflow pattern, treating successfully most central sleep apnea syndromes.

Hybrid Multiscale Finite Volume method for multiresolution simulations of flow and reactive transport in porous media

NASA Astrophysics Data System (ADS)

Barajas-Solano, D. A.; Tartakovsky, A. M.

2017-12-01

We present a multiresolution method for the numerical simulation of flow and reactive transport in porous, heterogeneous media, based on the hybrid Multiscale Finite Volume (h-MsFV) algorithm. The h-MsFV algorithm allows us to couple high-resolution (fine scale) flow and transport models with lower resolution (coarse) models to locally refine both spatial resolution and transport models. The fine scale problem is decomposed into various "local'' problems solved independently in parallel and coordinated via a "global'' problem. This global problem is then coupled with the coarse model to strictly ensure domain-wide coarse-scale mass conservation. The proposed method provides an alternative to adaptive mesh refinement (AMR), due to its capacity to rapidly refine spatial resolution beyond what's possible with state-of-the-art AMR techniques, and the capability to locally swap transport models. We illustrate our method by applying it to groundwater flow and reactive transport of multiple species.

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jeong, Yongjin; Park, Jinsu; Lee, Hyun Chul

2015-12-01

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also notedmore » that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.« less

Lagrangian Modeling of Evaporating Sprays at Diesel Engine Conditions: Effects of Multi-Hole Injector Nozzles With JP-8 Surrogates

DTIC Science & Technology

2014-05-01

solver to treat the spray process. An Adaptive Mesh Refinement (AMR) and fixed embedding technique is employed to capture the gas - liquid interface with...Adaptive Mesh Refinement (AMR) and fixed embedding technique is employed to capture the gas - liquid interface with high fidelity while keeping the cell...in single and multi-hole nozzle configurations. The models were added to the present CONVERGE liquid fuel database and validated extensively

DOE Office of Scientific and Technical Information (OSTI.GOV)

OWEN,STEVEN J.

A method for decomposing a volume with a prescribed quadrilateral surface mesh, into a hexahedral-dominated mesh is proposed. With this method, known as Hex-Morphing (H-Morph), an initial tetrahedral mesh is provided. Tetrahedral are transformed and combined starting from the boundary and working towards the interior of the volume. The quadrilateral faces of the hexahedra are treated as internal surfaces, which can be recovered using constrained triangulation techniques. Implementation details of the edge and face recovery process are included. Examples and performance of the H-Morph algorithm are also presented.

A vortex wake capturing method for potential flow calculations

NASA Technical Reports Server (NTRS)

Murman, E. M.; Stremel, P. M.

1982-01-01

A method is presented for modifying finite difference solutions of the potential equation to include the calculation of non-planar vortex wake features. The approach is an adaptation of Baker's 'cloud in cell' algorithm developed for the stream function-vorticity equations. The vortex wake is tracked in a Lagrangian frame of reference as a group of discrete vortex filaments. These are distributed to the Eulerian mesh system on which the velocity is calculated by a finite difference solution of the potential equation. An artificial viscosity introduced by the finite difference equations removes the singular nature of the vortex filaments. Computed examples are given for the two-dimensional time dependent roll-up of vortex wakes generated by wings with different spanwise loading distributions.

The dynamics of plate tectonics and mantle flow: from local to global scales.

PubMed

Stadler, Georg; Gurnis, Michael; Burstedde, Carsten; Wilcox, Lucas C; Alisic, Laura; Ghattas, Omar

2010-08-27

Plate tectonics is regulated by driving and resisting forces concentrated at plate boundaries, but observationally constrained high-resolution models of global mantle flow remain a computational challenge. We capitalized on advances in adaptive mesh refinement algorithms on parallel computers to simulate global mantle flow by incorporating plate motions, with individual plate margins resolved down to a scale of 1 kilometer. Back-arc extension and slab rollback are emergent consequences of slab descent in the upper mantle. Cold thermal anomalies within the lower mantle couple into oceanic plates through narrow high-viscosity slabs, altering the velocity of oceanic plates. Viscous dissipation within the bending lithosphere at trenches amounts to approximately 5 to 20% of the total dissipation through the entire lithosphere and mantle.

Effects of polyglactin mesh combined with resorbable calcium carbonate or replamineform hydroxyapatite on periodontal repair in dogs.

PubMed

Moon, I S; Chai, J K; Cho, K S; Wikesjö, U M; Kim, C K

1996-10-01

This study evaluates periodontal repair and biomaterial reaction following implantation of a polyglactin mesh with or without porous resorbable calcium carbonate (RCC) or porous replamineform hydroxyapatite (RHA) in conjunction with reconstructive surgery. Ligature- and surgically-induced interproximal periodontal defects of left and right mandibular premolar teeth in 7 dogs were used. Bilaterally, mesial defects of the 2nd, 3rd and 4th premolar teeth were treated with polyglactin mesh, polyglactin mesh and RHA, or polyglactin mesh and RCC, respectively. The polyglactin mesh, shaped according to the contour of the defect, was adapted to the experimental teeth; its coronal margin positioned immediately apical to the cemento-enamel junction. Gingival flap margins were adapted and sutured to cover the polyglactin mesh completely. Clinical healing was generally uneventful. The dogs were sacrificed to provide block sections for histologic evaluation at 1, 3, 6, 12, 26, 32 and 56 weeks following wound closure. Generally, cementum regeneration was observed beginning at week 6 in all groups. Bone regeneration was observed from week 3 in polyglactin mesh-treated groups, and from week 6 in polyglactin mesh+RCC or polyglactin mesh+RHA treated groups. Bone regeneration appeared enhanced in polyglactin mesh+RCC or polyglactin mesh+RHA treated defects at week 12 and 26, with little difference between the three experimental conditions at week 56. Polyglactin mesh degradation was observed at week 3 and appeared complete at week 12. The RHA did not appear to resorb, while the RCC was gradually replaced by bone from week 3. Within limitations of the study conditions, periodontal regeneration was observed following implantation of a polyglactin mesh with or without RCC or RHA in conjunction with reconstructive surgery. As a conclusion, there seems to be no significant difference in periodontal regeneration after 12 months of healing between the group treated with the membrane only, and the group treated with the membrane and the bone substitution material. Changes in connective fiber orientation over the 1st 12 weeks of healing may suggest that "fibrous encapsulation" observed in earlier studies may only represent a transient stage in periodontal regeneration.

