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.

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.

Unstructured mesh algorithms for aerodynamic calculations

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1992-01-01

The use of unstructured mesh techniques for solving complex aerodynamic flows is discussed. The principle advantages of unstructured mesh strategies, as they relate to complex geometries, adaptive meshing capabilities, and parallel processing are emphasized. The various aspects required for the efficient and accurate solution of aerodynamic flows are addressed. These include mesh generation, mesh adaptivity, solution algorithms, convergence acceleration, and turbulence modeling. Computations of viscous turbulent two-dimensional flows and inviscid three-dimensional flows about complex configurations are demonstrated. Remaining obstacles and directions for future research are also outlined.

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.

Self-Avoiding Walks Over Adaptive Triangular Grids

NASA Technical Reports Server (NTRS)

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

1999-01-01

Space-filling curves is a popular approach based on a geometric embedding for linearizing computational meshes. We present a new O(n log n) combinatorial algorithm for constructing a self avoiding walk through a two dimensional mesh containing n triangles. We show that for hierarchical adaptive meshes, the algorithm can be locally adapted and easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the runtime partitioning and load balancing of adaptive unstructured grids.

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.

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.

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.

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.

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.

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.

Self-Avoiding Walks over Adaptive Triangular Grids

NASA Technical Reports Server (NTRS)

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

1998-01-01

In this paper, we present a new approach to constructing a "self-avoiding" walk through a triangular mesh. Unlike the popular approach of visiting mesh elements using space-filling curves which is based on a geometric embedding, our approach is combinatorial in the sense that it uses the mesh connectivity only. We present an algorithm for constructing a self-avoiding walk which can be applied to any unstructured triangular mesh. The complexity of the algorithm is O(n x log(n)), where n is the number of triangles in the mesh. We show that for hierarchical adaptive meshes, the algorithm can be easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the run-time partitioning and load balancing of adaptive unstructured grids.

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.

A multi-block adaptive solving technique based on lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Zhang, Yang; Xie, Jiahua; Li, Xiaoyue; Ma, Zhenghai; Zou, Jianfeng; Zheng, Yao

2018-05-01

In this paper, a CFD parallel adaptive algorithm is self-developed by combining the multi-block Lattice Boltzmann Method (LBM) with Adaptive Mesh Refinement (AMR). The mesh refinement criterion of this algorithm is based on the density, velocity and vortices of the flow field. The refined grid boundary is obtained by extending outward half a ghost cell from the coarse grid boundary, which makes the adaptive mesh more compact and the boundary treatment more convenient. Two numerical examples of the backward step flow separation and the unsteady flow around circular cylinder demonstrate the vortex structure of the cold flow field accurately and specifically.

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.

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.

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.

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 (UA) NAS Parallel Benchmark. Version 1.0

NASA Technical Reports Server (NTRS)

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

2004-01-01

We present a complete specification of a new benchmark for measuring the performance of modern computer systems when solving scientific problems featuring irregular, dynamic memory accesses. It complements the existing NAS Parallel Benchmark suite. The benchmark involves the solution of a stylized heat transfer problem in a cubic domain, discretized on an adaptively refined, unstructured mesh.

Unstructured Adaptive Grid Computations on an Array of SMPs

NASA Technical Reports Server (NTRS)

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

1996-01-01

Dynamic load balancing is necessary for parallel adaptive methods to solve unsteady CFD problems on unstructured grids. We have presented such a dynamic load balancing framework called JOVE, in this paper. Results on a four-POWERnode POWER CHALLENGEarray demonstrated that load balancing gives significant performance improvements over no load balancing for such adaptive computations. The parallel speedup of JOVE, implemented using MPI on the POWER CHALLENCEarray, was significant, being as high as 31 for 32 processors. An implementation of JOVE that exploits 'an array of SMPS' architecture was also studied; this hybrid JOVE outperformed flat JOVE by up to 28% on the meshes and adaption models tested. With large, realistic meshes and actual flow-solver and adaption phases incorporated into JOVE, hybrid JOVE can be expected to yield significant advantage over flat JOVE, especially as the number of processors is increased, thus demonstrating the scalability of an array of SMPs architecture.

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.

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.

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.

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.

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.

Error estimation and adaptive mesh refinement for parallel analysis of shell structures

NASA Technical Reports Server (NTRS)

Keating, Scott C.; Felippa, Carlos A.; Park, K. C.

1994-01-01

The formulation and application of element-level, element-independent error indicators is investigated. This research culminates in the development of an error indicator formulation which is derived based on the projection of element deformation onto the intrinsic element displacement modes. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited for obtaining error values and driving adaptive mesh refinements on parallel computers where access to neighboring elements residing on different processors may incur significant overhead. In addition such estimators are insensitive to the presence of physical interfaces and junctures. An error indicator qualifies as 'element-independent' when only visible quantities such as element stiffness and nodal displacements are used to quantify error. Error evaluation at the element level and element independence for the error indicator are highly desired properties for computing error in production-level finite element codes. Four element-level error indicators have been constructed. Two of the indicators are based on variational formulation of the element stiffness and are element-dependent. Their derivations are retained for developmental purposes. The second two indicators mimic and exceed the first two in performance but require no special formulation of the element stiffness mesh refinement which we demonstrate for two dimensional plane stress problems. The parallelizing of substructures and adaptive mesh refinement is discussed and the final error indicator using two-dimensional plane-stress and three-dimensional shell problems is demonstrated.

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.

S-HARP: A parallel dynamic spectral partitioner

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

Sohn, A.; Simon, H.

1998-01-01

Computational science problems with adaptive meshes involve dynamic load balancing when implemented on parallel machines. This dynamic load balancing requires fast partitioning of computational meshes at run time. The authors present in this report a fast parallel dynamic partitioner, called S-HARP. The underlying principles of S-HARP are the fast feature of inertial partitioning and the quality feature of spectral partitioning. S-HARP partitions a graph from scratch, requiring no partition information from previous iterations. Two types of parallelism have been exploited in S-HARP, fine grain loop level parallelism and coarse grain recursive parallelism. The parallel partitioner has been implemented in Messagemore » Passing Interface on Cray T3E and IBM SP2 for portability. Experimental results indicate that S-HARP can partition a mesh of over 100,000 vertices into 256 partitions in 0.2 seconds on a 64 processor Cray T3E. S-HARP is much more scalable than other dynamic partitioners, giving over 15 fold speedup on 64 processors while ParaMeTiS1.0 gives a few fold speedup. Experimental results demonstrate that S-HARP is three to 10 times faster than the dynamic partitioners ParaMeTiS and Jostle on six computational meshes of size over 100,000 vertices.« less

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.

Visualization of Octree Adaptive Mesh Refinement (AMR) in Astrophysical Simulations

NASA Astrophysics Data System (ADS)

Labadens, M.; Chapon, D.; Pomaréde, D.; Teyssier, R.

2012-09-01

Computer simulations are important in current cosmological research. Those simulations run in parallel on thousands of processors, and produce huge amount of data. Adaptive mesh refinement is used to reduce the computing cost while keeping good numerical accuracy in regions of interest. RAMSES is a cosmological code developed by the Commissariat à l'énergie atomique et aux énergies alternatives (English: Atomic Energy and Alternative Energies Commission) which uses Octree adaptive mesh refinement. Compared to grid based AMR, the Octree AMR has the advantage to fit very precisely the adaptive resolution of the grid to the local problem complexity. However, this specific octree data type need some specific software to be visualized, as generic visualization tools works on Cartesian grid data type. This is why the PYMSES software has been also developed by our team. It relies on the python scripting language to ensure a modular and easy access to explore those specific data. In order to take advantage of the High Performance Computer which runs the RAMSES simulation, it also uses MPI and multiprocessing to run some parallel code. We would like to present with more details our PYMSES software with some performance benchmarks. PYMSES has currently two visualization techniques which work directly on the AMR. The first one is a splatting technique, and the second one is a custom ray tracing technique. Both have their own advantages and drawbacks. We have also compared two parallel programming techniques with the python multiprocessing library versus the use of MPI run. The load balancing strategy has to be smartly defined in order to achieve a good speed up in our computation. Results obtained with this software are illustrated in the context of a massive, 9000-processor parallel simulation of a Milky Way-like galaxy.

Parallel Processing of Adaptive Meshes with Load Balancing

NASA Technical Reports Server (NTRS)

Das, Sajal K.; Harvey, Daniel J.; Biswas, Rupak; Biegel, Bryan (Technical Monitor)

2001-01-01

Many scientific applications involve grids that lack a uniform underlying structure. These applications are often also dynamic in nature in that the grid structure significantly changes between successive phases of execution. In parallel computing environments, mesh adaptation of unstructured grids through selective refinement/coarsening has proven to be an effective approach. However, achieving load balance while minimizing interprocessor communication and redistribution costs is a difficult problem. Traditional dynamic load balancers are mostly inadequate because they lack a global view of system loads across processors. In this paper, we propose a novel and general-purpose load balancer that utilizes symmetric broadcast networks (SBN) as the underlying communication topology, and compare its performance with a successful global load balancing environment, called PLUM, specifically created to handle adaptive unstructured applications. Our experimental results on an IBM SP2 demonstrate that the SBN-based load balancer achieves lower redistribution costs than that under PLUM by overlapping processing and data migration.

Progress in Computational Simulation of Earthquakes

NASA Technical Reports Server (NTRS)

Donnellan, Andrea; Parker, Jay; Lyzenga, Gregory; Judd, Michele; Li, P. Peggy; Norton, Charles; Tisdale, Edwin; Granat, Robert

2006-01-01

GeoFEST(P) is a computer program written for use in the QuakeSim project, which is devoted to development and improvement of means of computational simulation of earthquakes. GeoFEST(P) models interacting earthquake fault systems from the fault-nucleation to the tectonic scale. The development of GeoFEST( P) has involved coupling of two programs: GeoFEST and the Pyramid Adaptive Mesh Refinement Library. GeoFEST is a message-passing-interface-parallel code that utilizes a finite-element technique to simulate evolution of stress, fault slip, and plastic/elastic deformation in realistic materials like those of faulted regions of the crust of the Earth. The products of such simulations are synthetic observable time-dependent surface deformations on time scales from days to decades. Pyramid Adaptive Mesh Refinement Library is a software library that facilitates the generation of computational meshes for solving physical problems. In an application of GeoFEST(P), a computational grid can be dynamically adapted as stress grows on a fault. Simulations on workstations using a few tens of thousands of stress and displacement finite elements can now be expanded to multiple millions of elements with greater than 98-percent scaled efficiency on over many hundreds of parallel processors (see figure).

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.

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.

Advances in Patch-Based Adaptive Mesh Refinement Scalability

DOE PAGES

Gunney, Brian T.N.; Anderson, Robert W.

2015-12-18

Patch-based structured adaptive mesh refinement (SAMR) is widely used for high-resolution simu- lations. Combined with modern supercomputers, it could provide simulations of unprecedented size and resolution. A persistent challenge for this com- bination has been managing dynamically adaptive meshes on more and more MPI tasks. The dis- tributed mesh management scheme in SAMRAI has made some progress SAMR scalability, but early al- gorithms still had trouble scaling past the regime of 105 MPI tasks. This work provides two critical SAMR regridding algorithms, which are integrated into that scheme to ensure efficiency of the whole. The clustering algorithm is an extensionmore » of the tile- clustering approach, making it more flexible and efficient in both clustering and parallelism. The partitioner is a new algorithm designed to prevent the network congestion experienced by its prede- cessor. We evaluated performance using weak- and strong-scaling benchmarks designed to be difficult for dynamic adaptivity. Results show good scaling on up to 1.5M cores and 2M MPI tasks. Detailed timing diagnostics suggest scaling would continue well past that.« less

Advances in Patch-Based Adaptive Mesh Refinement Scalability

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

Gunney, Brian T.N.; Anderson, Robert W.

Patch-based structured adaptive mesh refinement (SAMR) is widely used for high-resolution simu- lations. Combined with modern supercomputers, it could provide simulations of unprecedented size and resolution. A persistent challenge for this com- bination has been managing dynamically adaptive meshes on more and more MPI tasks. The dis- tributed mesh management scheme in SAMRAI has made some progress SAMR scalability, but early al- gorithms still had trouble scaling past the regime of 105 MPI tasks. This work provides two critical SAMR regridding algorithms, which are integrated into that scheme to ensure efficiency of the whole. The clustering algorithm is an extensionmore » of the tile- clustering approach, making it more flexible and efficient in both clustering and parallelism. The partitioner is a new algorithm designed to prevent the network congestion experienced by its prede- cessor. We evaluated performance using weak- and strong-scaling benchmarks designed to be difficult for dynamic adaptivity. Results show good scaling on up to 1.5M cores and 2M MPI tasks. Detailed timing diagnostics suggest scaling would continue well past that.« less

Three dimensional adaptive mesh refinement on a spherical shell for atmospheric models with lagrangian coordinates

NASA Astrophysics Data System (ADS)

Penner, Joyce E.; Andronova, Natalia; Oehmke, Robert C.; Brown, Jonathan; Stout, Quentin F.; Jablonowski, Christiane; van Leer, Bram; Powell, Kenneth G.; Herzog, Michael

2007-07-01

One of the most important advances needed in global climate models is the development of atmospheric General Circulation Models (GCMs) that can reliably treat convection. Such GCMs require high resolution in local convectively active regions, both in the horizontal and vertical directions. During previous research we have developed an Adaptive Mesh Refinement (AMR) dynamical core that can adapt its grid resolution horizontally. Our approach utilizes a finite volume numerical representation of the partial differential equations with floating Lagrangian vertical coordinates and requires resolving dynamical processes on small spatial scales. For the latter it uses a newly developed general-purpose library, which facilitates 3D block-structured AMR on spherical grids. The library manages neighbor information as the blocks adapt, and handles the parallel communication and load balancing, freeing the user to concentrate on the scientific modeling aspects of their code. In particular, this library defines and manages adaptive blocks on the sphere, provides user interfaces for interpolation routines and supports the communication and load-balancing aspects for parallel applications. We have successfully tested the library in a 2-D (longitude-latitude) implementation. During the past year, we have extended the library to treat adaptive mesh refinement in the vertical direction. Preliminary results are discussed. This research project is characterized by an interdisciplinary approach involving atmospheric science, computer science and mathematical/numerical aspects. The work is done in close collaboration between the Atmospheric Science, Computer Science and Aerospace Engineering Departments at the University of Michigan and NOAA GFDL.

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.

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.

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

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.

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.

A software platform for continuum modeling of ion channels based on unstructured mesh

NASA Astrophysics Data System (ADS)

Tu, B.; Bai, S. Y.; Chen, M. X.; Xie, Y.; Zhang, L. B.; Lu, B. Z.

2014-01-01

Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson-Nernst-Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module and a numerical module. A demonstration of the platform is provided with a study of two real proteins, the connexin 26 and hemolysin ion channels.

Innovative Language-Based & Object-Oriented Structured AMR Using Fortran 90 and OpenMP

NASA Technical Reports Server (NTRS)

Norton, C.; Balsara, D.

1999-01-01

Parallel adaptive mesh refinement (AMR) is an important numerical technique that leads to the efficient solution of many physical and engineering problems. In this paper, we describe how AMR programing can be performed in an object-oreinted way using the modern aspects of Fortran 90 combined with the parallelization features of OpenMP.

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

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

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Nyx: Adaptive mesh, massively-parallel, cosmological simulation code

NASA Astrophysics Data System (ADS)

Almgren, Ann; Beckner, Vince; Friesen, Brian; Lukic, Zarija; Zhang, Weiqun

2017-12-01

Nyx code solves equations of compressible hydrodynamics on an adaptive grid hierarchy coupled with an N-body treatment of dark matter. The gas dynamics in Nyx use a finite volume methodology on an adaptive set of 3-D Eulerian grids; dark matter is represented as discrete particles moving under the influence of gravity. Particles are evolved via a particle-mesh method, using Cloud-in-Cell deposition/interpolation scheme. Both baryonic and dark matter contribute to the gravitational field. In addition, Nyx includes physics for accurately modeling the intergalactic medium; in optically thin limits and assuming ionization equilibrium, the code calculates heating and cooling processes of the primordial-composition gas in an ionizing ultraviolet background radiation field.

Applying Parallel Adaptive Methods with GeoFEST/PYRAMID to Simulate Earth Surface Crustal Dynamics

NASA Technical Reports Server (NTRS)

Norton, Charles D.; Lyzenga, Greg; Parker, Jay; Glasscoe, Margaret; Donnellan, Andrea; Li, Peggy

2006-01-01

This viewgraph presentation reviews the use Adaptive Mesh Refinement (AMR) in simulating the Crustal Dynamics of Earth's Surface. AMR simultaneously improves solution quality, time to solution, and computer memory requirements when compared to generating/running on a globally fine mesh. The use of AMR in simulating the dynamics of the Earth's Surface is spurred by future proposed NASA missions, such as InSAR for Earth surface deformation and other measurements. These missions will require support for large-scale adaptive numerical methods using AMR to model observations. AMR was chosen because it has been successful in computation fluid dynamics for predictive simulation of complex flows around complex structures.

Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.

2015-07-01

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated that the adaptive mesh refinement can be particularly efficient in resolving complex shapes. The implemented inversion scheme was able to resolve a hemisphere object with sufficient resolution starting from a coarse discretization and refining mesh adaptively in a fully automatic process. The code is able to harness the computational power of modern distributed platforms and is shown to work with models consisting of millions of degrees of freedom. Significant computational savings were achieved by using locally refined decoupled meshes.

A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry

NASA Technical Reports Server (NTRS)

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

2001-01-01

This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.

A parallel finite element simulator for ion transport through three-dimensional ion channel systems.

PubMed

Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo

2013-09-15

A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. Copyright © 2013 Wiley Periodicals, Inc.

Parallel grid library for rapid and flexible simulation development

NASA Astrophysics Data System (ADS)

Honkonen, I.; von Alfthan, S.; Sandroos, A.; Janhunen, P.; Palmroth, M.