An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Lessard, Victor R.

1990-01-01

The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

Forwarding techniques for IP fragmented packets in a real 6LoWPAN network.

PubMed

Ludovici, Alessandro; Calveras, Anna; Casademont, Jordi

2011-01-01

Wireless Sensor Networks (WSNs) are attracting more and more interest since they offer a low-cost solution to the problem of providing a means to deploy large sensor networks in a number of application domains. We believe that a crucial aspect to facilitate WSN diffusion is to make them interoperable with external IP networks. This can be achieved by using the 6LoWPAN protocol stack. 6LoWPAN enables the transmission of IPv6 packets over WSNs based on the IEEE 802.15.4 standard. IPv6 packet size is considerably larger than that of IEEE 802.15.4 data frame. To overcome this problem, 6LoWPAN introduces an adaptation layer between the network and data link layers, allowing IPv6 packets to be adapted to the lower layer constraints. This adaptation layer provides fragmentation and header compression of IP packets. Furthermore, it also can be involved in routing decisions. Depending on which layer is responsible for routing decisions, 6LoWPAN divides routing in two categories: mesh under if the layer concerned is the adaptation layer and route over if it is the network layer. In this paper we analyze different routing solutions (route over, mesh under and enhanced route over) focusing on how they forward fragments. We evaluate their performance in terms of latency and energy consumption when transmitting IP fragmented packets. All the tests have been performed in a real 6LoWPAN implementation. After consideration of the main problems in forwarding of mesh frames in WSN, we propose and analyze a new alternative scheme based on mesh under, which we call controlled mesh under.

Forwarding Techniques for IP Fragmented Packets in a Real 6LoWPAN Network

PubMed Central

Ludovici, Alessandro; Calveras, Anna; Casademont, Jordi

2011-01-01

Wireless Sensor Networks (WSNs) are attracting more and more interest since they offer a low-cost solution to the problem of providing a means to deploy large sensor networks in a number of application domains. We believe that a crucial aspect to facilitate WSN diffusion is to make them interoperable with external IP networks. This can be achieved by using the 6LoWPAN protocol stack. 6LoWPAN enables the transmission of IPv6 packets over WSNs based on the IEEE 802.15.4 standard. IPv6 packet size is considerably larger than that of IEEE 802.15.4 data frame. To overcome this problem, 6LoWPAN introduces an adaptation layer between the network and data link layers, allowing IPv6 packets to be adapted to the lower layer constraints. This adaptation layer provides fragmentation and header compression of IP packets. Furthermore, it also can be involved in routing decisions. Depending on which layer is responsible for routing decisions, 6LoWPAN divides routing in two categories: mesh under if the layer concerned is the adaptation layer and route over if it is the network layer. In this paper we analyze different routing solutions (route over, mesh under and enhanced route over) focusing on how they forward fragments. We evaluate their performance in terms of latency and energy consumption when transmitting IP fragmented packets. All the tests have been performed in a real 6LoWPAN implementation. After consideration of the main problems in forwarding of mesh frames in WSN, we propose and analyze a new alternative scheme based on mesh under, which we call controlled mesh under. PMID:22346615

Discrete Surface Evolution and Mesh Deformation for Aircraft Icing Applications

NASA Technical Reports Server (NTRS)

Thompson, David; Tong, Xiaoling; Arnoldus, Qiuhan; Collins, Eric; McLaurin, David; Luke, Edward; Bidwell, Colin S.

2013-01-01

Robust, automated mesh generation for problems with deforming geometries, such as ice accreting on aerodynamic surfaces, remains a challenging problem. Here we describe a technique to deform a discrete surface as it evolves due to the accretion of ice. The surface evolution algorithm is based on a smoothed, face-offsetting approach. We also describe a fast algebraic technique to propagate the computed surface deformations into the surrounding volume mesh while maintaining geometric mesh quality. Preliminary results presented here demonstrate the ecacy of the approach for a sphere with a prescribed accretion rate, a rime ice accretion, and a more complex glaze ice accretion.

Mesh Denoising based on Normal Voting Tensor and Binary Optimization.

PubMed

Yadav, Sunil Kumar; Reitebuch, Ulrich; Polthier, Konrad

2017-08-17

This paper presents a two-stage mesh denoising algorithm. Unlike other traditional averaging approaches, our approach uses an element-based normal voting tensor to compute smooth surfaces. By introducing a binary optimization on the proposed tensor together with a local binary neighborhood concept, our algorithm better retains sharp features and produces smoother umbilical regions than previous approaches. On top of that, we provide a stochastic analysis on the different kinds of noise based on the average edge length. The quantitative results demonstrate that the performance of our method is better compared to state-of-the-art smoothing approaches.

A QoS Framework with Traffic Request in Wireless Mesh Network

NASA Astrophysics Data System (ADS)

Fu, Bo; Huang, Hejiao

In this paper, we consider major issues in ensuring greater Quality-of-Service (QoS) in Wireless Mesh Networks (WMNs), specifically with regard to reliability and delay. To this end, we use traffic request to record QoS requirements of data flows. In order to achieve required QoS for all data flows efficiently and with high portability, we develop Network State Update Algorithm. All assumptions, definitions, and algorithms are made exclusively with WMNs in mind, guaranteeing the portability of our framework to various environments in WMNs. The simulation results in proof that our framework is correct.

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

A simple smoothness indicator for the WENO scheme with adaptive order

NASA Astrophysics Data System (ADS)

Huang, Cong; Chen, Li Li

2018-01-01

The fifth order WENO scheme with adaptive order is competent for solving hyperbolic conservation laws, its reconstruction is a convex combination of a fifth order linear reconstruction and three third order linear reconstructions. Note that, on uniform mesh, the computational cost of smoothness indicator for fifth order linear reconstruction is comparable with the sum of ones for three third order linear reconstructions, thus it is too heavy; on non-uniform mesh, the explicit form of smoothness indicator for fifth order linear reconstruction is difficult to be obtained, and its computational cost is much heavier than the one on uniform mesh. In order to overcome these problems, a simple smoothness indicator for fifth order linear reconstruction is proposed in this paper.

Combinatorial Algorithms to Enable Computational Science and Engineering: Work from the CSCAPES Institute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Boman, Erik G.; Catalyurek, Umit V.; Chevalier, Cedric

2015-01-16

This final progress report summarizes the work accomplished at the Combinatorial Scientific Computing and Petascale Simulations Institute. We developed Zoltan, a parallel mesh partitioning library that made use of accurate hypergraph models to provide load balancing in mesh-based computations. We developed several graph coloring algorithms for computing Jacobian and Hessian matrices and organized them into a software package called ColPack. We developed parallel algorithms for graph coloring and graph matching problems, and also designed multi-scale graph algorithms. Three PhD students graduated, six more are continuing their PhD studies, and four postdoctoral scholars were advised. Six of these students and Fellowsmore » have joined DOE Labs (Sandia, Berkeley), as staff scientists or as postdoctoral scientists. We also organized the SIAM Workshop on Combinatorial Scientific Computing (CSC) in 2007, 2009, and 2011 to continue to foster the CSC community.« less

All-quad meshing without cleanup

DOE PAGES

Rushdi, Ahmad A.; Mitchell, Scott A.; Mahmoud, Ahmed H.; ...

2016-08-22

Here, we present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometry–quadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning wemore » have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.« less

Iterative methods for plasma sheath calculations: Application to spherical probe

NASA Technical Reports Server (NTRS)

Parker, L. W.; Sullivan, E. C.

1973-01-01

The computer cost of a Poisson-Vlasov iteration procedure for the numerical solution of a steady-state collisionless plasma-sheath problem depends on: (1) the nature of the chosen iterative algorithm, (2) the position of the outer boundary of the grid, and (3) the nature of the boundary condition applied to simulate a condition at infinity (as in three-dimensional probe or satellite-wake problems). Two iterative algorithms, in conjunction with three types of boundary conditions, are analyzed theoretically and applied to the computation of current-voltage characteristics of a spherical electrostatic probe. The first algorithm was commonly used by physicists, and its computer costs depend primarily on the boundary conditions and are only slightly affected by the mesh interval. The second algorithm is not commonly used, and its costs depend primarily on the mesh interval and slightly on the boundary conditions.

All-quad meshing without cleanup

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rushdi, Ahmad A.; Mitchell, Scott A.; Mahmoud, Ahmed H.

Here, we present an all-quad meshing algorithm for general domains. We start with a strongly balanced quadtree. In contrast to snapping the quadtree corners onto the geometric domain boundaries, we move them away from the geometry. Then we intersect the moved grid with the geometry. The resulting polygons are converted into quads with midpoint subdivision. Moving away avoids creating any flat angles, either at a quadtree corner or at a geometry–quadtree intersection. We are able to handle two-sided domains, and more complex topologies than prior methods. The algorithm is provably correct and robust in practice. It is cleanup-free, meaning wemore » have angle and edge length bounds without the use of any pillowing, swapping, or smoothing. Thus, our simple algorithm is fast and predictable. This paper has better quality bounds, and the algorithm is demonstrated over more complex domains, than our prior version.« less

Regularized finite element modeling of progressive failure in soils within nonlocal softening plasticity

NASA Astrophysics Data System (ADS)

Huang, Maosong; Qu, Xie; Lü, Xilin

2017-11-01

By solving a nonlinear complementarity problem for the consistency condition, an improved implicit stress return iterative algorithm for a generalized over-nonlocal strain softening plasticity was proposed, and the consistent tangent matrix was obtained. The proposed algorithm was embodied into existing finite element codes, and it enables the nonlocal regularization of ill-posed boundary value problem caused by the pressure independent and dependent strain softening plasticity. The algorithm was verified by the numerical modeling of strain localization in a plane strain compression test. The results showed that a fast convergence can be achieved and the mesh-dependency caused by strain softening can be effectively eliminated. The influences of hardening modulus and material characteristic length on the simulation were obtained. The proposed algorithm was further used in the simulations of the bearing capacity of a strip footing; the results are mesh-independent, and the progressive failure process of the soil was well captured.

NAVO MSRC Navigator. Fall 2006

DTIC Science & Technology

2006-01-01

UNIX Manual Pages: xdm (1x). 7. Buddenhagen, Oswald, “The KDM Handbook,” KDE Documentation, http://docs.kde.org/development/ en /kdebase/kdm/. 8... Linux Opteron cluster was recently determined through a series of simulations that employed both fixed and adaptive meshes. The fixed-mesh scalability...approximately eight in the total number of cells in the 3-D simulation. The fixed-mesh and AMR scalability results on the Linux Opteron cluster are

Tsunami modelling with adaptively refined finite volume methods

USGS Publications Warehouse

LeVeque, R.J.; George, D.L.; Berger, M.J.

2011-01-01

Numerical modelling of transoceanic tsunami propagation, together with the detailed modelling of inundation of small-scale coastal regions, poses a number of algorithmic challenges. The depth-averaged shallow water equations can be used to reduce this to a time-dependent problem in two space dimensions, but even so it is crucial to use adaptive mesh refinement in order to efficiently handle the vast differences in spatial scales. This must be done in a 'wellbalanced' manner that accurately captures very small perturbations to the steady state of the ocean at rest. Inundation can be modelled by allowing cells to dynamically change from dry to wet, but this must also be done carefully near refinement boundaries. We discuss these issues in the context of Riemann-solver-based finite volume methods for tsunami modelling. Several examples are presented using the GeoClaw software, and sample codes are available to accompany the paper. The techniques discussed also apply to a variety of other geophysical flows. ?? 2011 Cambridge University Press.

An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

DOE PAGES

McCorquodale, Peter; Ullrich, Paul; Johansen, Hans; ...

2015-09-04

We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed-sphere. This approach combines a Runge--Kutta time discretization with a fourth-order accurate spatial discretization, and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy, but with many fewer operations.

An edge-based solution-adaptive method applied to the AIRPLANE code

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Thomas, Scott D.; Cliff, Susan E.

1995-01-01

Computational methods to solve large-scale realistic problems in fluid flow can be made more efficient and cost effective by using them in conjunction with dynamic mesh adaption procedures that perform simultaneous coarsening and refinement to capture flow features of interest. This work couples the tetrahedral mesh adaption scheme, 3D_TAG, with the AIRPLANE code to solve complete aircraft configuration problems in transonic and supersonic flow regimes. Results indicate that the near-field sonic boom pressure signature of a cone-cylinder is improved, the oblique and normal shocks are better resolved on a transonic wing, and the bow shock ahead of an unstarted inlet is better defined.