2013-04-01

We present an easy to use and flexible grid library for developing highly scalable parallel simulations. The distributed cartesian cell-refinable grid (dccrg) supports adaptive mesh refinement and allows an arbitrary C++ class to be used as cell data. The amount of data in grid cells can vary both in space and time allowing dccrg to be used in very different types of simulations, for example in fluid and particle codes. Dccrg transfers the data between neighboring cells on different processes transparently and asynchronously allowing one to overlap computation and communication. This enables excellent scalability at least up to 32 k cores in magnetohydrodynamic tests depending on the problem and hardware. In the version of dccrg presented here part of the mesh metadata is replicated between MPI processes reducing the scalability of adaptive mesh refinement (AMR) to between 200 and 600 processes. Dccrg is free software that anyone can use, study and modify and is available at https://gitorious.org/dccrg. Users are also kindly requested to cite this work when publishing results obtained with dccrg. Catalogue identifier: AEOM_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEOM_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU Lesser General Public License version 3 No. of lines in distributed program, including test data, etc.: 54975 No. of bytes in distributed program, including test data, etc.: 974015 Distribution format: tar.gz Programming language: C++. Computer: PC, cluster, supercomputer. Operating system: POSIX. The code has been parallelized using MPI and tested with 1-32768 processes RAM: 10 MB-10 GB per process Classification: 4.12, 4.14, 6.5, 19.3, 19.10, 20. External routines: MPI-2 [1], boost [2], Zoltan [3], sfc++ [4] Nature of problem: Grid library supporting arbitrary data in grid cells, parallel adaptive mesh refinement, transparent remote neighbor data updates and load balancing. Solution method: The simulation grid is represented by an adjacency list (graph) with vertices stored into a hash table and edges into contiguous arrays. Message Passing Interface standard is used for parallelization. Cell data is given as a template parameter when instantiating the grid. Restrictions: Logically cartesian grid. Running time: Running time depends on the hardware, problem and the solution method. Small problems can be solved in under a minute and very large problems can take weeks. The examples and tests provided with the package take less than about one minute using default options. In the version of dccrg presented here the speed of adaptive mesh refinement is at most of the order of 106 total created cells per second. http://www.mpi-forum.org/. http://www.boost.org/. K. Devine, E. Boman, R. Heaphy, B. Hendrickson, C. Vaughan, Zoltan data management services for parallel dynamic applications, Comput. Sci. Eng. 4 (2002) 90-97. http://dx.doi.org/10.1109/5992.988653. https://gitorious.org/sfc++.

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.

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

Koniges, A.E.

The author describes the new T3D parallel computer at NERSC. The adaptive mesh ICF3D code is one of the current applications being ported and developed for use on the T3D. It has been stressed in other papers in this proceedings that the development environment and tools available on the parallel computer is similar to any planned for the future including networks of workstations.

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.

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.

Parallel Adaptive Simulation of Detonation Waves Using a Weighted Essentially Non-Oscillatory Scheme

NASA Astrophysics Data System (ADS)

McMahon, Sean

The purpose of this thesis was to develop a code that could be used to develop a better understanding of the physics of detonation waves. First, a detonation was simulated in one dimension using ZND theory. Then, using the 1D solution as an initial condition, a detonation was simulated in two dimensions using a weighted essentially non-oscillatory scheme on an adaptive mesh with the smallest lengthscales being equal to 2-3 flamelet lengths. The code development in linking Chemkin for chemical kinetics to the adaptive mesh refinement flow solver was completed. The detonation evolved in a way that, qualitatively, matched the experimental observations, however, the simulation was unable to progress past the formation of the triple point.

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.

Evaluation of French and English MeSH Indexing Systems with a Parallel Corpus

PubMed Central

Névéol, Aurélie; Mork, James G.; Aronson, Alan R.; Darmoni, Stefan J.

2005-01-01

Objective This paper presents the evaluation of two MeSH® indexing systems for French and English on a parallel corpus. Material and methods We describe two automatic MeSH indexing systems - MTI for English, and MAIF for French. The French version of the evaluation resources has been manually indexed with MeSH keyword/qualifier pairs. This professional indexing is used as our gold standard in the evaluation of both systems on keyword retrieval. Results The English system (MTI) obtains significantly better precision and recall (78% precision and 21% recall at rank 1, vs. 37%. precision and 6% recall for MAIF ). Moreover, the performance of both systems can be optimised by the breakage function used by the French system (MAIF), which selects an adaptive number of descriptors for each resource indexed. Conclusion MTI achieves better performance. However, both systems have features that can benefit each other. PMID:16779103

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.

Numerical simulation of h-adaptive immersed boundary method for freely falling disks

NASA Astrophysics Data System (ADS)

Zhang, Pan; Xia, Zhenhua; Cai, Qingdong

2018-05-01

In this work, a freely falling disk with aspect ratio 1/10 is directly simulated by using an adaptive numerical model implemented on a parallel computation framework JASMIN. The adaptive numerical model is a combination of the h-adaptive mesh refinement technique and the implicit immersed boundary method (IBM). Our numerical results agree well with the experimental results in all of the six degrees of freedom of the disk. Furthermore, very similar vortex structures observed in the experiment were also obtained.

GPU accelerated cell-based adaptive mesh refinement on unstructured quadrilateral grid

NASA Astrophysics Data System (ADS)

Luo, Xisheng; Wang, Luying; Ran, Wei; Qin, Fenghua

2016-10-01

A GPU accelerated inviscid flow solver is developed on an unstructured quadrilateral grid in the present work. For the first time, the cell-based adaptive mesh refinement (AMR) is fully implemented on GPU for the unstructured quadrilateral grid, which greatly reduces the frequency of data exchange between GPU and CPU. Specifically, the AMR is processed with atomic operations to parallelize list operations, and null memory recycling is realized to improve the efficiency of memory utilization. It is found that results obtained by GPUs agree very well with the exact or experimental results in literature. An acceleration ratio of 4 is obtained between the parallel code running on the old GPU GT9800 and the serial code running on E3-1230 V2. With the optimization of configuring a larger L1 cache and adopting Shared Memory based atomic operations on the newer GPU C2050, an acceleration ratio of 20 is achieved. The parallelized cell-based AMR processes have achieved 2x speedup on GT9800 and 18x on Tesla C2050, which demonstrates that parallel running of the cell-based AMR method on GPU is feasible and efficient. Our results also indicate that the new development of GPU architecture benefits the fluid dynamics computing significantly.

Advances in Parallelization for Large Scale Oct-Tree Mesh Generation

NASA Technical Reports Server (NTRS)

O'Connell, Matthew; Karman, Steve L.

2015-01-01

Despite great advancements in the parallelization of numerical simulation codes over the last 20 years, it is still common to perform grid generation in serial. Generating large scale grids in serial often requires using special "grid generation" compute machines that can have more than ten times the memory of average machines. While some parallel mesh generation techniques have been proposed, generating very large meshes for LES or aeroacoustic simulations is still a challenging problem. An automated method for the parallel generation of very large scale off-body hierarchical meshes is presented here. This work enables large scale parallel generation of off-body meshes by using a novel combination of parallel grid generation techniques and a hybrid "top down" and "bottom up" oct-tree method. Meshes are generated using hardware commonly found in parallel compute clusters. The capability to generate very large meshes is demonstrated by the generation of off-body meshes surrounding complex aerospace geometries. Results are shown including a one billion cell mesh generated around a Predator Unmanned Aerial Vehicle geometry, which was generated on 64 processors in under 45 minutes.

Parallelization of GeoClaw code for modeling geophysical flows with adaptive mesh refinement on many-core systems

USGS Publications Warehouse

Zhang, S.; Yuen, D.A.; Zhu, A.; Song, S.; George, D.L.

2011-01-01

We parallelized the GeoClaw code on one-level grid using OpenMP in March, 2011 to meet the urgent need of simulating tsunami waves at near-shore from Tohoku 2011 and achieved over 75% of the potential speed-up on an eight core Dell Precision T7500 workstation [1]. After submitting that work to SC11 - the International Conference for High Performance Computing, we obtained an unreleased OpenMP version of GeoClaw from David George, who developed the GeoClaw code as part of his PH.D thesis. In this paper, we will show the complementary characteristics of the two approaches used in parallelizing GeoClaw and the speed-up obtained by combining the advantage of each of the two individual approaches with adaptive mesh refinement (AMR), demonstrating the capabilities of running GeoClaw efficiently on many-core systems. We will also show a novel simulation of the Tohoku 2011 Tsunami waves inundating the Sendai airport and Fukushima Nuclear Power Plants, over which the finest grid distance of 20 meters is achieved through a 4-level AMR. This simulation yields quite good predictions about the wave-heights and travel time of the tsunami waves. ?? 2011 IEEE.

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.

Design of Unstructured Adaptive (UA) NAS Parallel Benchmark Featuring Irregular, Dynamic Memory Accesses

NASA Technical Reports Server (NTRS)

Feng, Hui-Yu; VanderWijngaart, Rob; Biswas, Rupak; Biegel, Bryan (Technical Monitor)

2001-01-01

We describe the design of a new method for the measurement of the performance of modern computer systems when solving scientific problems featuring irregular, dynamic memory accesses. The method involves the solution of a stylized heat transfer problem on an unstructured, adaptive grid. A Spectral Element Method (SEM) with an adaptive, nonconforming mesh is selected to discretize the transport equation. The relatively high order of the SEM lowers the fraction of wall clock time spent on inter-processor communication, which eases the load balancing task and allows us to concentrate on the memory accesses. The benchmark is designed to be three-dimensional. Parallelization and load balance issues of a reference implementation will be described in detail in future reports.

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.

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

A DAFT DL_POLY distributed memory adaptation of the Smoothed Particle Mesh Ewald method

NASA Astrophysics Data System (ADS)

Bush, I. J.; Todorov, I. T.; Smith, W.

2006-09-01

The Smoothed Particle Mesh Ewald method [U. Essmann, L. Perera, M.L. Berkowtz, T. Darden, H. Lee, L.G. Pedersen, J. Chem. Phys. 103 (1995) 8577] for calculating long ranged forces in molecular simulation has been adapted for the parallel molecular dynamics code DL_POLY_3 [I.T. Todorov, W. Smith, Philos. Trans. Roy. Soc. London 362 (2004) 1835], making use of a novel 3D Fast Fourier Transform (DAFT) [I.J. Bush, The Daresbury Advanced Fourier transform, Daresbury Laboratory, 1999] that perfectly matches the Domain Decomposition (DD) parallelisation strategy [W. Smith, Comput. Phys. Comm. 62 (1991) 229; M.R.S. Pinches, D. Tildesley, W. Smith, Mol. Sim. 6 (1991) 51; D. Rapaport, Comput. Phys. Comm. 62 (1991) 217] of the DL_POLY_3 code. In this article we describe software adaptations undertaken to import this functionality and provide a review of its performance.

Use of Hilbert Curves in Parallelized CUDA code: Interaction of Interstellar Atoms with the Heliosphere

NASA Astrophysics Data System (ADS)

Destefano, Anthony; Heerikhuisen, Jacob

2015-04-01

Fully 3D particle simulations can be a computationally and memory expensive task, especially when high resolution grid cells are required. The problem becomes further complicated when parallelization is needed. In this work we focus on computational methods to solve these difficulties. Hilbert curves are used to map the 3D particle space to the 1D contiguous memory space. This method of organization allows for minimized cache misses on the GPU as well as a sorted structure that is equivalent to an octal tree data structure. This type of sorted structure is attractive for uses in adaptive mesh implementations due to the logarithm search time. Implementations using the Message Passing Interface (MPI) library and NVIDIA's parallel computing platform CUDA will be compared, as MPI is commonly used on server nodes with many CPU's. We will also compare static grid structures with those of adaptive mesh structures. The physical test bed will be simulating heavy interstellar atoms interacting with a background plasma, the heliosphere, simulated from fully consistent coupled MHD/kinetic particle code. It is known that charge exchange is an important factor in space plasmas, specifically it modifies the structure of the heliosphere itself. We would like to thank the Alabama Supercomputer Authority for the use of their computational resources.

Implication of mountain shading and topographic scaling on energy for snowmelt

NASA Astrophysics Data System (ADS)

Marsh, C.; Pomeroy, J. W.; Spiteri, R.

2011-12-01

In many parts of the world, snowmelt energetics are dominated by incoming solar radiation. This is the case in the Canadian Rockies, where sunny winters result in high insolation. Solar irradiance on the snow surface is affected by the atmosphere, the slope and aspect of the immediate topography, and shading from surrounding terrain. Errors in estimating solar irradiation are cumulative over a season and can lead to large errors in snowmelt predictions. Adaptive triangular meshes, a type of unstructured triangular mesh that can adapt to fine-scale processes during model runtime, are more efficient in their use of DEM data than fixed grids when producing solar irradiance maps. An experimental design to calculate the effect of changes in DEM resolution on adaptive mesh irradiation calculations and implication for snowmelt is presented. As part of this experiment, the accuracy of these techniques is compared to measurements of mountain shadows and solar irradiance collected in Marmot Creek Research Basin, Alberta. Time-lapse digital cameras and networks of radiometers provide datasets for diagnosis of model accuracy. Further improvements in computational efficiency are achieved by taking advantage of parallel processing using graphical processing units (GPUs) is also discussed.

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.

''A Parallel Adaptive Simulation Tool for Two Phase Steady State Reacting Flows in Industrial Boilers and Furnaces''

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

Michael J. Bockelie

2002-01-04

This DOE SBIR Phase II final report summarizes research that has been performed to develop a parallel adaptive tool for modeling steady, two phase turbulent reacting flow. The target applications for the new tool are full scale, fossil-fuel fired boilers and furnaces such as those used in the electric utility industry, chemical process industry and mineral/metal process industry. The type of analyses to be performed on these systems are engineering calculations to evaluate the impact on overall furnace performance due to operational, process or equipment changes. To develop a Computational Fluid Dynamics (CFD) model of an industrial scale furnace requiresmore » a carefully designed grid that will capture all of the large and small scale features of the flowfield. Industrial systems are quite large, usually measured in tens of feet, but contain numerous burners, air injection ports, flames and localized behavior with dimensions that are measured in inches or fractions of inches. To create an accurate computational model of such systems requires capturing length scales within the flow field that span several orders of magnitude. In addition, to create an industrially useful model, the grid can not contain too many grid points - the model must be able to execute on an inexpensive desktop PC in a matter of days. An adaptive mesh provides a convenient means to create a grid that can capture both fine flow field detail within a very large domain with a ''reasonable'' number of grid points. However, the use of an adaptive mesh requires the development of a new flow solver. To create the new simulation tool, we have combined existing reacting CFD modeling software with new software based on emerging block structured Adaptive Mesh Refinement (AMR) technologies developed at Lawrence Berkeley National Laboratory (LBNL). Specifically, we combined: -physical models, modeling expertise, and software from existing combustion simulation codes used by Reaction Engineering International; -mesh adaption, data management, and parallelization software and technology being developed by users of the BoxLib library at LBNL; and -solution methods for problems formulated on block structured grids that were being developed in collaboration with technical staff members at the University of Utah Center for High Performance Computing (CHPC) and at LBNL. The combustion modeling software used by Reaction Engineering International represents an investment of over fifty man-years of development, conducted over a period of twenty years. Thus, it was impractical to achieve our objective by starting from scratch. The research program resulted in an adaptive grid, reacting CFD flow solver that can be used only on limited problems. In current form the code is appropriate for use on academic problems with simplified geometries. The new solver is not sufficiently robust or sufficiently general to be used in a ''production mode'' for industrial applications. The principle difficulty lies with the multi-level solver technology. The use of multi-level solvers on adaptive grids with embedded boundaries is not yet a mature field and there are many issues that remain to be resolved. From the lessons learned in this SBIR program, we have started work on a new flow solver with an AMR capability. The new code is based on a conventional cell-by-cell mesh refinement strategy used in unstructured grid solvers that employ hexahedral cells. The new solver employs several of the concepts and solution strategies developed within this research program. The formulation of the composite grid problem for the new solver has been designed to avoid the embedded boundary complications encountered in this SBIR project. This follow-on effort will result in a reacting flow CFD solver with localized mesh capability that can be used to perform engineering calculations on industrial problems in a production mode.« less

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

Implicit schemes and parallel computing in unstructured grid CFD

NASA Technical Reports Server (NTRS)

Venkatakrishnam, V.

1995-01-01

The development of implicit schemes for obtaining steady state solutions to the Euler and Navier-Stokes equations on unstructured grids is outlined. Applications are presented that compare the convergence characteristics of various implicit methods. Next, the development of explicit and implicit schemes to compute unsteady flows on unstructured grids is discussed. Next, the issues involved in parallelizing finite volume schemes on unstructured meshes in an MIMD (multiple instruction/multiple data stream) fashion are outlined. Techniques for partitioning unstructured grids among processors and for extracting parallelism in explicit and implicit solvers are discussed. Finally, some dynamic load balancing ideas, which are useful in adaptive transient computations, are presented.

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.

Parallel Programming Strategies for Irregular Adaptive Applications

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Biegel, Bryan (Technical Monitor)

2001-01-01

Achieving scalable performance for dynamic irregular applications is eminently challenging. Traditional message-passing approaches have been making steady progress towards this goal; however, they suffer from complex implementation requirements. The use of a global address space greatly simplifies the programming task, but can degrade the performance for such computations. In this work, we examine two typical irregular adaptive applications, Dynamic Remeshing and N-Body, under competing programming methodologies and across various parallel architectures. The Dynamic Remeshing application simulates flow over an airfoil, and refines localized regions of the underlying unstructured mesh. The N-Body experiment models two neighboring Plummer galaxies that are about to undergo a merger. Both problems demonstrate dramatic changes in processor workloads and interprocessor communication with time; thus, dynamic load balancing is a required component.

Developing parallel GeoFEST(P) using the PYRAMID AMR library

NASA Technical Reports Server (NTRS)

Norton, Charles D.; Lyzenga, Greg; Parker, Jay; Tisdale, Robert E.