Wind Farm LES Simulations Using an Overset Methodology

NASA Astrophysics Data System (ADS)

Ananthan, Shreyas; Yellapantula, Shashank

2017-11-01

Accurate simulation of wind farm wakes under realistic atmospheric inflow conditions and complex terrain requires modeling a wide range of length and time scales. The computational domain can span several kilometers while requiring mesh resolutions in O(10-6) to adequately resolve the boundary layer on the blade surface. Overset mesh methodology offers an attractive option to address the disparate range of length scales; it allows embedding body-confirming meshes around turbine geomtries within nested wake capturing meshes of varying resolutions necessary to accurately model the inflow turbulence and the resulting wake structures. Dynamic overset hole-cutting algorithms permit relative mesh motion that allow this nested mesh structure to track unsteady inflow direction changes, turbine control changes (yaw and pitch), and wake propagation. An LES model with overset mesh for localized mesh refinement is used to analyze wind farm wakes and performance and compared with local mesh refinements using non-conformal (hanging node) unstructured meshes. Turbine structures will be modeled using both actuator line approaches and fully-resolved structures to test the efficacy of overset methods for wind farm applications. Exascale Computing Project (ECP), Project Number: 17-SC-20-SC, a collaborative effort of two DOE organizations - the Office of Science and the National Nuclear Security Administration.

A new class of accurate, mesh-free hydrodynamic simulation methods

NASA Astrophysics Data System (ADS)

Hopkins, Philip F.

2015-06-01

We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, smoothed particle hydrodynamics (SPH), and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both SPH and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume `overlap'. We implement and test a parallel, second-order version of the method with self-gravity and cosmological integration, in the code GIZMO:1 this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require `artificial diffusion' terms; and allows the fluid elements to move with the flow, so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages versus SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced `particle noise' and numerical viscosity, more accurate sub-sonic flow evolution, and sharp shock-capturing. Advantages versus non-moving meshes include: automatic adaptivity, dramatically reduced advection errors and numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of `grid alignment' effects. We can, for example, follow hundreds of orbits of gaseous discs, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize `grid noise'. These differences are important for a range of astrophysical problems.

On the Use of CAD-Native Predicates and Geometry in Surface Meshing

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.

1999-01-01

Several paradigms for accessing CAD geometry during surface meshing for CFD are discussed. File translation, inconsistent geometry engines and non-native point construction are all identified as sources of non-robustness. The paper argues in favor of accessing CAD parts and assemblies in their native format, without translation, and for the use of CAD-native predicates and constructors in surface mesh generation. The discussion also emphasizes the importance of examining the computational requirements for exact evaluation of triangulation predicates during surface meshing. The native approach is demonstrated through an algorithm for the generation of closed manifold surface triangulations from CAD geometry. CAD parts and assemblies are used in their native format, and a part's native geometry engine is accessed through a modeler-independent application programming interface (API). In seeking a robust and fully automated procedure, the algorithm is based on a new physical space manifold triangulation technique specially developed to avoid robustness issues associated with poorly conditioned mappings. In addition, this approach avoids the usual ambiguities associated with floating-point predicate evaluation on constructed coordinate geometry in a mapped space. The technique is incremental, so that each new site improves the triangulation by some well defined quality measure. The algorithm terminates after achieving a prespecified measure of mesh quality and produces a triangulation such that no angle is less than a given angle bound, a or greater than pi - 2alpha. This result also sets bounds on the maximum vertex degree, triangle aspect-ratio and maximum stretching rate for the triangulation. In addition to the output triangulations for a variety of CAD parts, the discussion presents related theoretical results which assert the existence of such an angle bound, and demonstrate that maximum bounds of between 25 deg and 30 deg may be achieved in practice.

Automatic Thread-Level Parallelization in the Chombo AMR Library

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christen, Matthias; Keen, Noel; Ligocki, Terry

2011-05-26

The increasing on-chip parallelism has some substantial implications for HPC applications. Currently, hybrid programming models (typically MPI+OpenMP) are employed for mapping software to the hardware in order to leverage the hardware?s architectural features. In this paper, we present an approach that automatically introduces thread level parallelism into Chombo, a parallel adaptive mesh refinement framework for finite difference type PDE solvers. In Chombo, core algorithms are specified in the ChomboFortran, a macro language extension to F77 that is part of the Chombo framework. This domain-specific language forms an already used target language for an automatic migration of the large number ofmore » existing algorithms into a hybrid MPI+OpenMP implementation. It also provides access to the auto-tuning methodology that enables tuning certain aspects of an algorithm to hardware characteristics. Performance measurements are presented for a few of the most relevant kernels with respect to a specific application benchmark using this technique as well as benchmark results for the entire application. The kernel benchmarks show that, using auto-tuning, up to a factor of 11 in performance was gained with 4 threads with respect to the serial reference implementation.« less

Cold dark matter. 1: The formation of dark halos

NASA Technical Reports Server (NTRS)

Gelb, James M.; Bertschinger, Edmund

1994-01-01

We use numerical simulations of critically closed cold dark matter (CDM) models to study the effects of numerical resolution on observable quantities. We study simulations with up to 256(exp 3) particles using the particle-mesh (PM) method and with up to 144(exp 3) particles using the adaptive particle-particle-mesh (P3M) method. Comparisons of galaxy halo distributions are made among the various simulations. We also compare distributions with observations, and we explore methods for identifying halos, including a new algorithm that finds all particles within closed contours of the smoothed density field surrounding a peak. The simulated halos show more substructure than predicted by the Press-Schechter theory. We are able to rule out all omega = 1 CDM models for linear amplitude sigma(sub 8) greater than or approximately = 0.5 because the simulations produce too many massive halos compared with the observations. The simulations also produce too many low-mass halos. The distribution of halos characterized by their circular velocities for the P3M simulations is in reasonable agreement with the observations for 150 km/s less than or = V(sub circ) less than or = 350 km/s.

On the implementation of an accurate and efficient solver for convection-diffusion equations

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from the finite element solution.

Computational performance of Free Mesh Method applied to continuum mechanics problems

PubMed Central

YAGAWA, Genki

2011-01-01

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics. PMID:21558753

SU-E-J-119: Head-And-Neck Digital Phantoms for Geometric and Dosimetric Uncertainty Evaluation of CT-CBCT Deformable Image Registration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shen, Z; Koyfman, S; Xia, P

2015-06-15

Purpose: To evaluate geometric and dosimetric uncertainties of CT-CBCT deformable image registration (DIR) algorithms using digital phantoms generated from real patients. Methods: We selected ten H&N cancer patients with adaptive IMRT. For each patient, a planning CT (CT1), a replanning CT (CT2), and a pretreatment CBCT (CBCT1) were used as the basis for digital phantom creation. Manually adjusted meshes were created for selected ROIs (e.g. PTVs, brainstem, spinal cord, mandible, and parotids) on CT1 and CT2. The mesh vertices were input into a thin-plate spline algorithm to generate a reference displacement vector field (DVF). The reference DVF was applied tomore » CBCT1 to create a simulated mid-treatment CBCT (CBCT2). The CT-CBCT digital phantom consisted of CT1 and CBCT2, which were linked by the reference DVF. Three DIR algorithms (Demons, B-Spline, and intensity-based) were applied to these ten digital phantoms. The images, ROIs, and volumetric doses were mapped from CT1 to CBCT2 using the DVFs computed by these three DIRs and compared to those mapped using the reference DVF. Results: The average Dice coefficients for selected ROIs were from 0.83 to 0.94 for Demons, from 0.82 to 0.95 for B-Spline, and from 0.67 to 0.89 for intensity-based DIR. The average Hausdorff distances for selected ROIs were from 2.4 to 6.2 mm for Demons, from 1.8 to 5.9 mm for B-Spline, and from 2.8 to 11.2 mm for intensity-based DIR. The average absolute dose errors for selected ROIs were from 0.7 to 2.1 Gy for Demons, from 0.7 to 2.9 Gy for B- Spline, and from 1.3 to 4.5 Gy for intensity-based DIR. Conclusion: Using clinically realistic CT-CBCT digital phantoms, Demons and B-Spline were shown to have similar geometric and dosimetric uncertainties while intensity-based DIR had the worst uncertainties. CT-CBCT DIR has the potential to provide accurate CBCT-based dose verification for H&N adaptive radiotherapy. Z Shen: None; K Bzdusek: an employee of Philips Healthcare; S Koyfman: None; P Xia: received research grants from Philips Healthcare and Siemens Healthcare.« less

Three Dimensional Grid Generation for Complex Configurations - Recent Progress

DTIC Science & Technology

1988-03-01

Navier/Stokes finite difference calculations currently of interest. It has been amply demonstrated that the viability of a numerical solution depends...such as advanced fighters or logistic transports, where a multiblock mesh, for example, is necessary. There exist numerous reports and books on the...MESHES I 3.10 ADAPTIVE GRID SCHEMES 10 3.11 REFERENCES 12 4. CONTRIBUTIONS 13 4.1 SOLICITATION AND OVERVIEW 13 4.2 LESSONS LEARNED IN THE MESH

Efficient 3D geometric and Zernike moments computation from unstructured surface meshes.

PubMed

Pozo, José María; Villa-Uriol, Maria-Cruz; Frangi, Alejandro F

2011-03-01

This paper introduces and evaluates a fast exact algorithm and a series of faster approximate algorithms for the computation of 3D geometric moments from an unstructured surface mesh of triangles. Being based on the object surface reduces the computational complexity of these algorithms with respect to volumetric grid-based algorithms. In contrast, it can only be applied for the computation of geometric moments of homogeneous objects. This advantage and restriction is shared with other proposed algorithms based on the object boundary. The proposed exact algorithm reduces the computational complexity for computing geometric moments up to order N with respect to previously proposed exact algorithms, from N(9) to N(6). The approximate series algorithm appears as a power series on the rate between triangle size and object size, which can be truncated at any desired degree. The higher the number and quality of the triangles, the better the approximation. This approximate algorithm reduces the computational complexity to N(3). In addition, the paper introduces a fast algorithm for the computation of 3D Zernike moments from the computed geometric moments, with a computational complexity N(4), while the previously proposed algorithm is of order N(6). The error introduced by the proposed approximate algorithms is evaluated in different shapes and the cost-benefit ratio in terms of error, and computational time is analyzed for different moment orders.

An accuracy assessment of Cartesian-mesh approaches for the Euler equations

NASA Technical Reports Server (NTRS)

Coirier, William J.; Powell, Kenneth G.

1995-01-01

A critical assessment of the accuracy of Cartesian-mesh approaches for steady, transonic solutions of the Euler equations of gas dynamics is made. An exact solution of the Euler equations (Ringleb's flow) is used not only to infer the order of the truncation error of the Cartesian-mesh approaches, but also to compare the magnitude of the discrete error directly to that obtained with a structured mesh approach. Uniformly and adaptively refined solutions using a Cartesian-mesh approach are obtained and compared to each other and to uniformly refined structured mesh results. The effect of cell merging is investigated as well as the use of two different K-exact reconstruction procedures. The solution methodology of the schemes is explained and tabulated results are presented to compare the solution accuracies.

Three-dimensional analysis of implanted magnetic-resonance-visible meshes.

PubMed

Sindhwani, Nikhil; Feola, Andrew; De Keyzer, Frederik; Claus, Filip; Callewaert, Geertje; Urbankova, Iva; Ourselin, Sebastien; D'hooge, Jan; Deprest, Jan

2015-10-01

Our primary objective was to develop relevant algorithms for quantification of mesh position and 3D shape in magnetic resonance (MR) images. In this proof-of-principle study, one patient with severe anterior vaginal wall prolapse was implanted with an MR-visible mesh. High-resolution MR images of the pelvis were acquired 6 weeks and 8 months postsurgery. 3D models were created using semiautomatic segmentation techniques. Conformational changes were recorded quantitatively using part-comparison analysis. An ellipticity measure is proposed to record longitudinal conformational changes in the mesh arms. The surface that is the effective reinforcement provided by the mesh is calculated using a novel methodology. The area of this surface is the effective support area (ESA). MR-visible mesh was clearly outlined in the images, which allowed us to longitudinally quantify mesh configuration between 6 weeks and 8 months after implantation. No significant changes were found in mesh position, effective support area, conformation of the mesh's main body, and arm length during the period of observation. Ellipticity profiles show longitudinal conformational changes in posterior arms. This paper proposes novel methodologies for a systematic 3D assessment of the position and morphology of MR-visible meshes. A novel semiautomatic tool was developed to calculate the effective area of support provided by the mesh, a potentially clinically important parameter.