2004-01-01

The PYRAMID parallel unstructured adaptive mesh refinement (AMR) library has been coupled with the GeoFEST geophysical finite element simulation tool to support parallel active tectonics simulations. Specifically, we have demonstrated modeling of coseismic and postseismic surface displacement due to a simulated Earthquake for the Landers system of interacting faults in Southern California. The new software demonstrated a 25-times resolution improvement and a 4-times reduction in time to solution over the sequential baseline milestone case. Simulations on workstations using a few tens of thousands of stress displacement finite elements can now be expanded to multiple millions of elements with greater than 98% scaled efficiency on various parallel platforms over many hundreds of processors. Our most recent work has demonstrated that we can dynamically adapt the computational grid as stress grows on a fault. In this paper, we will describe the major issues and challenges associated with coupling these two programs to create GeoFEST(P). Performance and visualization results will also be described.

Vertical Scan (V-SCAN) for 3-D Grid Adaptive Mesh Refinement for an atmospheric Model Dynamical Core

NASA Astrophysics Data System (ADS)

Andronova, N. G.; Vandenberg, D.; Oehmke, R.; Stout, Q. F.; Penner, J. E.

2009-12-01

One of the major building blocks of a rigorous representation of cloud evolution in global atmospheric models is a parallel adaptive grid MPI-based communication library (an Adaptive Blocks for Locally Cartesian Topologies library -- ABLCarT), which manages the block-structured data layout, handles ghost cell updates among neighboring blocks and splits a block as refinements occur. The library has several modules that provide a layer of abstraction for adaptive refinement: blocks, which contain individual cells of user data; shells - the global geometry for the problem, including a sphere, reduced sphere, and now a 3D sphere; a load balancer for placement of blocks onto processors; and a communication support layer which encapsulates all data movement. A major performance concern with adaptive mesh refinement is how to represent calculations that have need to be sequenced in a particular order in a direction, such as calculating integrals along a specific path (e.g. atmospheric pressure or geopotential in the vertical dimension). This concern is compounded if the blocks have varying levels of refinement, or are scattered across different processors, as can be the case in parallel computing. In this paper we describe an implementation in ABLCarT of a vertical scan operation, which allows computing along vertical paths in the correct order across blocks transparent to their resolution and processor location. We test this functionality on a 2D and a 3D advection problem, which tests the performance of the model’s dynamics (transport) and physics (sources and sinks) for different model resolutions needed for inclusion of cloud formation.

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.

Collisionless stellar hydrodynamics as an efficient alternative to N-body methods

NASA Astrophysics Data System (ADS)

Mitchell, Nigel L.; Vorobyov, Eduard I.; Hensler, Gerhard

2013-01-01

The dominant constituents of the Universe's matter are believed to be collisionless in nature and thus their modelling in any self-consistent simulation is extremely important. For simulations that deal only with dark matter or stellar systems, the conventional N-body technique is fast, memory efficient and relatively simple to implement. However when extending simulations to include the effects of gas physics, mesh codes are at a distinct disadvantage compared to Smooth Particle Hydrodynamics (SPH) codes. Whereas implementing the N-body approach into SPH codes is fairly trivial, the particle-mesh technique used in mesh codes to couple collisionless stars and dark matter to the gas on the mesh has a series of significant scientific and technical limitations. These include spurious entropy generation resulting from discreteness effects, poor load balancing and increased communication overhead which spoil the excellent scaling in massively parallel grid codes. In this paper we propose the use of the collisionless Boltzmann moment equations as a means to model the collisionless material as a fluid on the mesh, implementing it into the massively parallel FLASH Adaptive Mesh Refinement (AMR) code. This approach which we term `collisionless stellar hydrodynamics' enables us to do away with the particle-mesh approach and since the parallelization scheme is identical to that used for the hydrodynamics, it preserves the excellent scaling of the FLASH code already demonstrated on peta-flop machines. We find that the classic hydrodynamic equations and the Boltzmann moment equations can be reconciled under specific conditions, allowing us to generate analytic solutions for collisionless systems using conventional test problems. We confirm the validity of our approach using a suite of demanding test problems, including the use of a modified Sod shock test. By deriving the relevant eigenvalues and eigenvectors of the Boltzmann moment equations, we are able to use high order accurate characteristic tracing methods with Riemann solvers to generate numerical solutions which show excellent agreement with our analytic solutions. We conclude by demonstrating the ability of our code to model complex phenomena by simulating the evolution of a two-armed spiral galaxy whose properties agree with those predicted by the swing amplification theory.

Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

NASA Astrophysics Data System (ADS)

Xing, F.; Masson, R.; Lopez, S.

2017-09-01

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non-immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.

Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods

NASA Astrophysics Data System (ADS)

Kozdon, J. E.; Wilcox, L.

2013-12-01

Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel library known as bfam (available at http://bfam.in). The first application to be developed on top of bfam is an earthquake rupture dynamics solver using high-order discontinuous Galerkin methods and summation-by-parts finite difference methods. In earthquake rupture dynamics, wave propagation in the Earth's crust is coupled to frictional sliding on fault interfaces. This coupling is two-way, required the simultaneous simulation of both processes. The use of laboratory-measured friction parameters requires near-fault resolution that is 4-5 orders of magnitude higher than that needed to resolve the frequencies of interest in the volume. This, along with earlier simulations using a low-order, finite volume based adaptive mesh refinement framework, suggest that adaptive mesh refinement is ideally suited for this problem. The use of high-order methods is motivated by the high level of resolution required off the fault in earlier the low-order finite volume simulations; we believe this need for resolution is a result of the excessive numerical dissipation of low-order methods. In bfam spatial adaptivity is handled using the p4est library and temporal adaptivity will be accomplished through local time stepping. In this presentation we will present the guiding principles behind the library as well as verification of code against the Southern California Earthquake Center dynamic rupture code validation test problems.

Jali - Unstructured Mesh Infrastructure for Multi-Physics Applications

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

Garimella, Rao V; Berndt, Markus; Coon, Ethan

2017-04-13

Jali is a parallel unstructured mesh infrastructure library designed for use by multi-physics simulations. It supports 2D and 3D arbitrary polyhedral meshes distributed over hundreds to thousands of nodes. Jali can read write Exodus II meshes along with fields and sets on the mesh and support for other formats is partially implemented or is (https://github.com/MeshToolkit/MSTK), an open source general purpose unstructured mesh infrastructure library from Los Alamos National Laboratory. While it has been made to work with other mesh frameworks such as MOAB and STKmesh in the past, support for maintaining the interface to these frameworks has been suspended formore » now. Jali supports distributed as well as on-node parallelism. Support of on-node parallelism is through direct use of the the mesh in multi-threaded constructs or through the use of "tiles" which are submeshes or sub-partitions of a partition destined for a compute node.« less

On computational methods for crashworthiness

NASA Technical Reports Server (NTRS)

Belytschko, T.

1992-01-01

The evolution of computational methods for crashworthiness and related fields is described and linked with the decreasing cost of computational resources and with improvements in computation methodologies. The latter includes more effective time integration procedures and more efficient elements. Some recent developments in methodologies and future trends are also summarized. These include multi-time step integration (or subcycling), further improvements in elements, adaptive meshes, and the exploitation of parallel computers.

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

Using the GeoFEST Faulted Region Simulation System

NASA Technical Reports Server (NTRS)

Parker, Jay W.; Lyzenga, Gregory A.; Donnellan, Andrea; Judd, Michele A.; Norton, Charles D.; Baker, Teresa; Tisdale, Edwin R.; Li, Peggy

2004-01-01

GeoFEST (the Geophysical Finite Element Simulation Tool) simulates stress evolution, fault slip and plastic/elastic processes in realistic materials, and so is suitable for earthquake cycle studies in regions such as Southern California. Many new capabilities and means of access for GeoFEST are now supported. New abilities include MPI-based cluster parallel computing using automatic PYRAMID/Parmetis-based mesh partitioning, automatic mesh generation for layered media with rectangular faults, and results visualization that is integrated with remote sensing data. The parallel GeoFEST application has been successfully run on over a half-dozen computers, including Intel Xeon clusters, Itanium II and Altix machines, and the Apple G5 cluster. It is not separately optimized for different machines, but relies on good domain partitioning for load-balance and low communication, and careful writing of the parallel diagonally preconditioned conjugate gradient solver to keep communication overhead low. Demonstrated thousand-step solutions for over a million finite elements on 64 processors require under three hours, and scaling tests show high efficiency when using more than (order of) 4000 elements per processor. The source code and documentation for GeoFEST is available at no cost from Open Channel Foundation. In addition GeoFEST may be used through a browser-based portal environment available to approved users. That environment includes semi-automated geometry creation and mesh generation tools, GeoFEST, and RIVA-based visualization tools that include the ability to generate a flyover animation showing deformations and topography. Work is in progress to support simulation of a region with several faults using 16 million elements, using a strain energy metric to adapt the mesh to faithfully represent the solution in a region of widely varying strain.

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.

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

Clough, Katy; Figueras, Pau; Finkel, Hal

In this work, we introduce GRChombo: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured Berger-Rigoutsos grid generation. The code supports non-trivial 'many-boxes-in-many-boxes' mesh hierarchies and massive parallelism through the message passing interface. GRChombo evolves the Einstein equation using the standard BSSN formalism, with an option to turn on CCZ4 constraint damping if required. The AMR capability permits the study of a range of new physics which has previously been computationally infeasible in a full 3 + 1 setting, while also significantly simplifying the process of setting up the mesh for these problems. Wemore » show that GRChombo can stably and accurately evolve standard spacetimes such as binary black hole mergers and scalar collapses into black holes, demonstrate the performance characteristics of our code, and discuss various physics problems which stand to benefit from the AMR technique.« less

Parallel Unsteady Overset Mesh Methodology for Adaptive and Moving Grids with Multiple Solvers

DTIC Science & Technology

2010-01-01

Research Laboratory Hampton, Virginia Jayanarayanan Sitaraman National Institute of Aerospace Hampton, Virginia ABSTRACT This paper describes a new...Army Research Laboratory ,Hampton, VA, , , 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) NATO/RTO...results section ( 3.6 and 3.5). Good linear scalability was observed for all three cases up to 12 processors. Beyond that the scalability drops off

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 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.

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

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.

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

Unstructured mesh generation and adaptivity

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1995-01-01

An overview of current unstructured mesh generation and adaptivity techniques is given. Basic building blocks taken from the field of computational geometry are first described. Various practical mesh generation techniques based on these algorithms are then constructed and illustrated with examples. Issues of adaptive meshing and stretched mesh generation for anisotropic problems are treated in subsequent sections. The presentation is organized in an education manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.

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.

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

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.

Efficient Parallelization of a Dynamic Unstructured Application on the Tera MTA

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Biswas, Rupak

1999-01-01

The success of parallel computing in solving real-life computationally-intensive problems relies on their efficient mapping and execution on large-scale multiprocessor architectures. Many important applications are both unstructured and dynamic in nature, making their efficient parallel implementation a daunting task. This paper presents the parallelization of a dynamic unstructured mesh adaptation algorithm using three popular programming paradigms on three leading supercomputers. We examine an MPI message-passing implementation on the Cray T3E and the SGI Origin2OOO, a shared-memory implementation using cache coherent nonuniform memory access (CC-NUMA) of the Origin2OOO, and a multi-threaded version on the newly-released Tera Multi-threaded Architecture (MTA). We compare several critical factors of this parallel code development, including runtime, scalability, programmability, and memory overhead. Our overall results demonstrate that multi-threaded systems offer tremendous potential for quickly and efficiently solving some of the most challenging real-life problems on parallel computers.

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.

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.

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

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.

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.

Portable Parallel Programming for the Dynamic Load Balancing of Unstructured Grid Applications

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Das, Sajal K.; Harvey, Daniel; Oliker, Leonid

1999-01-01

The ability to dynamically adapt an unstructured -rid (or mesh) is a powerful tool for solving computational problems with evolving physical features; however, an efficient parallel implementation is rather difficult, particularly from the view point of portability on various multiprocessor platforms We address this problem by developing PLUM, tin automatic anti architecture-independent framework for adaptive numerical computations in a message-passing environment. Portability is demonstrated by comparing performance on an SP2, an Origin2000, and a T3E, without any code modifications. We also present a general-purpose load balancer that utilizes symmetric broadcast networks (SBN) as the underlying communication pattern, with a goal to providing a global view of system loads across processors. Experiments on, an SP2 and an Origin2000 demonstrate the portability of our approach which achieves superb load balance at the cost of minimal extra overhead.

A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS

NASA Technical Reports Server (NTRS)

Chatterjee, A.; Volakis, J. L.; Nguyen, J.; Nurnberger, M.; Ross, D.

1993-01-01

Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).

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.

An Immersed Boundary - Adaptive Mesh Refinement solver (IB-AMR) for high fidelity fully resolved wind turbine simulations

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Sotiropoulos, Fotis

2015-11-01

The geometrical details of wind turbines determine the structure of the turbulence in the near and far wake and should be taken in account when performing high fidelity calculations. Multi-resolution simulations coupled with an immersed boundary method constitutes a powerful framework for high-fidelity calculations past wind farms located over complex terrains. We develop a 3D Immersed-Boundary Adaptive Mesh Refinement flow solver (IB-AMR) which enables turbine-resolving LES of wind turbines. The idea of using a hybrid staggered/non-staggered grid layout adopted in the Curvilinear Immersed Boundary Method (CURVIB) has been successfully incorporated on unstructured meshes and the fractional step method has been employed. The overall performance and robustness of the second order accurate, parallel, unstructured solver is evaluated by comparing the numerical simulations against conforming grid calculations and experimental measurements of laminar and turbulent flows over complex geometries. We also present turbine-resolving multi-scale LES considering all the details affecting the induced flow field; including the geometry of the tower, the nacelle and especially the rotor blades of a wind tunnel scale turbine. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482 and the Sandia National Laboratories.

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

Generating unstructured nuclear reactor core meshes in parallel

DOE PAGES

Jain, Rajeev; Tautges, Timothy J.

2014-10-24

Recent advances in supercomputers and parallel solver techniques have enabled users to run large simulations problems using millions of processors. Techniques for multiphysics nuclear reactor core simulations are under active development in several countries. Most of these techniques require large unstructured meshes that can be hard to generate in a standalone desktop computers because of high memory requirements, limited processing power, and other complexities. We have previously reported on a hierarchical lattice-based approach for generating reactor core meshes. Here, we describe efforts to exploit coarse-grained parallelism during reactor assembly and reactor core mesh generation processes. We highlight several reactor coremore » examples including a very high temperature reactor, a full-core model of the Korean MONJU reactor, a ¼ pressurized water reactor core, the fast reactor Experimental Breeder Reactor-II core with a XX09 assembly, and an advanced breeder test reactor core. The times required to generate large mesh models, along with speedups obtained from running these problems in parallel, are reported. A graphical user interface to the tools described here has also been developed.« less

Discontinuous Galerkin Approaches for Stokes Flow and Flow in Porous Media

NASA Astrophysics Data System (ADS)

Lehmann, Ragnar; Kaus, Boris; Lukacova, Maria

2014-05-01

Firstly, we present results of a study comparing two different numerical approaches for solving the Stokes equations with strongly varying viscosity: the continuous Galerkin (i.e., FEM) and the discontinuous Galerkin (DG) method. Secondly, we show how the latter method can be extended and applied to flow in porous media governed by Darcy's law. Nonlinearities in the viscosity or other material parameters can lead to discontinuities in the velocity-pressure solution that may not be approximated well with continuous elements. The DG method allows for discontinuities across interior edges of the underlying mesh. Furthermore, depending on the chosen basis functions, it naturally enforces local mass conservation, i.e., in every mesh cell. Computationally, it provides the capability to locally adapt the polynomial degree and needs communication only between directly adjacent mesh cells making it highly flexible and easy to parallelize. The methods are compared for several geophysically relevant benchmarking setups and discussed with respect to speed, accuracy, computational efficiency.

Reliability Analysis and Modeling of ZigBee Networks

NASA Astrophysics Data System (ADS)

Lin, Cheng-Min

The architecture of ZigBee networks focuses on developing low-cost, low-speed ubiquitous communication between devices. The ZigBee technique is based on IEEE 802.15.4, which specifies the physical layer and medium access control (MAC) for a low rate wireless personal area network (LR-WPAN). Currently, numerous wireless sensor networks have adapted the ZigBee open standard to develop various services to promote improved communication quality in our daily lives. The problem of system and network reliability in providing stable services has become more important because these services will be stopped if the system and network reliability is unstable. The ZigBee standard has three kinds of networks; star, tree and mesh. The paper models the ZigBee protocol stack from the physical layer to the application layer and analyzes these layer reliability and mean time to failure (MTTF). Channel resource usage, device role, network topology and application objects are used to evaluate reliability in the physical, medium access control, network, and application layers, respectively. In the star or tree networks, a series system and the reliability block diagram (RBD) technique can be used to solve their reliability problem. However, a division technology is applied here to overcome the problem because the network complexity is higher than that of the others. A mesh network using division technology is classified into several non-reducible series systems and edge parallel systems. Hence, the reliability of mesh networks is easily solved using series-parallel systems through our proposed scheme. The numerical results demonstrate that the reliability will increase for mesh networks when the number of edges in parallel systems increases while the reliability quickly drops when the number of edges and the number of nodes increase for all three networks. More use of resources is another factor impact on reliability decreasing. However, lower network reliability will occur due to network complexity, more resource usage and complex object relationship.

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

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.

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

NASA Technical Reports Server (NTRS)

Chung, T. J. (Editor); Karr, Gerald R. (Editor)

1989-01-01

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Adaptive Skin Meshes Coarsening for Biomolecular Simulation

PubMed Central

Shi, Xinwei; Koehl, Patrice

2011-01-01

In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedral that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry. PMID:21779137

Performance Characteristics of the Multi-Zone NAS Parallel Benchmarks

NASA Technical Reports Server (NTRS)

Jin, Haoqiang; VanderWijngaart, Rob F.