Methods for prismatic/tetrahedral grid generation and adaptation

NASA Technical Reports Server (NTRS)

Kallinderis, Y.

1995-01-01

The present work involves generation of hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is a method for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A High Speed Civil Transport (HSCT) type of aircraft geometry is considered. The generated hybrid grid required only 170 K tetrahedra instead of an estimated two million had a tetrahedral mesh been used in the prisms region as well. A solution adaptive scheme for viscous computations on hybrid grids is also presented. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples 3-D, isotropic division of tetrahedra and 2-D, directional division of prisms.

Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dolbow, John; Zhang, Ziyu; Spencer, Benjamin

Efforts are underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). A capability was previously developed to calculate three-dimensional interaction- integrals to extract mixed-mode stress-intensity factors. This capability requires the use of a finite element mesh that conforms to the crack geometry. The eXtended Finite Element Method (X-FEM) provides a means to represent a crack geometry without explicitly fitting the finite element mesh to it. This is effected by enhancing the element kinematics to represent jump discontinuities at arbitrary locations inside ofmore » the element, as well as the incorporation of asymptotic near-tip fields to better capture crack singularities. In this work, use of only the discontinuous enrichment functions was examined to see how accurate stress intensity factors could still be calculated. This report documents the following work to enhance Grizzly’s engineering fracture capabilities by introducing arbitrary jump discontinuities for prescribed crack geometries; X-FEM Mesh Cutting in 3D: to enhance the kinematics of elements that are intersected by arbitrary crack geometries, a mesh cutting algorithm was implemented in Grizzly. The algorithm introduces new virtual nodes and creates partial elements, and then creates a new mesh connectivity; Interaction Integral Modifications: the existing code for evaluating the interaction integral in Grizzly was based on the assumption of a mesh that was fitted to the crack geometry. Modifications were made to allow for the possibility of a crack front that passes arbitrarily through the mesh; and Benchmarking for 3D Fracture: the new capabilities were benchmarked against mixed-mode three-dimensional fracture problems with known analytical solutions.« less

MeSHy: Mining unanticipated PubMed information using frequencies of occurrences and concurrences of MeSH terms.

PubMed

Theodosiou, T; Vizirianakis, I S; Angelis, L; Tsaftaris, A; Darzentas, N

2011-12-01

PubMed is the most widely used database of biomedical literature. To the detriment of the user though, the ranking of the documents retrieved for a query is not content-based, and important semantic information in the form of assigned Medical Subject Headings (MeSH) terms is not readily presented or productively utilized. The motivation behind this work was the discovery of unanticipated information through the appropriate ranking of MeSH term pairs and, indirectly, documents. Such information can be useful in guiding novel research and following promising trends. A web-based tool, called MeSHy, was developed implementing a mainly statistical algorithm. The algorithm takes into account the frequencies of occurrences, concurrences, and the semantic similarities of MeSH terms in retrieved PubMed documents to create MeSH term pairs. These are then scored and ranked, focusing on their unexpectedly frequent or infrequent occurrences. MeSHy presents results through an online interactive interface facilitating further manipulation through filtering and sorting. The results themselves include the MeSH term pairs, along with MeSH categories, the score, and document IDs, all of which are hyperlinked for convenience. To highlight the applicability of the tool, we report the findings of an expert in the pharmacology field on querying the molecularly-targeted drug imatinib and nutrition-related flavonoids. To the best of our knowledge, MeSHy is the first publicly available tool able to directly provide such a different perspective on the complex nature of published work. Implemented in Perl and served by Apache2 at http://bat.ina.certh.gr/tools/meshy/ with all major browsers supported. Copyright © 2011 Elsevier Inc. All rights reserved.

Geometric identification and damage detection of structural elements by terrestrial laser scanner

NASA Astrophysics Data System (ADS)

Hou, Tsung-Chin; Liu, Yu-Wei; Su, Yu-Min

2016-04-01

In recent years, three-dimensional (3D) terrestrial laser scanning technologies with higher precision and higher capability are developing rapidly. The growing maturity of laser scanning has gradually approached the required precision as those have been provided by traditional structural monitoring technologies. Together with widely available fast computation for massive point cloud data processing, 3D laser scanning can serve as an efficient structural monitoring alternative for civil engineering communities. Currently most research efforts have focused on integrating/calculating the measured multi-station point cloud data, as well as modeling/establishing the 3D meshes of the scanned objects. Very little attention has been spent on extracting the information related to health conditions and mechanical states of structures. In this study, an automated numerical approach that integrates various existing algorithms for geometric identification and damage detection of structural elements were established. Specifically, adaptive meshes were employed for classifying the point cloud data of the structural elements, and detecting the associated damages from the calculated eigenvalues in each area of the structural element. Furthermore, kd-tree was used to enhance the searching efficiency of plane fitting which were later used for identifying the boundaries of structural elements. The results of geometric identification were compared with M3C2 algorithm provided by CloudCompare, as well as validated by LVDT measurements of full-scale reinforced concrete beams tested in laboratory. It shows that 3D laser scanning, through the established processing approaches of the point cloud data, can offer a rapid, nondestructive, remote, and accurate solution for geometric identification and damage detection of structural elements.

Multi-dimensional Upwind Fluctuation Splitting Scheme with Mesh Adaption for Hypersonic Viscous Flow. Degree awarded by Virginia Polytechnic Inst. and State Univ., 9 Nov. 2001

NASA Technical Reports Server (NTRS)

Wood, William A., III

2002-01-01

A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two-dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil, full upwinding, and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout, the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach, a second-order, dual mesh upwind flux difference splitting scheme (DMFDSFV), and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. A Blasius flat plate viscous validation case reveals a more accurate upsilon-velocity profile for fluctuation splitting, and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably, the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. The second half of the report develops a local, compact, anisotropic unstructured mesh adaptation scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. The adaptation strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization.

Some observations on mesh refinement schemes applied to shock wave phenomena

NASA Technical Reports Server (NTRS)

Quirk, James J.

1995-01-01

This workshop's double-wedge test problem is taken from one of a sequence of experiments which were performed in order to classify the various canonical interactions between a planar shock wave and a double wedge. Therefore to build up a reasonably broad picture of the performance of our mesh refinement algorithm we have simulated three of these experiments and not just the workshop case. Here, using the results from these simulations together with their experimental counterparts, we make some general observations concerning the development of mesh refinement schemes for shock wave phenomena.

A template-based approach for parallel hexahedral two-refinement

DOE PAGES

Owen, Steven J.; Shih, Ryan M.; Ernst, Corey D.

2016-10-17

Here, we provide a template-based approach for generating locally refined all-hex meshes. We focus specifically on refinement of initially structured grids utilizing a 2-refinement approach where uniformly refined hexes are subdivided into eight child elements. The refinement algorithm consists of identifying marked nodes that are used as the basis for a set of four simple refinement templates. The target application for 2-refinement is a parallel grid-based all-hex meshing tool for high performance computing in a distributed environment. The result is a parallel consistent locally refined mesh requiring minimal communication and where minimum mesh quality is greater than scaled Jacobian 0.3more » prior to smoothing.« less

A template-based approach for parallel hexahedral two-refinement

DOE Office of Scientific and Technical Information (OSTI.GOV)

Owen, Steven J.; Shih, Ryan M.; Ernst, Corey D.

Here, we provide a template-based approach for generating locally refined all-hex meshes. We focus specifically on refinement of initially structured grids utilizing a 2-refinement approach where uniformly refined hexes are subdivided into eight child elements. The refinement algorithm consists of identifying marked nodes that are used as the basis for a set of four simple refinement templates. The target application for 2-refinement is a parallel grid-based all-hex meshing tool for high performance computing in a distributed environment. The result is a parallel consistent locally refined mesh requiring minimal communication and where minimum mesh quality is greater than scaled Jacobian 0.3more » prior to smoothing.« less

Modelling Detailed-Chemistry Effects on Turbulent Diffusion Flames using a Parallel Solution-Adaptive Scheme

NASA Astrophysics Data System (ADS)

Jha, Pradeep Kumar

Capturing the effects of detailed-chemistry on turbulent combustion processes is a central challenge faced by the numerical combustion community. However, the inherent complexity and non-linear nature of both turbulence and chemistry require that combustion models rely heavily on engineering approximations to remain computationally tractable. This thesis proposes a computationally efficient algorithm for modelling detailed-chemistry effects in turbulent diffusion flames and numerically predicting the associated flame properties. The cornerstone of this combustion modelling tool is the use of parallel Adaptive Mesh Refinement (AMR) scheme with the recently proposed Flame Prolongation of Intrinsic low-dimensional manifold (FPI) tabulated-chemistry approach for modelling complex chemistry. The effect of turbulence on the mean chemistry is incorporated using a Presumed Conditional Moment (PCM) approach based on a beta-probability density function (PDF). The two-equation k-w turbulence model is used for modelling the effects of the unresolved turbulence on the mean flow field. The finite-rate of methane-air combustion is represented here by using the GRI-Mech 3.0 scheme. This detailed mechanism is used to build the FPI tables. A state of the art numerical scheme based on a parallel block-based solution-adaptive algorithm has been developed to solve the Favre-averaged Navier-Stokes (FANS) and other governing partial-differential equations using a second-order accurate, fully-coupled finite-volume formulation on body-fitted, multi-block, quadrilateral/hexahedral mesh for two-dimensional and three-dimensional flow geometries, respectively. A standard fourth-order Runge-Kutta time-marching scheme is used for time-accurate temporal discretizations. Numerical predictions of three different diffusion flames configurations are considered in the present work: a laminar counter-flow flame; a laminar co-flow diffusion flame; and a Sydney bluff-body turbulent reacting flow. Comparisons are made between the predicted results of the present FPI scheme and Steady Laminar Flamelet Model (SLFM) approach for diffusion flames. The effects of grid resolution on the predicted overall flame solutions are also assessed. Other non-reacting flows have also been considered to further validate other aspects of the numerical scheme. The present schemes predict results which are in good agreement with published experimental results and reduces the computational cost involved in modelling turbulent diffusion flames significantly, both in terms of storage and processing time.

Chi-square-based scoring function for categorization of MEDLINE citations.

PubMed

Kastrin, A; Peterlin, B; Hristovski, D

2010-01-01

Text categorization has been used in biomedical informatics for identifying documents containing relevant topics of interest. We developed a simple method that uses a chi-square-based scoring function to determine the likelihood of MEDLINE citations containing genetic relevant topic. Our procedure requires construction of a genetic and a nongenetic domain document corpus. We used MeSH descriptors assigned to MEDLINE citations for this categorization task. We compared frequencies of MeSH descriptors between two corpora applying chi-square test. A MeSH descriptor was considered to be a positive indicator if its relative observed frequency in the genetic domain corpus was greater than its relative observed frequency in the nongenetic domain corpus. The output of the proposed method is a list of scores for all the citations, with the highest score given to those citations containing MeSH descriptors typical for the genetic domain. Validation was done on a set of 734 manually annotated MEDLINE citations. It achieved predictive accuracy of 0.87 with 0.69 recall and 0.64 precision. We evaluated the method by comparing it to three machine-learning algorithms (support vector machines, decision trees, naïve Bayes). Although the differences were not statistically significantly different, results showed that our chi-square scoring performs as good as compared machine-learning algorithms. We suggest that the chi-square scoring is an effective solution to help categorize MEDLINE citations. The algorithm is implemented in the BITOLA literature-based discovery support system as a preprocessor for gene symbol disambiguation process.

A Novel Coarsening Method for Scalable and Efficient Mesh Generation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yoo, A; Hysom, D; Gunney, B