2003-01-01

We describe a new suite of computational benchmarks that models applications featuring multiple levels of parallelism. Such parallelism is often available in realistic flow computations on systems of grids, but had not previously been captured in bench-marks. The new suite, named NPB Multi-Zone, is extended from the NAS Parallel Benchmarks suite, and involves solving the application benchmarks LU, BT and SP on collections of loosely coupled discretization meshes. The solutions on the meshes are updated independently, but after each time step they exchange boundary value information. This strategy provides relatively easily exploitable coarse-grain parallelism between meshes. Three reference implementations are available: one serial, one hybrid using the Message Passing Interface (MPI) and OpenMP, and another hybrid using a shared memory multi-level programming model (SMP+OpenMP). We examine the effectiveness of hybrid parallelization paradigms in these implementations on three different parallel computers. We also use an empirical formula to investigate the performance characteristics of the multi-zone benchmarks.

Fully-Implicit Navier-Stokes (FIN-S)

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.

2010-01-01

FIN-S is a SUPG finite element code for flow problems under active development at NASA Lyndon B. Johnson Space Center and within PECOS: a) The code is built on top of the libMesh parallel, adaptive finite element library. b) The initial implementation of the code targeted supersonic/hypersonic laminar calorically perfect gas flows & conjugate heat transfer. c) Initial extension to thermochemical nonequilibrium about 9 months ago. d) The technologies in FIN-S have been enhanced through a strongly collaborative research effort with Sandia National Labs.

Parallel Unsteady Overset Mesh Methodology for a Multi-Solver Paradigm with Adaptive Cartesian Grids

DTIC Science & Technology

2008-08-21

Engineer, U.S. Army Research Laboratory ., Matthew.W.Floros@nasa.gov, AIAA Member ‡Senior Research Scientist, Scaled Numerical Physics LLC., awissink...IV.E and IV.D). Good linear scalability was observed for all three cases up to 12 processors. Beyond that the scalability drops off depending on grid...Research Laboratory for the usage of SUGGAR module and Yikloon Lee at NAVAIR for the usage of the NAVAIR-IHC code. 13 of 22 American Institute of

Auto-adaptive finite element meshes

NASA Technical Reports Server (NTRS)

Richter, Roland; Leyland, Penelope

1995-01-01

Accurate capturing of discontinuities within compressible flow computations is achieved by coupling a suitable solver with an automatic adaptive mesh algorithm for unstructured triangular meshes. The mesh adaptation procedures developed rely on non-hierarchical dynamical local refinement/derefinement techniques, which hence enable structural optimization as well as geometrical optimization. The methods described are applied for a number of the ICASE test cases are particularly interesting for unsteady flow simulations.

Multitasking for flows about multiple body configurations using the chimera grid scheme

NASA Technical Reports Server (NTRS)

Dougherty, F. C.; Morgan, R. L.

1987-01-01

The multitasking of a finite-difference scheme using multiple overset meshes is described. In this chimera, or multiple overset mesh approach, a multiple body configuration is mapped using a major grid about the main component of the configuration, with minor overset meshes used to map each additional component. This type of code is well suited to multitasking. Both steady and unsteady two dimensional computations are run on parallel processors on a CRAY-X/MP 48, usually with one mesh per processor. Flow field results are compared with single processor results to demonstrate the feasibility of running multiple mesh codes on parallel processors and to show the increase in efficiency.

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.

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.

3D streamers simulation in a pin to plane configuration using massively parallel computing

NASA Astrophysics Data System (ADS)

Plewa, J.-M.; Eichwald, O.; Ducasse, O.; Dessante, P.; Jacobs, C.; Renon, N.; Yousfi, M.

2018-03-01

This paper concerns the 3D simulation of corona discharge using high performance computing (HPC) managed with the message passing interface (MPI) library. In the field of finite volume methods applied on non-adaptive mesh grids and in the case of a specific 3D dynamic benchmark test devoted to streamer studies, the great efficiency of the iterative R&B SOR and BiCGSTAB methods versus the direct MUMPS method was clearly demonstrated in solving the Poisson equation using HPC resources. The optimization of the parallelization and the resulting scalability was undertaken as a function of the HPC architecture for a number of mesh cells ranging from 8 to 512 million and a number of cores ranging from 20 to 1600. The R&B SOR method remains at least about four times faster than the BiCGSTAB method and requires significantly less memory for all tested situations. The R&B SOR method was then implemented in a 3D MPI parallelized code that solves the classical first order model of an atmospheric pressure corona discharge in air. The 3D code capabilities were tested by following the development of one, two and four coplanar streamers generated by initial plasma spots for 6 ns. The preliminary results obtained allowed us to follow in detail the formation of the tree structure of a corona discharge and the effects of the mutual interactions between the streamers in terms of streamer velocity, trajectory and diameter. The computing time for 64 million of mesh cells distributed over 1000 cores using the MPI procedures is about 30 min ns-1, regardless of the number of streamers.

A Framework for Parallel Unstructured Grid Generation for Complex Aerodynamic Simulations

NASA Technical Reports Server (NTRS)

Zagaris, George; Pirzadeh, Shahyar Z.; Chrisochoides, Nikos

2009-01-01

A framework for parallel unstructured grid generation targeting both shared memory multi-processors and distributed memory architectures is presented. The two fundamental building-blocks of the framework consist of: (1) the Advancing-Partition (AP) method used for domain decomposition and (2) the Advancing Front (AF) method used for mesh generation. Starting from the surface mesh of the computational domain, the AP method is applied recursively to generate a set of sub-domains. Next, the sub-domains are meshed in parallel using the AF method. The recursive nature of domain decomposition naturally maps to a divide-and-conquer algorithm which exhibits inherent parallelism. For the parallel implementation, the Master/Worker pattern is employed to dynamically balance the varying workloads of each task on the set of available CPUs. Performance results by this approach are presented and discussed in detail as well as future work and improvements.

Adaptive mesh fluid simulations on GPU

NASA Astrophysics Data System (ADS)

Wang, Peng; Abel, Tom; Kaehler, Ralf

2010-10-01

We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture. Using the method of lines approach with the second order total variation diminishing Runge-Kutta time integration scheme, piecewise linear reconstruction, and a Harten-Lax-van Leer Riemann solver, we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer. We attain this speedup in uniform grid runs as well as in problems with deep AMR hierarchies. Our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes. This is shown directly by an implementation of a magneto-hydrodynamic solver and comparing its performance to the pure hydrodynamic case. Finally, we also combined our CUDA parallel scheme with MPI to make the code run on GPU clusters. Close to ideal speedup is observed on up to four GPUs.

Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

DOE PAGES

Zhang, Bo; Lu, Benzhuo; Cheng, Xiaolin; ...

2013-01-01

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numericalmore » results.« less

Global magnetosphere simulations using constrained-transport Hall-MHD with CWENO reconstruction

NASA Astrophysics Data System (ADS)

Lin, L.; Germaschewski, K.; Maynard, K. M.; Abbott, S.; Bhattacharjee, A.; Raeder, J.

2013-12-01

We present a new CWENO (Centrally-Weighted Essentially Non-Oscillatory) reconstruction based MHD solver for the OpenGGCM global magnetosphere code. The solver was built using libMRC, a library for creating efficient parallel PDE solvers on structured grids. The use of libMRC gives us access to its core functionality of providing an automated code generation framework which takes a user provided PDE right hand side in symbolic form to generate an efficient, computer architecture specific, parallel code. libMRC also supports block-structured adaptive mesh refinement and implicit-time stepping through integration with the PETSc library. We validate the new CWENO Hall-MHD solver against existing solvers both in standard test problems as well as in global magnetosphere simulations.

Introducing a distributed unstructured mesh into gyrokinetic particle-in-cell code, XGC

NASA Astrophysics Data System (ADS)

Yoon, Eisung; Shephard, Mark; Seol, E. Seegyoung; Kalyanaraman, Kaushik

2017-10-01

XGC has shown good scalability for large leadership supercomputers. The current production version uses a copy of the entire unstructured finite element mesh on every MPI rank. Although an obvious scalability issue if the mesh sizes are to be dramatically increased, the current approach is also not optimal with respect to data locality of particles and mesh information. To address these issues we have initiated the development of a distributed mesh PIC method. This approach directly addresses the base scalability issue with respect to mesh size and, through the use of a mesh entity centric view of the particle mesh relationship, provides opportunities to address data locality needs of many core and GPU supported heterogeneous systems. The parallel mesh PIC capabilities are being built on the Parallel Unstructured Mesh Infrastructure (PUMI). The presentation will first overview the form of mesh distribution used and indicate the structures and functions used to support the mesh, the particles and their interaction. Attention will then focus on the node-level optimizations being carried out to ensure performant operation of all PIC operations on the distributed mesh. Partnership for Edge Physics Simulation (EPSI) Grant No. DE-SC0008449 and Center for Extended Magnetohydrodynamic Modeling (CEMM) Grant No. DE-SC0006618.

Parallel Adaptive High-Order CFD Simulations Characterizing Cavity Acoustics for the Complete SOFIA Aircraft

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.; Biswas, Rupak

2014-01-01

This paper presents one-of-a-kind MPI-parallel computational fluid dynamics simulations for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is an airborne, 2.5-meter infrared telescope mounted in an open cavity in the aft of a Boeing 747SP. These simulations focus on how the unsteady flow field inside and over the cavity interferes with the optical path and mounting of the telescope. A temporally fourth-order Runge-Kutta, and spatially fifth-order WENO-5Z scheme was used to perform implicit large eddy simulations. An immersed boundary method provides automated gridding for complex geometries and natural coupling to a block-structured Cartesian adaptive mesh refinement framework. Strong scaling studies using NASA's Pleiades supercomputer with up to 32,000 cores and 4 billion cells shows excellent scaling. Dynamic load balancing based on execution time on individual AMR blocks addresses irregularities caused by the highly complex geometry. Limits to scaling beyond 32K cores are identified, and targeted code optimizations are discussed.

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.

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.

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.

Large-scale Parallel Unstructured Mesh Computations for 3D High-lift Analysis

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.; Pirzadeh, S.

1999-01-01

A complete "geometry to drag-polar" analysis capability for the three-dimensional high-lift configurations is described. The approach is based on the use of unstructured meshes in order to enable rapid turnaround for complicated geometries that arise in high-lift configurations. Special attention is devoted to creating a capability for enabling analyses on highly resolved grids. Unstructured meshes of several million vertices are initially generated on a work-station, and subsequently refined on a supercomputer. The flow is solved on these refined meshes on large parallel computers using an unstructured agglomeration multigrid algorithm. Good prediction of lift and drag throughout the range of incidences is demonstrated on a transport take-off configuration using up to 24.7 million grid points. The feasibility of using this approach in a production environment on existing parallel machines is demonstrated, as well as the scalability of the solver on machines using up to 1450 processors.

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 Generic Mesh Data Structure with Parallel Applications

ERIC Educational Resources Information Center

Cochran, William Kenneth, Jr.

2009-01-01

High performance, massively-parallel multi-physics simulations are built on efficient mesh data structures. Most data structures are designed from the bottom up, focusing on the implementation of linear algebra routines. In this thesis, we explore a top-down approach to design, evaluating the various needs of many aspects of simulation, not just…

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.

AMRZone: A Runtime AMR Data Sharing Framework For Scientific Applications

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

Zhang, Wenzhao; Tang, Houjun; Harenberg, Steven

Frameworks that facilitate runtime data sharing across multiple applications are of great importance for scientific data analytics. Although existing frameworks work well over uniform mesh data, they can not effectively handle adaptive mesh refinement (AMR) data. Among the challenges to construct an AMR-capable framework include: (1) designing an architecture that facilitates online AMR data management; (2) achieving a load-balanced AMR data distribution for the data staging space at runtime; and (3) building an effective online index to support the unique spatial data retrieval requirements for AMR data. Towards addressing these challenges to support runtime AMR data sharing across scientific applications,more » we present the AMRZone framework. Experiments over real-world AMR datasets demonstrate AMRZone's effectiveness at achieving a balanced workload distribution, reading/writing large-scale datasets with thousands of parallel processes, and satisfying queries with spatial constraints. Moreover, AMRZone's performance and scalability are even comparable with existing state-of-the-art work when tested over uniform mesh data with up to 16384 cores; in the best case, our framework achieves a 46% performance improvement.« 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

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.

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.

Final Technical Report for "Applied Mathematics Research: Simulation Based Optimization and Application to Electromagnetic Inverse Problems"

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

Haber, Eldad

2014-03-17

The focus of research was: Developing adaptive mesh for the solution of Maxwell's equations; Developing a parallel framework for time dependent inverse Maxwell's equations; Developing multilevel methods for optimization problems with inequality constraints; A new inversion code for inverse Maxwell's equations in the 0th frequency (DC resistivity); A new inversion code for inverse Maxwell's equations in low frequency regime. Although the research concentrated on electromagnetic forward and in- verse problems the results of the research was applied to the problem of image registration.

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

NASA Astrophysics Data System (ADS)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

An integrated runtime and compile-time approach for parallelizing structured and block structured applications

NASA Technical Reports Server (NTRS)

Agrawal, Gagan; Sussman, Alan; Saltz, Joel

1993-01-01

Scientific and engineering applications often involve structured meshes. These meshes may be nested (for multigrid codes) and/or irregularly coupled (called multiblock or irregularly coupled regular mesh problems). A combined runtime and compile-time approach for parallelizing these applications on distributed memory parallel machines in an efficient and machine-independent fashion was described. A runtime library which can be used to port these applications on distributed memory machines was designed and implemented. The library is currently implemented on several different systems. To further ease the task of application programmers, methods were developed for integrating this runtime library with compilers for HPK-like parallel programming languages. How this runtime library was integrated with the Fortran 90D compiler being developed at Syracuse University is discussed. Experimental results to demonstrate the efficacy of our approach are presented. A multiblock Navier-Stokes solver template and a multigrid code were experimented with. Our experimental results show that our primitives have low runtime communication overheads. Further, the compiler parallelized codes perform within 20 percent of the code parallelized by manually inserting calls to the runtime library.

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.

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.

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.

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

Ramses-GPU: Second order MUSCL-Handcock finite volume fluid solver

NASA Astrophysics Data System (ADS)

Kestener, Pierre

2017-10-01

RamsesGPU is a reimplementation of RAMSES (ascl:1011.007) which drops the adaptive mesh refinement (AMR) features to optimize 3D uniform grid algorithms for modern graphics processor units (GPU) to provide an efficient software package for astrophysics applications that do not need AMR features but do require a very large number of integration time steps. RamsesGPU provides an very efficient C++/CUDA/MPI software implementation of a second order MUSCL-Handcock finite volume fluid solver for compressible hydrodynamics as a magnetohydrodynamics solver based on the constraint transport technique. Other useful modules includes static gravity, dissipative terms (viscosity, resistivity), and forcing source term for turbulence studies, and special care was taken to enhance parallel input/output performance by using state-of-the-art libraries such as HDF5 and parallel-netcdf.

Repartitioning Strategies for Massively Parallel Simulation of Reacting Flow

NASA Astrophysics Data System (ADS)

Pisciuneri, Patrick; Zheng, Angen; Givi, Peyman; Labrinidis, Alexandros; Chrysanthis, Panos

2015-11-01

The majority of parallel CFD simulators partition the domain into equal regions and assign the calculations for a particular region to a unique processor. This type of domain decomposition is vital to the efficiency of the solver. However, as the simulation develops, the workload among the partitions often become uneven (e.g. by adaptive mesh refinement, or chemically reacting regions) and a new partition should be considered. The process of repartitioning adjusts the current partition to evenly distribute the load again. We compare two repartitioning tools: Zoltan, an architecture-agnostic graph repartitioner developed at the Sandia National Laboratories; and Paragon, an architecture-aware graph repartitioner developed at the University of Pittsburgh. The comparative assessment is conducted via simulation of the Taylor-Green vortex flow with chemical reaction.

Arbitrary-level hanging nodes for adaptive hphp-FEM approximations in 3D

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

Pavel Kus; Pavel Solin; David Andrs

2014-11-01

In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hphp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.

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.

High-Resolution Numerical Simulation and Analysis of Mach Reflection Structures in Detonation Waves in Low-Pressure H 2 –O 2 –Ar Mixtures: A Summary of Results Obtained with the Adaptive Mesh Refinement Framework AMROC

DOE PAGES

Deiterding, Ralf

2011-01-01

Numerical simulation can be key to the understanding of the multidimensional nature of transient detonation waves. However, the accurate approximation of realistic detonations is demanding as a wide range of scales needs to be resolved. This paper describes a successful solution strategy that utilizes logically rectangular dynamically adaptive meshes. The hydrodynamic transport scheme and the treatment of the nonequilibrium reaction terms are sketched. A ghost fluid approach is integrated into the method to allow for embedded geometrically complex boundaries. Large-scale parallel simulations of unstable detonation structures of Chapman-Jouguet detonations in low-pressure hydrogen-oxygen-argon mixtures demonstrate the efficiency of the described techniquesmore » in practice. In particular, computations of regular cellular structures in two and three space dimensions and their development under transient conditions, that is, under diffraction and for propagation through bends are presented. Some of the observed patterns are classified by shock polar analysis, and a diagram of the transition boundaries between possible Mach reflection structures is constructed.« less

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.

THE PLUTO CODE FOR ADAPTIVE MESH COMPUTATIONS IN ASTROPHYSICAL FLUID DYNAMICS

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

Mignone, A.; Tzeferacos, P.; Zanni, C.

We present a description of the adaptive mesh refinement (AMR) implementation of the PLUTO code for solving the equations of classical and special relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits, in addition to the static grid version of the code, the distributed infrastructure of the CHOMBO library for multidimensional parallel computations over block-structured, adaptively refined grids. We employ a conservative finite-volume approach where primary flow quantities are discretized at the cell center in a dimensionally unsplit fashion using the Corner Transport Upwind method. Time stepping relies on a characteristic tracing step where piecewise parabolic method, weighted essentially non-oscillatory,more » or slope-limited linear interpolation schemes can be handily adopted. A characteristic decomposition-free version of the scheme is also illustrated. The solenoidal condition of the magnetic field is enforced by augmenting the equations with a generalized Lagrange multiplier providing propagation and damping of divergence errors through a mixed hyperbolic/parabolic explicit cleaning step. Among the novel features, we describe an extension of the scheme to include non-ideal dissipative processes, such as viscosity, resistivity, and anisotropic thermal conduction without operator splitting. Finally, we illustrate an efficient treatment of point-local, potentially stiff source terms over hierarchical nested grids by taking advantage of the adaptivity in time. Several multidimensional benchmarks and applications to problems of astrophysical relevance assess the potentiality of the AMR version of PLUTO in resolving flow features separated by large spatial and temporal disparities.« less

Method and structure for skewed block-cyclic distribution of lower-dimensional data arrays in higher-dimensional processor grids

DOEpatents

Chatterjee, Siddhartha [Yorktown Heights, NY; Gunnels, John A [Brewster, NY

2011-11-08

A method and structure of distributing elements of an array of data in a computer memory to a specific processor of a multi-dimensional mesh of parallel processors includes designating a distribution of elements of at least a portion of the array to be executed by specific processors in the multi-dimensional mesh of parallel processors. The pattern of the designating includes a cyclical repetitive pattern of the parallel processor mesh, as modified to have a skew in at least one dimension so that both a row of data in the array and a column of data in the array map to respective contiguous groupings of the processors such that a dimension of the contiguous groupings is greater than one.

HARP: A Dynamic Inertial Spectral Partitioner

NASA Technical Reports Server (NTRS)

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

1997-01-01

Partitioning unstructured graphs is central to the parallel solution of computational science and engineering problems. Spectral partitioners, such recursive spectral bisection (RSB), have proven effecfive in generating high-quality partitions of realistically-sized meshes. The major problem which hindered their wide-spread use was their long execution times. This paper presents a new inertial spectral partitioner, called HARP. The main objective of the proposed approach is to quickly partition the meshes at runtime in a manner that works efficiently for real applications in the context of distributed-memory machines. The underlying principle of HARP is to find the eigenvectors of the unpartitioned vertices and then project them onto the eigerivectors of the original mesh. Results for various meshes ranging in size from 1000 to 100,000 vertices indicate that HARP can indeed partition meshes rapidly at runtime. Experimental results show that our largest mesh can be partitioned sequentially in only a few seconds on an SP2 which is several times faster than other spectral partitioners while maintaining the solution quality of the proven RSB method. A parallel WI version of HARP has also been implemented on IBM SP2 and Cray T3E. Parallel HARP, running on 64 processors SP2 and T3E, can partition a mesh containing more than 100,000 vertices into 64 subgrids in about half a second. These results indicate that graph partitioning can now be truly embedded in dynamically-changing real-world applications.

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

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.

Parallel performance optimizations on unstructured mesh-based simulations

DOE PAGES

Sarje, Abhinav; Song, Sukhyun; Jacobsen, Douglas; ...

2015-06-01

This paper addresses two key parallelization challenges the unstructured mesh-based ocean modeling code, MPAS-Ocean, which uses a mesh based on Voronoi tessellations: (1) load imbalance across processes, and (2) unstructured data access patterns, that inhibit intra- and inter-node performance. Our work analyzes the load imbalance due to naive partitioning of the mesh, and develops methods to generate mesh partitioning with better load balance and reduced communication. Furthermore, we present methods that minimize both inter- and intranode data movement and maximize data reuse. Our techniques include predictive ordering of data elements for higher cache efficiency, as well as communication reduction approaches.more » We present detailed performance data when running on thousands of cores using the Cray XC30 supercomputer and show that our optimization strategies can exceed the original performance by over 2×. Additionally, many of these solutions can be broadly applied to a wide variety of unstructured grid-based computations.« less

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.

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.

A massively parallel adaptive scheme for melt migration in geodynamics computations

NASA Astrophysics Data System (ADS)

Dannberg, Juliane; Heister, Timo; Grove, Ryan

2016-04-01

Melt generation and migration are important processes for the evolution of the Earth's interior and impact the global convection of the mantle. While they have been the subject of numerous investigations, the typical time and length-scales of melt transport are vastly different from global mantle convection, which determines where melt is generated. This makes it difficult to study mantle convection and melt migration in a unified framework. In addition, modelling magma dynamics poses the challenge of highly non-linear and spatially variable material properties, in particular the viscosity. We describe our extension of the community mantle convection code ASPECT that adds equations describing the behaviour of silicate melt percolating through and interacting with a viscously deforming host rock. We use the original compressible formulation of the McKenzie equations, augmented by an equation for the conservation of energy. This approach includes both melt migration and melt generation with the accompanying latent heat effects, and it incorporates the individual compressibilities of the solid and the fluid phase. For this, we derive an accurate and stable Finite Element scheme that can be combined with adaptive mesh refinement. This is particularly advantageous for this type of problem, as the resolution can be increased in mesh cells where melt is present and viscosity gradients are high, whereas a lower resolution is sufficient in regions without melt. Together with a high-performance, massively parallel implementation, this allows for high resolution, 3d, compressible, global mantle convection simulations coupled with melt migration. Furthermore, scalable iterative linear solvers are required to solve the large linear systems arising from the discretized system. Finally, we present benchmarks and scaling tests of our solver up to tens of thousands of cores, show the effectiveness of adaptive mesh refinement when applied to melt migration and compare the compressible and incompressible formulation. We then apply our software to large-scale 3d simulations of melting and melt transport in mantle plumes interacting with the lithosphere. Our model of magma dynamics provides a framework for modelling processes on different scales and investigating links between processes occurring in the deep mantle and melt generation and migration. The presented implementation is available online under an Open Source license together with an extensive documentation.

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

Parallel Adaptive High-Order CFD Simulations Characterizing SOFIA Cavitiy Acoustics

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.; Biswas, Rupak

2015-01-01

This paper presents large-scale MPI-parallel computational uid dynamics simulations for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is an airborne, 2.5-meter infrared telescope mounted in an open cavity in the aft fuselage of a Boeing 747SP. These simulations focus on how the unsteady ow eld inside and over the cavity interferes with the optical path and mounting structure of the telescope. A tempo- rally fourth-order accurate Runge-Kutta, and a spatially fth-order accurate WENO-5Z scheme were used to perform implicit large eddy simulations. An immersed boundary method provides automated gridding for complex geometries and natural coupling to a block-structured Cartesian adaptive mesh re nement framework. Strong scaling studies using NASA's Pleiades supercomputer with up to 32k CPU cores and 4 billion compu- tational cells shows excellent scaling. Dynamic load balancing based on execution time on individual AMR blocks addresses irregular numerical cost associated with blocks con- taining boundaries. Limits to scaling beyond 32k cores are identi ed, and targeted code optimizations are discussed.

Analysis and improvements of Adaptive Particle Refinement (APR) through CPU time, accuracy and robustness considerations

NASA Astrophysics Data System (ADS)

Chiron, L.; Oger, G.; de Leffe, M.; Le Touzé, D.

2018-02-01

While smoothed-particle hydrodynamics (SPH) simulations are usually performed using uniform particle distributions, local particle refinement techniques have been developed to concentrate fine spatial resolutions in identified areas of interest. Although the formalism of this method is relatively easy to implement, its robustness at coarse/fine interfaces can be problematic. Analysis performed in [16] shows that the radius of refined particles should be greater than half the radius of unrefined particles to ensure robustness. In this article, the basics of an Adaptive Particle Refinement (APR) technique, inspired by AMR in mesh-based methods, are presented. This approach ensures robustness with alleviated constraints. Simulations applying the new formalism proposed achieve accuracy comparable to fully refined spatial resolutions, together with robustness, low CPU times and maintained parallel efficiency.

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.

MUTILS - a set of efficient modeling tools for multi-core CPUs implemented in MEX

NASA Astrophysics Data System (ADS)

Krotkiewski, Marcin; Dabrowski, Marcin

2013-04-01

The need for computational performance is common in scientific applications, and in particular in numerical simulations, where high resolution models require efficient processing of large amounts of data. Especially in the context of geological problems the need to increase the model resolution to resolve physical and geometrical complexities seems to have no limits. Alas, the performance of new generations of CPUs does not improve any longer by simply increasing clock speeds. Current industrial trends are to increase the number of computational cores. As a result, parallel implementations are required in order to fully utilize the potential of new processors, and to study more complex models. We target simulations on small to medium scale shared memory computers: laptops and desktop PCs with ~8 CPU cores and up to tens of GB of memory to high-end servers with ~50 CPU cores and hundereds of GB of memory. In this setting MATLAB is often the environment of choice for scientists that want to implement their own models with little effort. It is a useful general purpose mathematical software package, but due to its versatility some of its functionality is not as efficient as it could be. In particular, the challanges of modern multi-core architectures are not fully addressed. We have developed MILAMIN 2 - an efficient FEM modeling environment written in native MATLAB. Amongst others, MILAMIN provides functions to define model geometry, generate and convert structured and unstructured meshes (also through interfaces to external mesh generators), compute element and system matrices, apply boundary conditions, solve the system of linear equations, address non-linear and transient problems, and perform post-processing. MILAMIN strives to combine the ease of code development and the computational efficiency. Where possible, the code is optimized and/or parallelized within the MATLAB framework. Native MATLAB is augmented with the MUTILS library - a set of MEX functions that implement the computationally intensive, performance critical parts of the code, which we have identified to be bottlenecks. Here, we discuss the functionality and performance of the MUTILS library. Currently, it includes: 1. time and memory efficient assembly of sparse matrices for FEM simulations 2. parallel sparse matrix - vector product with optimizations speficic to symmetric matrices and multiple degrees of freedom per node 3. parallel point in triangle location and point in tetrahedron location for unstructured, adaptive 2D and 3D meshes (useful for 'marker in cell' type of methods) 4. parallel FEM interpolation for 2D and 3D meshes of elements of different types and orders, and for different number of degrees of freedom per node 5. a stand-alone, MEX implementation of the Conjugate Gradients iterative solver 6. interface to METIS graph partitioning and a fast implementation of RCM reordering

Floating shock fitting via Lagrangian adaptive meshes

NASA Technical Reports Server (NTRS)

Vanrosendale, John

1995-01-01

In recent work we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.

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

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.

Parallel performance investigations of an unstructured mesh Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

2000-01-01

A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense of additional memory usage. The solver is cache efficient and fully vectorizable, and is parallelized using a two-level hybrid MPI-OpenMP implementation suitable for shared and/or distributed memory architectures, as well as clusters of shared memory machines. Convergence and scalability results are illustrated for various high-lift cases.

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport

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

Hyman, Jeffrey D.; Karra, Satish; Makedonska, Nataliia

DFNWORKS is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using DFNGEN, which combines FRAM (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the LaGriT meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in anmore » intrinsically parallel fashion. Flow through the network is simulated in dfnFlow, which utilizes the massively parallel subsurface flow and reactive transport finite volume code PFLOTRAN. A Lagrangian approach to simulating transport through the DFN is adopted within DFNTRANS to determine pathlines and solute transport through the DFN. Example applications of this suite in the areas of nuclear waste repository science, hydraulic fracturing and CO 2 sequestration are also included.« less

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport

DOE PAGES

Hyman, Jeffrey D.; Karra, Satish; Makedonska, Nataliia; ...

2015-11-01

DFNWORKS is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using DFNGEN, which combines FRAM (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the LaGriT meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in anmore » intrinsically parallel fashion. Flow through the network is simulated in dfnFlow, which utilizes the massively parallel subsurface flow and reactive transport finite volume code PFLOTRAN. A Lagrangian approach to simulating transport through the DFN is adopted within DFNTRANS to determine pathlines and solute transport through the DFN. Example applications of this suite in the areas of nuclear waste repository science, hydraulic fracturing and CO 2 sequestration are also included.« less

Parallel-In-Time For Moving Meshes

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

Falgout, R. D.; Manteuffel, T. A.; Southworth, B.

2016-02-04

With steadily growing computational resources available, scientists must develop e ective ways to utilize the increased resources. High performance, highly parallel software has be- come a standard. However until recent years parallelism has focused primarily on the spatial domain. When solving a space-time partial di erential equation (PDE), this leads to a sequential bottleneck in the temporal dimension, particularly when taking a large number of time steps. The XBraid parallel-in-time library was developed as a practical way to add temporal parallelism to existing se- quential codes with only minor modi cations. In this work, a rezoning-type moving mesh is appliedmore » to a di usion problem and formulated in a parallel-in-time framework. Tests and scaling studies are run using XBraid and demonstrate excellent results for the simple model problem considered herein.« less

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.

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.

ISSM: Ice Sheet System Model

NASA Technical Reports Server (NTRS)

Larour, Eric; Schiermeier, John E.; Seroussi, Helene; Morlinghem, Mathieu

2013-01-01

In order to have the capability to use satellite data from its own missions to inform future sea-level rise projections, JPL needed a full-fledged ice-sheet/iceshelf flow model, capable of modeling the mass balance of Antarctica and Greenland into the near future. ISSM was developed with such a goal in mind, as a massively parallelized, multi-purpose finite-element framework dedicated to ice-sheet modeling. ISSM features unstructured meshes (Tria in 2D, and Penta in 3D) along with corresponding finite elements for both types of meshes. Each finite element can carry out diagnostic, prognostic, transient, thermal 3D, surface, and bed slope simulations. Anisotropic meshing enables adaptation of meshes to a certain metric, and the 2D Shelfy-Stream, 3D Blatter/Pattyn, and 3D Full-Stokes formulations capture the bulk of the ice-flow physics. These elements can be coupled together, based on the Arlequin method, so that on a large scale model such as Antarctica, each type of finite element is used in the most efficient manner. For each finite element referenced above, ISSM implements an adjoint. This adjoint can be used to carry out model inversions of unknown model parameters, typically ice rheology and basal drag at the ice/bedrock interface, using a metric such as the observed InSAR surface velocity. This data assimilation capability is crucial to allow spinning up of ice flow models using available satellite data. ISSM relies on the PETSc library for its vectors, matrices, and solvers. This allows ISSM to run efficiently on any parallel platform, whether shared or distrib- ISSM: Ice Sheet System Model NASA's Jet Propulsion Laboratory, Pasadena, California uted. It can run on the largest clusters, and is fully scalable. This allows ISSM to tackle models the size of continents. ISSM is embedded into MATLAB and Python, both open scientific platforms. This improves its outreach within the science community. It is entirely written in C/C++, which gives it flexibility in its design, and the power/speed that C/C++ allows. ISSM is svn (subversion) hosted, on a JPL repository, to facilitate its development and maintenance. ISSM can also model propagation of rifts using contact mechanics and mesh splitting, and can interface to the Dakota software. To carry out sensitivity analysis, mesh partitioning algorithms are available, based on the Scotch, Chaco, and Metis partitioners that ensure equal area mesh partitions can be done, which are then usable for sampling and local reliability methods.

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).

Parallel flow diffusion battery

DOEpatents

Yeh, H.C.; Cheng, Y.S.

1984-01-01

A parallel flow diffusion battery for determining the mass distribution of an aerosol has a plurality of diffusion cells mounted in parallel to an aerosol stream, each diffusion cell including a stack of mesh wire screens of different density.

Parallel flow diffusion battery

DOEpatents

Yeh, Hsu-Chi; Cheng, Yung-Sung

1984-08-07

A parallel flow diffusion battery for determining the mass distribution of an aerosol has a plurality of diffusion cells mounted in parallel to an aerosol stream, each diffusion cell including a stack of mesh wire screens of different density.

Parallel Performance Optimizations on Unstructured Mesh-based Simulations

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

Sarje, Abhinav; Song, Sukhyun; Jacobsen, Douglas

2015-01-01

© The Authors. Published by Elsevier B.V. This paper addresses two key parallelization challenges the unstructured mesh-based ocean modeling code, MPAS-Ocean, which uses a mesh based on Voronoi tessellations: (1) load imbalance across processes, and (2) unstructured data access patterns, that inhibit intra- and inter-node performance. Our work analyzes the load imbalance due to naive partitioning of the mesh, and develops methods to generate mesh partitioning with better load balance and reduced communication. Furthermore, we present methods that minimize both inter- and intranode data movement and maximize data reuse. Our techniques include predictive ordering of data elements for higher cachemore » efficiency, as well as communication reduction approaches. We present detailed performance data when running on thousands of cores using the Cray XC30 supercomputer and show that our optimization strategies can exceed the original performance by over 2×. Additionally, many of these solutions can be broadly applied to a wide variety of unstructured grid-based computations.« less

The Tera Multithreaded Architecture and Unstructured Meshes

NASA Technical Reports Server (NTRS)

Bokhari, Shahid H.; Mavriplis, Dimitri J.

1998-01-01

The Tera Multithreaded Architecture (MTA) is a new parallel supercomputer currently being installed at San Diego Supercomputing Center (SDSC). This machine has an architecture quite different from contemporary parallel machines. The computational processor is a custom design and the machine uses hardware to support very fine grained multithreading. The main memory is shared, hardware randomized and flat. These features make the machine highly suited to the execution of unstructured mesh problems, which are difficult to parallelize on other architectures. We report the results of a study carried out during July-August 1998 to evaluate the execution of EUL3D, a code that solves the Euler equations on an unstructured mesh, on the 2 processor Tera MTA at SDSC. Our investigation shows that parallelization of an unstructured code is extremely easy on the Tera. We were able to get an existing parallel code (designed for a shared memory machine), running on the Tera by changing only the compiler directives. Furthermore, a serial version of this code was compiled to run in parallel on the Tera by judicious use of directives to invoke the "full/empty" tag bits of the machine to obtain synchronization. This version achieves 212 and 406 Mflop/s on one and two processors respectively, and requires no attention to partitioning or placement of data issues that would be of paramount importance in other parallel architectures.

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.

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.

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.

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.

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.

A new procedure for dynamic adaption of three-dimensional unstructured grids

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Strawn, Roger

1993-01-01

A new procedure is presented for the simultaneous coarsening and refinement of three-dimensional unstructured tetrahedral meshes. This algorithm allows for localized grid adaption that is used to capture aerodynamic flow features such as vortices and shock waves in helicopter flowfield simulations. The mesh-adaption algorithm is implemented in the C programming language and uses a data structure consisting of a series of dynamically-allocated linked lists. These lists allow the mesh connectivity to be rapidly reconstructed when individual mesh points are added and/or deleted. The algorithm allows the mesh to change in an anisotropic manner in order to efficiently resolve directional flow features. The procedure has been successfully implemented on a single processor of a Cray Y-MP computer. Two sample cases are presented involving three-dimensional transonic flow. Computed results show good agreement with conventional structured-grid solutions for the Euler equations.