2010-12-02

In this paper, we propose a novel mesh coarsening method called brick coarsening method. The proposed method can be used in conjunction with any graph partitioners and scales to very large meshes. This method reduces problem space by decomposing the original mesh into fixed-size blocks of nodes called bricks, layered in a similar way to conventional brick laying, and then assigning each node of the original mesh to appropriate brick. Our experiments indicate that the proposed method scales to very large meshes while allowing simple RCB partitioner to produce higher-quality partitions with significantly less edge cuts. Our results further indicatemore » that the proposed brick-coarsening method allows more complicated partitioners like PT-Scotch to scale to very large problem size while still maintaining good partitioning performance with relatively good edge-cut metric. Graph partitioning is an important problem that has many scientific and engineering applications in such areas as VLSI design, scientific computing, and resource management. Given a graph G = (V,E), where V is the set of vertices and E is the set of edges, (k-way) graph partitioning problem is to partition the vertices of the graph (V) into k disjoint groups such that each group contains roughly equal number of vertices and the number of edges connecting vertices in different groups is minimized. Graph partitioning plays a key role in large scientific computing, especially in mesh-based computations, as it is used as a tool to minimize the volume of communication and to ensure well-balanced load across computing nodes. The impact of graph partitioning on the reduction of communication can be easily seen, for example, in different iterative methods to solve a sparse system of linear equation. Here, a graph partitioning technique is applied to the matrix, which is basically a graph in which each edge is a non-zero entry in the matrix, to allocate groups of vertices to processors in such a way that many of matrix-vector multiplication can be performed locally on each processor and hence to minimize communication. Furthermore, a good graph partitioning scheme ensures the equal amount of computation performed on each processor. Graph partitioning is a well known NP-complete problem, and thus the most commonly used graph partitioning algorithms employ some forms of heuristics. These algorithms vary in terms of their complexity, partition generation time, and the quality of partitions, and they tend to trade off these factors. A significant challenge we are currently facing at the Lawrence Livermore National Laboratory is how to partition very large meshes on massive-size distributed memory machines like IBM BlueGene/P, where scalability becomes a big issue. For example, we have found that the ParMetis, a very popular graph partitioning tool, can only scale to 16K processors. An ideal graph partitioning method on such an environment should be fast and scale to very large meshes, while producing high quality partitions. This is an extremely challenging task, as to scale to that level, the partitioning algorithm should be simple and be able to produce partitions that minimize inter-processor communications and balance the load imposed on the processors. Our goals in this work are two-fold: (1) To develop a new scalable graph partitioning method with good load balancing and communication reduction capability. (2) To study the performance of the proposed partitioning method on very large parallel machines using actual data sets and compare the performance to that of existing methods. The proposed method achieves the desired scalability by reducing the mesh size. For this, it coarsens an input mesh into a smaller size mesh by coalescing the vertices and edges of the original mesh into a set of mega-vertices and mega-edges. A new coarsening method called brick algorithm is developed in this research. In the brick algorithm, the zones in a given mesh are first grouped into fixed size blocks called bricks. These brick are then laid in a way similar to conventional brick laying technique, which reduces the number of neighboring blocks each block needs to communicate. Contributions of this research are as follows: (1) We have developed a novel method that scales to a really large problem size while producing high quality mesh partitions; (2) We measured the performance and scalability of the proposed method on a machine of massive size using a set of actual large complex data sets, where we have scaled to a mesh with 110 million zones using our method. To the best of our knowledge, this is the largest complex mesh that a partitioning method is successfully applied to; and (3) We have shown that proposed method can reduce the number of edge cuts by as much as 65%.« less

A method for data handling numerical results in parallel OpenFOAM simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anton, Alin; Muntean, Sebastian

Parallel computational fluid dynamics simulations produce vast amount of numerical result data. This paper introduces a method for reducing the size of the data by replaying the interprocessor traffic. The results are recovered only in certain regions of interest configured by the user. A known test case is used for several mesh partitioning scenarios using the OpenFOAM toolkit{sup ®}[1]. The space savings obtained with classic algorithms remain constant for more than 60 Gb of floating point data. Our method is most efficient on large simulation meshes and is much better suited for compressing large scale simulation results than the regular algorithms.

Interfacing WIPL-D with Mechanical CAD Software

NASA Technical Reports Server (NTRS)

Bliznyuk, Nataliya; Janic, Bojan

2007-01-01

of almost any popular CAD format, e.g. IGES, Parasolid, DXF, ACIS etc. The solid models are processed (simplified) and meshed in GiD(R), and then converted into WIPL-D Pro input file by simple Fortran or Matlab code. This algorithm allows the user to control the mesh of imported geometry, and to assign electric pperties to metalic and dielectric surfaces. Implementation of the algorithm is demonstrated by examples obtained from the NASA Discovery mission, Phoenix Lander 2008. Results for radiation pattern of Phoenix Lander UHF relay antenna with effect of Martian surface, both simulated in WIPL-D Pro and measured, are shown for comparison.

Deploy Nalu/Kokkos algorithmic infrastructure with performance benchmarking.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Domino, Stefan P.; Ananthan, Shreyas; Knaus, Robert C.

The former Nalu interior heterogeneous algorithm design, which was originally designed to manage matrix assembly operations over all elemental topology types, has been modified to operate over homogeneous collections of mesh entities. This newly templated kernel design allows for removal of workset variable resize operations that were formerly required at each loop over a Sierra ToolKit (STK) bucket (nominally, 512 entities in size). Extensive usage of the Standard Template Library (STL) std::vector has been removed in favor of intrinsic Kokkos memory views. In this milestone effort, the transition to Kokkos as the underlying infrastructure to support performance and portability onmore » many-core architectures has been deployed for key matrix algorithmic kernels. A unit-test driven design effort has developed a homogeneous entity algorithm that employs a team-based thread parallelism construct. The STK Single Instruction Multiple Data (SIMD) infrastructure is used to interleave data for improved vectorization. The collective algorithm design, which allows for concurrent threading and SIMD management, has been deployed for the core low-Mach element- based algorithm. Several tests to ascertain SIMD performance on Intel KNL and Haswell architectures have been carried out. The performance test matrix includes evaluation of both low- and higher-order methods. The higher-order low-Mach methodology builds on polynomial promotion of the core low-order control volume nite element method (CVFEM). Performance testing of the Kokkos-view/SIMD design indicates low-order matrix assembly kernel speed-up ranging between two and four times depending on mesh loading and node count. Better speedups are observed for higher-order meshes (currently only P=2 has been tested) especially on KNL. The increased workload per element on higher-order meshes bene ts from the wide SIMD width on KNL machines. Combining multiple threads with SIMD on KNL achieves a 4.6x speedup over the baseline, with assembly timings faster than that observed on Haswell architecture. The computational workload of higher-order meshes, therefore, seems ideally suited for the many-core architecture and justi es further exploration of higher-order on NGP platforms. A Trilinos/Tpetra-based multi-threaded GMRES preconditioned by symmetric Gauss Seidel (SGS) represents the core solver infrastructure for the low-Mach advection/diffusion implicit solves. The threaded solver stack has been tested on small problems on NREL's Peregrine system using the newly developed and deployed Kokkos-view/SIMD kernels. fforts are underway to deploy the Tpetra-based solver stack on NERSC Cori system to benchmark its performance at scale on KNL machines.« less