Graph Partitioning for Parallel Applications in Heterogeneous Grid Environments

NASA Technical Reports Server (NTRS)

Bisws, Rupak; Kumar, Shailendra; Das, Sajal K.; Biegel, Bryan (Technical Monitor)

2002-01-01

The problem of partitioning irregular graphs and meshes for parallel computations on homogeneous systems has been extensively studied. However, these partitioning schemes fail when the target system architecture exhibits heterogeneity in resource characteristics. With the emergence of technologies such as the Grid, it is imperative to study the partitioning problem taking into consideration the differing capabilities of such distributed heterogeneous systems. In our model, the heterogeneous system consists of processors with varying processing power and an underlying non-uniform communication network. We present in this paper a novel multilevel partitioning scheme for irregular graphs and meshes, that takes into account issues pertinent to Grid computing environments. Our partitioning algorithm, called MiniMax, generates and maps partitions onto a heterogeneous system with the objective of minimizing the maximum execution time of the parallel distributed application. For experimental performance study, we have considered both a realistic mesh problem from NASA as well as synthetic workloads. Simulation results demonstrate that MiniMax generates high quality partitions for various classes of applications targeted for parallel execution in a distributed heterogeneous environment.

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.

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.

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.

Scan Directed Load Balancing for Highly-Parallel Mesh-Connected Computers

DTIC Science & Technology

1991-07-01

DTIC ~ ELECTE OCT 2 41991 AD-A242 045 Scan Directed Load Balancing for Highly-Parallel Mesh-Connected Computers’ Edoardo S. Biagioni Jan F. Prins...Department of Computer Science University of North Carolina Chapel Hill, N.C. 27599-3175 USA biagioni @cs.unc.edu prinsOcs.unc.edu Abstract Scan Directed...MasPar Computer Corpora- tion. Bibliography [1] Edoardo S. Biagioni . Scan Directed Load Balancing. PhD thesis., University of North Carolina, Chapel Hill

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.

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.

Application of parallel distributed Lagrange multiplier technique to simulate coupled Fluid-Granular flows in pipes with varying Cross-Sectional area

DOE PAGES

Kanarska, Yuliya; Walton, Otis

2015-11-30

Fluid-granular flows are common phenomena in nature and industry. Here, an efficient computational technique based on the distributed Lagrange multiplier method is utilized to simulate complex fluid-granular flows. Each particle is explicitly resolved on an Eulerian grid as a separate domain, using solid volume fractions. The fluid equations are solved through the entire computational domain, however, Lagrange multiplier constrains are applied inside the particle domain such that the fluid within any volume associated with a solid particle moves as an incompressible rigid body. The particle–particle interactions are implemented using explicit force-displacement interactions for frictional inelastic particles similar to the DEMmore » method with some modifications using the volume of an overlapping region as an input to the contact forces. Here, a parallel implementation of the method is based on the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) library.« less

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.

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.

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.

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.

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.

Scalable Computing of the Mesh Size Effect on Modeling Damage Mechanics in Woven Armor Composites

DTIC Science & Technology

2008-12-01

manner of a user defined material subroutine to provide overall stress increments to, the parallel LS-DYNA3D a Lagrangian explicit code used in...finite element code, as a user defined material subroutine . The ability of this subroutine to model the effect of the progressions of a select number...is added as a user defined material subroutine to parallel LS-DYNA3D. The computations of the global mesh are handled by LS-DYNA3D and are spread

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

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.

Detached eddy simulation for turbulent fluid-structure interaction of moving bodies using the constraint-based immersed boundary method

NASA Astrophysics Data System (ADS)

Nangia, Nishant; Bhalla, Amneet P. S.; Griffith, Boyce E.; Patankar, Neelesh A.

2016-11-01

Flows over bodies of industrial importance often contain both an attached boundary layer region near the structure and a region of massively separated flow near its trailing edge. When simulating these flows with turbulence modeling, the Reynolds-averaged Navier-Stokes (RANS) approach is more efficient in the former, whereas large-eddy simulation (LES) is more accurate in the latter. Detached-eddy simulation (DES), based on the Spalart-Allmaras model, is a hybrid method that switches from RANS mode of solution in attached boundary layers to LES in detached flow regions. Simulations of turbulent flows over moving structures on a body-fitted mesh incur an enormous remeshing cost every time step. The constraint-based immersed boundary (cIB) method eliminates this operation by placing the structure on a Cartesian mesh and enforcing a rigidity constraint as an additional forcing in the Navier-Stokes momentum equation. We outline the formulation and development of a parallel DES-cIB method using adaptive mesh refinement. We show preliminary validation results for flows past stationary bodies with both attached and separated boundary layers along with results for turbulent flows past moving bodies. This work is supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1324585.

Assessment of Near-Field Sonic Boom Simulation Tools

NASA Technical Reports Server (NTRS)

Casper, J. H.; Cliff, S. E.; Thomas, S. D.; Park, M. A.; McMullen, M. S.; Melton, J. E.; Durston, D. A.

2008-01-01

A recent study for the Supersonics Project, within the National Aeronautics and Space Administration, has been conducted to assess current in-house capabilities for the prediction of near-field sonic boom. Such capabilities are required to simulate the highly nonlinear flow near an aircraft, wherein a sonic-boom signature is generated. There are many available computational fluid dynamics codes that could be used to provide the near-field flow for a sonic boom calculation. However, such codes have typically been developed for applications involving aerodynamic configuration, for which an efficiently generated computational mesh is usually not optimum for a sonic boom prediction. Preliminary guidelines are suggested to characterize a state-of-the-art sonic boom prediction methodology. The available simulation tools that are best suited to incorporate into that methodology are identified; preliminary test cases are presented in support of the selection. During this phase of process definition and tool selection, parallel research was conducted in an attempt to establish criteria that link the properties of a computational mesh to the accuracy of a sonic boom prediction. Such properties include sufficient grid density near shocks and within the zone of influence, which are achieved by adaptation and mesh refinement strategies. Prediction accuracy is validated by comparison with wind tunnel data.

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.

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.

GPU surface extraction using the closest point embedding

NASA Astrophysics Data System (ADS)

Kim, Mark; Hansen, Charles

2015-01-01

Isosurface extraction is a fundamental technique used for both surface reconstruction and mesh generation. One method to extract well-formed isosurfaces is a particle system; unfortunately, particle systems can be slow. In this paper, we introduce an enhanced parallel particle system that uses the closest point embedding as the surface representation to speedup the particle system for isosurface extraction. The closest point embedding is used in the Closest Point Method (CPM), a technique that uses a standard three dimensional numerical PDE solver on two dimensional embedded surfaces. To fully take advantage of the closest point embedding, it is coupled with a Barnes-Hut tree code on the GPU. This new technique produces well-formed, conformal unstructured triangular and tetrahedral meshes from labeled multi-material volume datasets. Further, this new parallel implementation of the particle system is faster than any known methods for conformal multi-material mesh extraction. The resulting speed-ups gained in this implementation can reduce the time from labeled data to mesh from hours to minutes and benefits users, such as bioengineers, who employ triangular and tetrahedral meshes

Extending a CAD-Based Cartesian Mesh Generator for the Lattice Boltzmann Method

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

Cantrell, J Nathan; Inclan, Eric J; Joshi, Abhijit S

2012-01-01

This paper describes the development of a custom preprocessor for the PaRAllel Thermal Hydraulics simulations using Advanced Mesoscopic methods (PRATHAM) code based on an open-source mesh generator, CartGen [1]. PRATHAM is a three-dimensional (3D) lattice Boltzmann method (LBM) based parallel flow simulation software currently under development at the Oak Ridge National Laboratory. The LBM algorithm in PRATHAM requires a uniform, coordinate system-aligned, non-body-fitted structured mesh for its computational domain. CartGen [1], which is a GNU-licensed open source code, already comes with some of the above needed functionalities. However, it needs to be further extended to fully support the LBM specificmore » preprocessing requirements. Therefore, CartGen is being modified to (i) be compiler independent while converting a neutral-format STL (Stereolithography) CAD geometry to a uniform structured Cartesian mesh, (ii) provide a mechanism for PRATHAM to import the mesh and identify the fluid/solid domains, and (iii) provide a mechanism to visually identify and tag the domain boundaries on which to apply different boundary conditions.« less

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.

Mesh-matrix analysis method for electromagnetic launchers

NASA Technical Reports Server (NTRS)

Elliott, David G.

1989-01-01

The mesh-matrix method is a procedure for calculating the current distribution in the conductors of electromagnetic launchers with coil or flat-plate geometry. Once the current distribution is known the launcher performance can be calculated. The method divides the conductors into parallel current paths, or meshes, and finds the current in each mesh by matrix inversion. The author presents procedures for writing equations for the current and voltage relations for a few meshes to serve as a pattern for writing the computer code. An available subroutine package provides routines for field and flux coefficients and equation solution.

A parallel graded-mesh FDTD algorithm for human-antenna interaction problems.

PubMed

Catarinucci, Luca; Tarricone, Luciano

2009-01-01

The finite difference time domain method (FDTD) is frequently used for the numerical solution of a wide variety of electromagnetic (EM) problems and, among them, those concerning human exposure to EM fields. In many practical cases related to the assessment of occupational EM exposure, large simulation domains are modeled and high space resolution adopted, so that strong memory and central processing unit power requirements have to be satisfied. To better afford the computational effort, the use of parallel computing is a winning approach; alternatively, subgridding techniques are often implemented. However, the simultaneous use of subgridding schemes and parallel algorithms is very new. In this paper, an easy-to-implement and highly-efficient parallel graded-mesh (GM) FDTD scheme is proposed and applied to human-antenna interaction problems, demonstrating its appropriateness in dealing with complex occupational tasks and showing its capability to guarantee the advantages of a traditional subgridding technique without affecting the parallel FDTD performance.

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

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

DOE PAGES

Osborn, Sarah; Zulian, Patrick; Benson, Thomas; ...

2018-01-30

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

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

Osborn, Sarah; Zulian, Patrick; Benson, Thomas

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less

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

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

Revised Extended Grid Library

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

Martz, Roger L.

The Revised Eolus Grid Library (REGL) is a mesh-tracking library that was developed for use with the MCNP6TM computer code so that (radiation) particles can track on an unstructured mesh. The unstructured mesh is a finite element representation of any geometric solid model created with a state-of-the-art CAE/CAD tool. The mesh-tracking library is written using modern Fortran and programming standards; the library is Fortran 2003 compliant. The library was created with a defined application programmer interface (API) so that it could easily integrate with other particle tracking/transport codes. The library does not handle parallel processing via the message passing interfacemore » (mpi), but has been used successfully where the host code handles the mpi calls. The library is thread-safe and supports the OpenMP paradigm. As a library, all features are available through the API and overall a tight coupling between it and the host code is required. Features of the library are summarized with the following list: Can accommodate first and second order 4, 5, and 6-sided polyhedra; any combination of element types may appear in a single geometry model; parts may not contain tetrahedra mixed with other element types; pentahedra and hexahedra can be together in the same part; robust handling of overlaps and gaps; tracks element-to-element to produce path length results at the element level; finds element numbers for a given mesh location; finds intersection points on element faces for the particle tracks; produce a data file for post processing results analysis; reads Abaqus .inp input (ASCII) files to obtain information for the global mesh-model; supports parallel input processing via mpi; and support parallel particle transport by both mpi and OpenMP.« less

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.

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.

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.

Robust moving mesh algorithms for hybrid stretched meshes: Application to moving boundaries problems

NASA Astrophysics Data System (ADS)

Landry, Jonathan; Soulaïmani, Azzeddine; Luke, Edward; Ben Haj Ali, Amine

2016-12-01

A robust Mesh-Mover Algorithm (MMA) approach is designed to adapt meshes of moving boundaries problems. A new methodology is developed from the best combination of well-known algorithms in order to preserve the quality of initial meshes. In most situations, MMAs distribute mesh deformation while preserving a good mesh quality. However, invalid meshes are generated when the motion is complex and/or involves multiple bodies. After studying a few MMA limitations, we propose the following approach: use the Inverse Distance Weighting (IDW) function to produce the displacement field, then apply the Geometric Element Transformation Method (GETMe) smoothing algorithms to improve the resulting mesh quality, and use an untangler to revert negative elements. The proposed approach has been proven efficient to adapt meshes for various realistic aerodynamic motions: a symmetric wing that has suffered large tip bending and twisting and the high-lift components of a swept wing that has moved to different flight stages. Finally, the fluid flow problem has been solved on meshes that have moved and they have produced results close to experimental ones. However, for situations where moving boundaries are too close to each other, more improvements need to be made or other approaches should be taken, such as an overset grid method.

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.

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.

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.

Floating shock fitting via Lagrangian adaptive meshes

NASA Technical Reports Server (NTRS)

Vanrosendale, John

1994-01-01

In recent works we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM) is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence. Shock-capturing algorithms like this, which warp the mesh to yield shock-fitted accuracy, are new and relatively untried. However, their potential is clear. In the context of sonic booms, accurate calculation of near-field sonic boom signatures is critical to the design of the High Speed Civil Transport (HSCT). SLAM should allow computation of accurate N-wave pressure signatures on comparatively coarse meshes, significantly enhancing our ability to design low-boom configurations for high-speed aircraft.

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.

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).

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

Domain decomposition methods in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Gropp, William D.; Keyes, David E.

1991-01-01

The divide-and-conquer paradigm of iterative domain decomposition, or substructuring, has become a practical tool in computational fluid dynamic applications because of its flexibility in accommodating adaptive refinement through locally uniform (or quasi-uniform) grids, its ability to exploit multiple discretizations of the operator equations, and the modular pathway it provides towards parallelism. These features are illustrated on the classic model problem of flow over a backstep using Newton's method as the nonlinear iteration. Multiple discretizations (second-order in the operator and first-order in the preconditioner) and locally uniform mesh refinement pay dividends separately, and they can be combined synergistically. Sample performance results are included from an Intel iPSC/860 hypercube implementation.

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.

DETERIORATION IN BIOMECHANICAL PROPERTIES OF THE VAGINA FOLLOWING IMPLANTATION OF A HIGH STIFFNESS PROLAPSE MESH

PubMed Central

Feola, Andrew; Abramowitch, Steven; Jallah, Zegbeh; Stein, Suzan; Barone, William; Palcsey, Stacy; Moalli, Pamela

2012-01-01

Objective Define the impact of prolapse mesh on the biomechanical properties of the vagina by comparing the prototype Gynemesh PS (Ethicon, Somerville, NJ) to 2 new generation lower stiffness meshes, SmartMesh (Coloplast, Minneapolis, MN) and UltraPro (Ethicon). Design A study employing a non-human primate model Setting University of Pittsburgh Population 45 parous rhesus macaques Methods Meshes were implanted via sacrocolpexy after hysterectomy and compared to Sham. Because its stiffness is highly directional UltraPro was implanted in two directions: UltraPro Perpendicular (less stiff) and UltraPro Parallel (more stiff), with the indicated direction referring to the blue orientation lines. The mesh-vaginal complex (MVC) was excised en toto after 3 months. Main Outcome Measures Active mechanical properties were quantified as contractile force generated in the presence of 120 mM KCl. Passive mechanical properties (a tissues ability to resist an applied force) were measured using a multi-axial protocol. Results Vaginal contractility decreased 80% following implantation with the Gynemesh PS (p=0.001), 48% after SmartMesh (p=0.001), 68% after UltraPro parallel (p=0.001) and was highly variable after UltraPro perpendicular (p =0.16). The tissue contribution to the passive mechanical behavior of the MVC was drastically reduced for Gynemesh PS (p=0.003) but not SmartMesh (p=0.9) or UltraPro independent of the direction of implantation (p=0.68 and p=0.66, respectively). Conclusions Deterioration of the mechanical properties of the vagina was highest following implantation with the stiffest mesh, Gynemesh PS. Such a decrease associated with implantation of a device of increased stiffness is consistent with findings from other systems employing prostheses for support. PMID:23240801

Deterioration in biomechanical properties of the vagina following implantation of a high-stiffness prolapse mesh.

PubMed

Feola, A; Abramowitch, S; Jallah, Z; Stein, S; Barone, W; Palcsey, S; Moalli, P

2013-01-01

To define the impact of prolapse mesh on the biomechanical properties of the vagina by comparing the prototype Gynemesh PS (Ethicon) to two new-generation lower stiffness meshes, SmartMesh (Coloplast) and UltraPro (Ethicon). A study employing a nonhuman primate model. University of Pittsburgh, PA, USA. Forty-five parous rhesus macaques. Meshes were implanted via sacrocolpopexy after hysterectomy and compared with sham. Because its stiffness is highly directional, UltraPro was implanted in two directions: UltraPro Perpendicular (less stiff) and UltraPro Parallel (more stiff), with the indicated direction referring to the position of the blue orientation lines relative to the longitudinal axis of the vagina. The mesh-vaginal complex (MVC) was excised in toto after 3 months. Active mechanical properties were quantified as the contractile force generated in the presence of 120 mmol/l KCl. Passive mechanical properties (a tissue's ability to resist an applied force) were measured using a multiaxial protocol. Vaginal contractility decreased by 80% following implantation with the Gynemesh PS (P = 0.001), 48% after SmartMesh (P = 0.001), 68% after UltraPro Parallel (P = 0.001) and was highly variable after UltraPro Perpendicular (P = 0.16). The tissue contribution to the passive mechanical behaviour of the MVC was drastically reduced for Gynemesh PS (P = 0.003), but not for SmartMesh (P = 0.9) or UltraPro independent of the direction of implantation (P = 0.68 and P = 0.66, respectively). Deterioration of the mechanical properties of the vagina was highest following implantation with the stiffest mesh, Gynemesh PS. Such a decrease associated with implantation of a device of increased stiffness is consistent with findings from other systems employing prostheses for support. © 2013 The Authors BJOG An International Journal of Obstetrics and Gynaecology © 2013 RCOG.

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.

Syringe-injectable mesh electronics integrate seamlessly with minimal chronic immune response in the brain

PubMed Central

Zhou, Tao; Hong, Guosong; Fu, Tian-Ming; Yang, Xiao; Schuhmann, Thomas G.; Viveros, Robert D.; Lieber, Charles M.

2017-01-01

Implantation of electrical probes into the brain has been central to both neuroscience research and biomedical applications, although conventional probes induce gliosis in surrounding tissue. We recently reported ultraflexible open mesh electronics implanted into rodent brains by syringe injection that exhibit promising chronic tissue response and recording stability. Here we report time-dependent histology studies of the mesh electronics/brain-tissue interface obtained from sections perpendicular and parallel to probe long axis, as well as studies of conventional flexible thin-film probes. Confocal fluorescence microscopy images of the perpendicular and parallel brain slices containing mesh electronics showed that the distribution of astrocytes, microglia, and neurons became uniform from 2–12 wk, whereas flexible thin-film probes yield a marked accumulation of astrocytes and microglia and decrease of neurons for the same period. Quantitative analyses of 4- and 12-wk data showed that the signals for neurons, axons, astrocytes, and microglia are nearly the same from the mesh electronics surface to the baseline far from the probes, in contrast to flexible polymer probes, which show decreases in neuron and increases in astrocyte and microglia signals. Notably, images of sagittal brain slices containing nearly the entire mesh electronics probe showed that the tissue interface was uniform and neurons and neurofilaments penetrated through the mesh by 3 mo postimplantation. The minimal immune response and seamless interface with brain tissue postimplantation achieved by ultraflexible open mesh electronics probes provide substantial advantages and could enable a wide range of opportunities for in vivo chronic recording and modulation of brain activity in the future. PMID:28533392

Syringe-injectable mesh electronics integrate seamlessly with minimal chronic immune response in the brain.

PubMed

Zhou, Tao; Hong, Guosong; Fu, Tian-Ming; Yang, Xiao; Schuhmann, Thomas G; Viveros, Robert D; Lieber, Charles M

2017-06-06

Implantation of electrical probes into the brain has been central to both neuroscience research and biomedical applications, although conventional probes induce gliosis in surrounding tissue. We recently reported ultraflexible open mesh electronics implanted into rodent brains by syringe injection that exhibit promising chronic tissue response and recording stability. Here we report time-dependent histology studies of the mesh electronics/brain-tissue interface obtained from sections perpendicular and parallel to probe long axis, as well as studies of conventional flexible thin-film probes. Confocal fluorescence microscopy images of the perpendicular and parallel brain slices containing mesh electronics showed that the distribution of astrocytes, microglia, and neurons became uniform from 2-12 wk, whereas flexible thin-film probes yield a marked accumulation of astrocytes and microglia and decrease of neurons for the same period. Quantitative analyses of 4- and 12-wk data showed that the signals for neurons, axons, astrocytes, and microglia are nearly the same from the mesh electronics surface to the baseline far from the probes, in contrast to flexible polymer probes, which show decreases in neuron and increases in astrocyte and microglia signals. Notably, images of sagittal brain slices containing nearly the entire mesh electronics probe showed that the tissue interface was uniform and neurons and neurofilaments penetrated through the mesh by 3 mo postimplantation. The minimal immune response and seamless interface with brain tissue postimplantation achieved by ultraflexible open mesh electronics probes provide substantial advantages and could enable a wide range of opportunities for in vivo chronic recording and modulation of brain activity in the future.

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

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

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 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

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.

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.

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.

The P-Mesh: A Commodity-based Scalable Network Architecture for Clusters

NASA Technical Reports Server (NTRS)

Nitzberg, Bill; Kuszmaul, Chris; Stockdale, Ian; Becker, Jeff; Jiang, John; Wong, Parkson; Tweten, David (Technical Monitor)

1998-01-01

We designed a new network architecture, the P-Mesh which combines the scalability and fault resilience of a torus with the performance of a switch. We compare the scalability, performance, and cost of the hub, switch, torus, tree, and P-Mesh architectures. The latter three are capable of scaling to thousands of nodes, however, the torus has severe performance limitations with that many processors. The tree and P-Mesh have similar latency, bandwidth, and bisection bandwidth, but the P-Mesh outperforms the switch architecture (a lower bound for tree performance) on 16-node NAB Parallel Benchmark tests by up to 23%, and costs 40% less. Further, the P-Mesh has better fault resilience characteristics. The P-Mesh architecture trades increased management overhead for lower cost, and is a good bridging technology while the price of tree uplinks is expensive.

ColDICE: A parallel Vlasov–Poisson solver using moving adaptive simplicial tessellation

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

Sousbie, Thierry, E-mail: tsousbie@gmail.com; Department of Physics, The University of Tokyo, Tokyo 113-0033; Research Center for the Early Universe, School of Science, The University of Tokyo, Tokyo 113-0033

2016-09-15

Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the bestmore » way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65–67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.« less

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.

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.

Mesh quality control for multiply-refined tetrahedral grids

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Strawn, Roger

1994-01-01

A new algorithm for controlling the quality of multiply-refined tetrahedral meshes is presented in this paper. The basic dynamic mesh adaption procedure allows localized grid refinement and coarsening to efficiently capture aerodynamic flow features in computational fluid dynamics problems; however, repeated application of the procedure may significantly deteriorate the quality of the mesh. Results presented show the effectiveness of this mesh quality algorithm and its potential in the area of helicopter aerodynamics and acoustics.

An Implicit Solver on A Parallel Block-Structured Adaptive Mesh Grid for FLASH

NASA Astrophysics Data System (ADS)

Lee, D.; Gopal, S.; Mohapatra, P.

2012-07-01

We introduce a fully implicit solver for FLASH based on a Jacobian-Free Newton-Krylov (JFNK) approach with an appropriate preconditioner. The main goal of developing this JFNK-type implicit solver is to provide efficient high-order numerical algorithms and methodology for simulating stiff systems of differential equations on large-scale parallel computer architectures. A large number of natural problems in nonlinear physics involve a wide range of spatial and time scales of interest. A system that encompasses such a wide magnitude of scales is described as "stiff." A stiff system can arise in many different fields of physics, including fluid dynamics/aerodynamics, laboratory/space plasma physics, low Mach number flows, reactive flows, radiation hydrodynamics, and geophysical flows. One of the big challenges in solving such a stiff system using current-day computational resources lies in resolving time and length scales varying by several orders of magnitude. We introduce FLASH's preliminary implementation of a time-accurate JFNK-based implicit solver in the framework of FLASH's unsplit hydro solver.

LBMD : a layer-based mesh data structure tailored for generic API infrastructures.

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

Ebeida, Mohamed S.; Knupp, Patrick Michael

2010-11-01

A new mesh data structure is introduced for the purpose of mesh processing in Application Programming Interface (API) infrastructures. This data structure utilizes a reduced mesh representation to increase its ability to handle significantly larger meshes compared to full mesh representation. In spite of the reduced representation, each mesh entity (vertex, edge, face, and region) is represented using a unique handle, with no extra storage cost, which is a crucial requirement in most API libraries. The concept of mesh layers makes the data structure more flexible for mesh generation and mesh modification operations. This flexibility can have a favorable impactmore » in solver based queries of finite volume and multigrid methods. The capabilities of LBMD make it even more attractive for parallel implementations using Message Passing Interface (MPI) or Graphics Processing Units (GPUs). The data structure is associated with a new classification method to relate mesh entities to their corresponding geometrical entities. The classification technique stores the related information at the node level without introducing any ambiguities. Several examples are presented to illustrate the strength of this new data structure.« less

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.

Shear Alignment of Diblock Copolymers for Patterning Nanowire Meshes

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

Gustafson, Kyle T.

2016-09-08

Metallic nanowire meshes are useful as cheap, flexible alternatives to indium tin oxide – an expensive, brittle material used in transparent conductive electrodes. We have fabricated nanowire meshes over areas up to 2.5 cm 2 by: 1) mechanically aligning parallel rows of diblock copolymer (diBCP) microdomains; 2) selectively infiltrating those domains with metallic ions; 3) etching away the diBCP template; 4) sintering to reduce ions to metal nanowires; and, 5) repeating steps 1 – 4 on the same sample at a 90° offset. We aligned parallel rows of polystyrene-b-poly(2-vinylpyridine) [PS(48.5 kDa)-b-P2VP(14.5 kDa)] microdomains by heating above its glass transition temperaturemore » (T g ≈ 100°C), applying mechanical shear pressure (33 kPa) and normal force (13.7 N), and cooling below T g. DiBCP samples were submerged in aqueous solutions of metallic ions (15 – 40 mM ions; 0.1 – 0.5 M HCl) for 30 – 90 minutes, which coordinate to nitrogen in P2VP. Subsequent ozone-etching and sintering steps yielded parallel nanowires. We aimed to optimize alignment parameters (e.g. shear and normal pressures, alignment duration, and PDMS thickness) to improve the quality, reproducibility, and scalability of meshes. We also investigated metals other than Pt and Au that may be patterned using this technique (Cu, Ag).« less

An Element-Based Concurrent Partitioner for Unstructured Finite Element Meshes

NASA Technical Reports Server (NTRS)

Ding, Hong Q.; Ferraro, Robert D.

1996-01-01

A concurrent partitioner for partitioning unstructured finite element meshes on distributed memory architectures is developed. The partitioner uses an element-based partitioning strategy. Its main advantage over the more conventional node-based partitioning strategy is its modular programming approach to the development of parallel applications. The partitioner first partitions element centroids using a recursive inertial bisection algorithm. Elements and nodes then migrate according to the partitioned centroids, using a data request communication template for unpredictable incoming messages. Our scalable implementation is contrasted to a non-scalable implementation which is a straightforward parallelization of a sequential partitioner.

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

Adaption of unstructured meshes using node movement

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

Carpenter, J.G.; McRae, V.D.S.

1996-12-31

The adaption algorithm of Benson and McRae is modified for application to unstructured grids. The weight function generation was modified for application to unstructured grids and movement was limited to prevent cross over. A NACA 0012 airfoil is used as a test case to evaluate the modified algorithm when applied to unstructured grids and compared to results obtained by Warren. An adaptive mesh solution for the Sudhoo and Hall four element airfoil is included as a demonstration case.

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.

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.

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.

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.

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.

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.

Link failure detection in a parallel computer

DOEpatents

Archer, Charles J.; Blocksome, Michael A.; Megerian, Mark G.; Smith, Brian E.

2010-11-09

Methods, apparatus, and products are disclosed for link failure detection in a parallel computer including compute nodes connected in a rectangular mesh network, each pair of adjacent compute nodes in the rectangular mesh network connected together using a pair of links, that includes: assigning each compute node to either a first group or a second group such that adjacent compute nodes in the rectangular mesh network are assigned to different groups; sending, by each of the compute nodes assigned to the first group, a first test message to each adjacent compute node assigned to the second group; determining, by each of the compute nodes assigned to the second group, whether the first test message was received from each adjacent compute node assigned to the first group; and notifying a user, by each of the compute nodes assigned to the second group, whether the first test message was received.

High-performance parallel analysis of coupled problems for aircraft propulsion

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Lanteri, S.; Maman, N.; Piperno, S.; Gumaste, U.

1994-01-01

This research program deals with the application of high-performance computing methods for the analysis of complete jet engines. We have entitled this program by applying the two dimensional parallel aeroelastic codes to the interior gas flow problem of a bypass jet engine. The fluid mesh generation, domain decomposition, and solution capabilities were successfully tested. We then focused attention on methodology for the partitioned analysis of the interaction of the gas flow with a flexible structure and with the fluid mesh motion that results from these structural displacements. This is treated by a new arbitrary Lagrangian-Eulerian (ALE) technique that models the fluid mesh motion as that of a fictitious mass-spring network. New partitioned analysis procedures to treat this coupled three-component problem are developed. These procedures involved delayed corrections and subcycling. Preliminary results on the stability, accuracy, and MPP computational efficiency are reported.

High performance Python for direct numerical simulations of turbulent flows

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Langtangen, Hans Petter

2016-06-01

Direct Numerical Simulations (DNS) of the Navier Stokes equations is an invaluable research tool in fluid dynamics. Still, there are few publicly available research codes and, due to the heavy number crunching implied, available codes are usually written in low-level languages such as C/C++ or Fortran. In this paper we describe a pure scientific Python pseudo-spectral DNS code that nearly matches the performance of C++ for thousands of processors and billions of unknowns. We also describe a version optimized through Cython, that is found to match the speed of C++. The solvers are written from scratch in Python, both the mesh, the MPI domain decomposition, and the temporal integrators. The solvers have been verified and benchmarked on the Shaheen supercomputer at the KAUST supercomputing laboratory, and we are able to show very good scaling up to several thousand cores. A very important part of the implementation is the mesh decomposition (we implement both slab and pencil decompositions) and 3D parallel Fast Fourier Transforms (FFT). The mesh decomposition and FFT routines have been implemented in Python using serial FFT routines (either NumPy, pyFFTW or any other serial FFT module), NumPy array manipulations and with MPI communications handled by MPI for Python (mpi4py). We show how we are able to execute a 3D parallel FFT in Python for a slab mesh decomposition using 4 lines of compact Python code, for which the parallel performance on Shaheen is found to be slightly better than similar routines provided through the FFTW library. For a pencil mesh decomposition 7 lines of code is required to execute a transform.

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.

Trinity Phase 2 Open Science: CTH

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

Ruggirello, Kevin Patrick; Vogler, Tracy

CTH is an Eulerian hydrocode developed by Sandia National Laboratories (SNL) to solve a wide range of shock wave propagation and material deformation problems. Adaptive mesh refinement is also used to improve efficiency for problems with a wide range of spatial scales. The code has a history of running on a variety of computing platforms ranging from desktops to massively parallel distributed-data systems. For the Trinity Phase 2 Open Science campaign, CTH was used to study mesoscale simulations of the hypervelocity penetration of granular SiC powders. The simulations were compared to experimental data. A scaling study of CTH up tomore » 8192 KNL nodes was also performed, and several improvements were made to the code to improve the scalability.« less

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.

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.

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.

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.

Development of the Fully Adaptive Storm Tide (FAST) Model for hurricane induced storm surges and associated inundation

NASA Astrophysics Data System (ADS)

Teng, Y. C.; Kelly, D.; Li, Y.; Zhang, K.

2016-02-01

A new state-of-the-art model (the Fully Adaptive Storm Tide model, FAST) for the prediction of storm surges over complex landscapes is presented. The FAST model is based on the conservation form of the full non-linear depth-averaged long wave equations. The equations are solved via an explicit finite volume scheme with interfacial fluxes being computed via Osher's approximate Riemann solver. Geometric source terms are treated in a high order manner that is well-balanced. The numerical solution technique has been chosen to enable the accurate simulation of wetting and drying over complex topography. Another important feature of the FAST model is the use of a simple underlying Cartesian mesh with tree-based static and dynamic adaptive mesh refinement (AMR). This permits the simulation of unsteady flows over varying landscapes (including localized features such as canals) by locally increasing (or relaxing) grid resolution in a dynamic fashion. The use of (dynamic) AMR lowers the computational cost of the storm surge model whilst retaining high resolution (and thus accuracy) where and when it is required. In additional, the FAST model has been designed to execute in a parallel computational environment with localized time-stepping. The FAST model has already been carefully verified against a series of benchmark type problems (Kelly et al. 2015). Here we present two simulations of the storm tide due to Hurricane Ike(2008) and Hurricane Sandy (2012). The model incorporates high resolution LIDAR data for the major portion of the New York City. Results compare favorably with water elevations measured by NOAA tidal gauges, by mobile sensors deployed and high water marks collected by the USGS.

Compressible magma/mantle dynamics: 3-D, adaptive simulations in ASPECT

NASA Astrophysics Data System (ADS)

Dannberg, Juliane; Heister, Timo

2016-12-01

Melt generation and migration are an important link between surface processes and the thermal and chemical evolution of the Earth's interior. However, their vastly different timescales make it difficult to study mantle convection and melt migration in a unified framework, especially for 3-D global models. And although experiments suggest an increase in melt volume of up to 20 per cent from the depth of melt generation to the surface, previous computations have neglected the individual compressibilities of the solid and the fluid phase. Here, we describe our extension of the finite element mantle convection code ASPECT that adds melt generation and migration. We use the original compressible formulation of the McKenzie equations, augmented by an equation for the conservation of energy. Applying adaptive mesh refinement to this type of problems is particularly advantageous, as the resolution can be increased in areas where melt is present and viscosity gradients are high, whereas a lower resolution is sufficient in regions without melt. Together with a high-performance, massively parallel implementation, this allows for high-resolution, 3-D, compressible, global mantle convection simulations coupled with melt migration. We evaluate the functionality and potential of this method using a series of benchmarks and model setups, compare results of the compressible and incompressible formulation, and show the effectiveness of adaptive mesh refinement when applied to melt migration. Our model of magma dynamics provides a framework for modelling processes on different scales and investigating links between processes occurring in the deep mantle and melt generation and migration. This approach could prove particularly useful applied to modelling the generation of komatiites or other melts originating in greater depths. The implementation is available in the Open Source ASPECT repository.

CUBE: Information-optimized parallel cosmological N-body simulation code

NASA Astrophysics Data System (ADS)

Yu, Hao-Ran; Pen, Ue-Li; Wang, Xin

2018-05-01

CUBE, written in Coarray Fortran, is a particle-mesh based parallel cosmological N-body simulation code. The memory usage of CUBE can approach as low as 6 bytes per particle. Particle pairwise (PP) force, cosmological neutrinos, spherical overdensity (SO) halofinder are included.

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.

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

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 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.

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.

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

Heat exchange apparatus

DOEpatents

Degtiarenko, Pavel V.

2003-08-12

A heat exchange apparatus comprising a coolant conduit or heat sink having attached to its surface a first radial array of spaced-apart parallel plate fins or needles and a second radial array of spaced-apart parallel plate fins or needles thermally coupled to a body to be cooled and meshed with, but not contacting the first radial array of spaced-apart parallel plate fins or needles.

P-HARP: A parallel dynamic spectral partitioner

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

Sohn, A.; Biswas, R.; Simon, H.D.

1997-05-01

Partitioning unstructured graphs is central to the parallel solution of problems in computational science and engineering. The authors have introduced earlier the sequential version of an inertial spectral partitioner called HARP which maintains the quality of recursive spectral bisection (RSB) while forming the partitions an order of magnitude faster than RSB. The serial HARP is known to be the fastest spectral partitioner to date, three to four times faster than similar partitioners on a variety of meshes. This paper presents a parallel version of HARP, called P-HARP. Two types of parallelism have been exploited: loop level parallelism and recursive parallelism.more » P-HARP has been implemented in MPI on the SGI/Cray T3E and the IBM SP2. Experimental results demonstrate that P-HARP can partition a mesh of over 100,000 vertices into 256 partitions in 0.25 seconds on a 64-processor T3E. Experimental results further show that P-HARP can give nearly a 20-fold speedup on 64 processors. These results indicate that graph partitioning is no longer a major bottleneck that hinders the advancement of computational science and engineering for dynamically-changing real-world applications.« less

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

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.

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.

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

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.

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.

Automatic mesh adaptivity for hybrid Monte Carlo/deterministic neutronics modeling of difficult shielding problems

DOE PAGES

Ibrahim, Ahmad M.; Wilson, Paul P.H.; Sawan, Mohamed E.; ...

2015-06-30

The CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques dramatically increase the efficiency of neutronics modeling, but their use in the accurate design analysis of very large and geometrically complex nuclear systems has been limited by the large number of processors and memory requirements for their preliminary deterministic calculations and final Monte Carlo calculation. Three mesh adaptivity algorithms were developed to reduce the memory requirements of CADIS and FW-CADIS without sacrificing their efficiency improvement. First, a macromaterial approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as muchmore » geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm decouples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation and, additionally, increased the efficiency of the Monte Carlo simulation by a factor of at least 3.4. The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a regular computer cluster, eliminating the need for a world-class super computer.« less

Silicon-fiber blanket solar-cell array concept

NASA Technical Reports Server (NTRS)

Eliason, J. T.

1973-01-01

Proposed economical manufacture of solar-cell arrays involves parallel, planar weaving of filaments made of doped silicon fibers with diffused radial junction. Each filament is a solar cell connected either in series or parallel with others to form a blanket of deposited grids or attached electrode wire mesh screens.

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

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

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-06-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner formore » scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.« less

Automatic mesh refinement and parallel load balancing for Fokker-Planck-DSMC algorithm

NASA Astrophysics Data System (ADS)

Küchlin, Stephan; Jenny, Patrick

2018-06-01

Recently, a parallel Fokker-Planck-DSMC algorithm for rarefied gas flow simulation in complex domains at all Knudsen numbers was developed by the authors. Fokker-Planck-DSMC (FP-DSMC) is an augmentation of the classical DSMC algorithm, which mitigates the near-continuum deficiencies in terms of computational cost of pure DSMC. At each time step, based on a local Knudsen number criterion, the discrete DSMC collision operator is dynamically switched to the Fokker-Planck operator, which is based on the integration of continuous stochastic processes in time, and has fixed computational cost per particle, rather than per collision. In this contribution, we present an extension of the previous implementation with automatic local mesh refinement and parallel load-balancing. In particular, we show how the properties of discrete approximations to space-filling curves enable an efficient implementation. Exemplary numerical studies highlight the capabilities of the new code.

Accurate reaction-diffusion operator splitting on tetrahedral meshes for parallel stochastic molecular simulations

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

Hepburn, I.; De Schutter, E., E-mail: erik@oist.jp; Theoretical Neurobiology & Neuroengineering, University of Antwerp, Antwerp 2610

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, which has led to the development of parallel methods that can take advantage of the power of modern supercomputers in recent years. We systematically test suggested components of stochastic reaction-diffusion operator splitting in the literature and discuss their effects on accuracy. We introduce an operator splitting implementation for irregular meshes that enhances accuracy with minimal performance cost. We test a range of models in small-scale MPI simulations from simple diffusion models to realisticmore » biological models and find that multi-dimensional geometry partitioning is an important consideration for optimum performance. We demonstrate performance gains of 1-3 orders of magnitude in the parallel implementation, with peak performance strongly dependent on model specification.« less

MARE2DEM: a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data

NASA Astrophysics Data System (ADS)

Key, Kerry

2016-10-01

This work presents MARE2DEM, a freely available code for 2-D anisotropic inversion of magnetotelluric (MT) data and frequency-domain controlled-source electromagnetic (CSEM) data from onshore and offshore surveys. MARE2DEM parametrizes the inverse model using a grid of arbitrarily shaped polygons, where unstructured triangular or quadrilateral grids are typically used due to their ease of construction. Unstructured grids provide significantly more geometric flexibility and parameter efficiency than the structured rectangular grids commonly used by most other inversion codes. Transmitter and receiver components located on topographic slopes can be tilted parallel to the boundary so that the simulated electromagnetic fields accurately reproduce the real survey geometry. The forward solution is implemented with a goal-oriented adaptive finite-element method that automatically generates and refines unstructured triangular element grids that conform to the inversion parameter grid, ensuring accurate responses as the model conductivity changes. This dual-grid approach is significantly more efficient than the conventional use of a single grid for both the forward and inverse meshes since the more detailed finite-element meshes required for accurate responses do not increase the memory requirements of the inverse problem. Forward solutions are computed in parallel with a highly efficient scaling by partitioning the data into smaller independent modeling tasks consisting of subsets of the input frequencies, transmitters and receivers. Non-linear inversion is carried out with a new Occam inversion approach that requires fewer forward calls. Dense matrix operations are optimized for memory and parallel scalability using the ScaLAPACK parallel library. Free parameters can be bounded using a new non-linear transformation that leaves the transformed parameters nearly the same as the original parameters within the bounds, thereby reducing non-linear smoothing effects. Data balancing normalization weights for the joint inversion of two or more data sets encourages the inversion to fit each data type equally well. A synthetic joint inversion of marine CSEM and MT data illustrates the algorithm's performance and parallel scaling on up to 480 processing cores. CSEM inversion of data from the Middle America Trench offshore Nicaragua demonstrates a real world application. The source code and MATLAB interface tools are freely available at http://mare2dem.ucsd.edu.

High-performance parallel analysis of coupled problems for aircraft propulsion

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Chen, P.-S.; Gumaste, U.; Leoinne, M.; Stern, P.

1995-01-01

This research program deals with the application of high-performance computing methods to the numerical simulation of complete jet engines. The program was initiated in 1993 by applying two-dimensional parallel aeroelastic codes to the interior gas flow problem of a by-pass jet engine. The fluid mesh generation, domain decomposition and solution capabilities were successfully tested. Attention was then focused on methodology for the partitioned analysis of the interaction of the gas flow with a flexible structure and with the fluid mesh motion driven by these structural displacements. The latter is treated by an ALE technique that models the fluid mesh motion as that of a fictitious mechanical network laid along the edges of near-field fluid elements. New partitioned analysis procedures to treat this coupled 3-component problem were developed in 1994. These procedures involved delayed corrections and subcycling, and have been successfully tested on several massively parallel computers. For the global steady-state axisymmetric analysis of a complete engine we have decided to use the NASA-sponsored ENG10 program, which uses a regular FV-multiblock-grid discretization in conjunction with circumferential averaging to include effects of blade forces, loss, combustor heat addition, blockage, bleeds and convective mixing. A load-balancing preprocessor for parallel versions of ENG10 has been developed. It is planned to use the steady-state global solution provided by ENG10 as input to a localized three-dimensional FSI analysis for engine regions where aeroelastic effects may be important.

Parallel Adjective High-Order CFD Simulations Characterizing SOFIA Cavity Acoustics

NASA Technical Reports Server (NTRS)

Barad, Michael F.; Brehm, Christoph; Kiris, Cetin C.; Biswas, Rupak

2016-01-01

This paper presents large-scale MPI-parallel computational uid dynamics simulations for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is an airborne, 2.5-meter infrared telescope mounted in an open cavity in the aft fuselage of a Boeing 747SP. These simulations focus on how the unsteady ow eld inside and over the cavity interferes with the optical path and mounting structure of the telescope. A temporally fourth-order accurate Runge-Kutta, and spatially fth-order accurate WENO- 5Z scheme was used to perform implicit large eddy simulations. An immersed boundary method provides automated gridding for complex geometries and natural coupling to a block-structured Cartesian adaptive mesh re nement framework. Strong scaling studies using NASA's Pleiades supercomputer with up to 32k CPU cores and 4 billion compu- tational cells shows excellent scaling. Dynamic load balancing based on execution time on individual AMR blocks addresses irregular numerical cost associated with blocks con- taining boundaries. Limits to scaling beyond 32k cores are identi ed, and targeted code optimizations are discussed.

Three dimensional modelling of earthquake rupture cycles on frictional faults

NASA Astrophysics Data System (ADS)

Simpson, Guy; May, Dave

2017-04-01

We are developing an efficient MPI-parallel numerical method to simulate earthquake sequences on preexisting faults embedding within a three dimensional viscoelastic half-space. We solve the velocity form of the elasto(visco)dynamic equations using a continuous Galerkin Finite Element Method on an unstructured pentahedral mesh, which thus permits local spatial refinement in the vicinity of the fault. Friction sliding is coupled to the viscoelastic solid via rate- and state-dependent friction laws using the split-node technique. Our coupled formulation employs a picard-type non-linear solver with a fully implicit, first order accurate time integrator that utilises an adaptive time step that efficiently evolves the system through multiple seismic cycles. The implementation leverages advanced parallel solvers, preconditioners and linear algebra from the Portable Extensible Toolkit for Scientific Computing (PETSc) library. The model can treat heterogeneous frictional properties and stress states on the fault and surrounding solid as well as non-planar fault geometries. Preliminary tests show that the model successfully reproduces dynamic rupture on a vertical strike-slip fault in a half-space governed by rate-state friction with the ageing law.

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.

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.

The AIS-5000 parallel processor

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

Schmitt, L.A.; Wilson, S.S.

1988-05-01

The AIS-5000 is a commercially available massively parallel processor which has been designed to operate in an industrial environment. It has fine-grained parallelism with up to 1024 processing elements arranged in a single-instruction multiple-data (SIMD) architecture. The processing elements are arranged in a one-dimensional chain that, for computer vision applications, can be as wide as the image itself. This architecture has superior cost/performance characteristics than two-dimensional mesh-connected systems. The design of the processing elements and their interconnections as well as the software used to program the system allow a wide variety of algorithms and applications to be implemented. In thismore » paper, the overall architecture of the system is described. Various components of the system are discussed, including details of the processing elements, data I/O pathways and parallel memory organization. A virtual two-dimensional model for programming image-based algorithms for the system is presented. This model is supported by the AIS-5000 hardware and software and allows the system to be treated as a full-image-size, two-dimensional, mesh-connected parallel processor. Performance bench marks are given for certain simple and complex functions.« less

Scaling Optimization of the SIESTA MHD Code

NASA Astrophysics Data System (ADS)

Seal, Sudip; Hirshman, Steven; Perumalla, Kalyan

2013-10-01

SIESTA is a parallel three-dimensional plasma equilibrium code capable of resolving magnetic islands at high spatial resolutions for toroidal plasmas. Originally designed to exploit small-scale parallelism, SIESTA has now been scaled to execute efficiently over several thousands of processors P. This scaling improvement was accomplished with minimal intrusion to the execution flow of the original version. First, the efficiency of the iterative solutions was improved by integrating the parallel tridiagonal block solver code BCYCLIC. Krylov-space generation in GMRES was then accelerated using a customized parallel matrix-vector multiplication algorithm. Novel parallel Hessian generation algorithms were integrated and memory access latencies were dramatically reduced through loop nest optimizations and data layout rearrangement. These optimizations sped up equilibria calculations by factors of 30-50. It is possible to compute solutions with granularity N/P near unity on extremely fine radial meshes (N > 1024 points). Grid separation in SIESTA, which manifests itself primarily in the resonant components of the pressure far from rational surfaces, is strongly suppressed by finer meshes. Large problem sizes of up to 300 K simultaneous non-linear coupled equations have been solved on the NERSC supercomputers. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

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.

Implementation of a parallel unstructured Euler solver on the CM-5

NASA Technical Reports Server (NTRS)

Morano, Eric; Mavriplis, D. J.

1995-01-01

An efficient unstructured 3D Euler solver is parallelized on a Thinking Machine Corporation Connection Machine 5, distributed memory computer with vectoring capability. In this paper, the single instruction multiple data (SIMD) strategy is employed through the use of the CM Fortran language and the CMSSL scientific library. The performance of the CMSSL mesh partitioner is evaluated and the overall efficiency of the parallel flow solver is discussed.

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

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

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers

PubMed Central

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation. PMID:28239346

Parallel STEPS: Large Scale Stochastic Spatial Reaction-Diffusion Simulation with High Performance Computers.

PubMed

Chen, Weiliang; De Schutter, Erik

2017-01-01

Stochastic, spatial reaction-diffusion simulations have been widely used in systems biology and computational neuroscience. However, the increasing scale and complexity of models and morphologies have exceeded the capacity of any serial implementation. This led to the development of parallel solutions that benefit from the boost in performance of modern supercomputers. In this paper, we describe an MPI-based, parallel operator-splitting implementation for stochastic spatial reaction-diffusion simulations with irregular tetrahedral meshes. The performance of our implementation is first examined and analyzed with simulations of a simple model. We then demonstrate its application to real-world research by simulating the reaction-diffusion components of a published calcium burst model in both Purkinje neuron sub-branch and full dendrite morphologies. Simulation results indicate that our implementation is capable of achieving super-linear speedup for balanced loading simulations with reasonable molecule density and mesh quality. In the best scenario, a parallel simulation with 2,000 processes runs more than 3,600 times faster than its serial SSA counterpart, and achieves more than 20-fold speedup relative to parallel simulation with 100 processes. In a more realistic scenario with dynamic calcium influx and data recording, the parallel simulation with 1,000 processes and no load balancing is still 500 times faster than the conventional serial SSA simulation.

Mesh Intercomparisons of Fog Water Collected Yield Insight Into the Nature of Fog-Drip Collection Mechanisms

NASA Astrophysics Data System (ADS)

Fernandez, D.; Torregrosa, A.; Weiss-Penzias, P. S.; Oliphant, A. J.; Dodge, C.; Bowman, M.; Wilson, S.; Mairs, A. A.; Gravelle, M.; Barkley, T.

2016-12-01

At multiple sites across central CA, several passive fog water collectors have been deployed for the past 3 years. All of the sites employ standard Raschel polypropylene mesh as the fog collection medium and five of them also integrated a novel polypropylene mesh of German manufacture with a 3-dimensional internal structure. Additionally, six metal mesh manufactured by McMaster-Carr of various hole sizing were coated with a POSS-PEMA substance at the Massachusetts Institute of Technology and deployed in parallel with the Raschel mesh at six distinct locations. Finally, fluorine-free versions of the POSS-PEMA substance were generated by NBD Nanotechnology and coated on a much finer mesh substrate. Three of those and one control (uncoated mesh) were deployed at one of the fog collection sites for one season, along with a standard Raschel mesh. Preliminary results from one intercomparison from just one pair of mesh over two seasons seem to reveal a wind speed and also, possibly, a droplet-size dependence on the fog collection efficiency for the mesh. This study will continue to intercompare the various mesh in conjunction with the wind speed and direction data. If a collection efficiency dependence on mesh size or coating is confirmed, it may point to interesting and relevant mechanisms for fog droplet capture and collection hitherto unobserved in field conditions.

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

Evaluating the performance of the particle finite element method in parallel architectures

NASA Astrophysics Data System (ADS)

Gimenez, Juan M.; Nigro, Norberto M.; Idelsohn, Sergio R.

2014-05-01

This paper presents a high performance implementation for the particle-mesh based method called particle finite element method two (PFEM-2). It consists of a material derivative based formulation of the equations with a hybrid spatial discretization which uses an Eulerian mesh and Lagrangian particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical Eulerian alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for Finite Element Method have been widely studied and many libraries can be used to solve Eulerian stages of PFEM-2. However, Lagrangian stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant-Friedrichs-Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical Eulerian strategies.

High-Performance Parallel Analysis of Coupled Problems for Aircraft Propulsion

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Gumaste, U.; Chen, P.-S.; Lesoinne, M.; Stern, P.

1996-01-01

This research program dealt with the application of high-performance computing methods to the numerical simulation of complete jet engines. The program was initiated in January 1993 by applying two-dimensional parallel aeroelastic codes to the interior gas flow problem of a bypass jet engine. The fluid mesh generation, domain decomposition and solution capabilities were successfully tested. Attention was then focused on methodology for the partitioned analysis of the interaction of the gas flow with a flexible structure and with the fluid mesh motion driven by these structural displacements. The latter is treated by a ALE technique that models the fluid mesh motion as that of a fictitious mechanical network laid along the edges of near-field fluid elements. New partitioned analysis procedures to treat this coupled three-component problem were developed during 1994 and 1995. These procedures involved delayed corrections and subcycling, and have been successfully tested on several massively parallel computers, including the iPSC-860, Paragon XP/S and the IBM SP2. For the global steady-state axisymmetric analysis of a complete engine we have decided to use the NASA-sponsored ENG10 program, which uses a regular FV-multiblock-grid discretization in conjunction with circumferential averaging to include effects of blade forces, loss, combustor heat addition, blockage, bleeds and convective mixing. A load-balancing preprocessor tor parallel versions of ENG10 was developed. During 1995 and 1996 we developed the capability tor the first full 3D aeroelastic simulation of a multirow engine stage. This capability was tested on the IBM SP2 parallel supercomputer at NASA Ames. Benchmark results were presented at the 1196 Computational Aeroscience meeting.

Analysis of ground-motion simulation big data

NASA Astrophysics Data System (ADS)

Maeda, T.; Fujiwara, H.

2016-12-01

We developed a parallel distributed processing system which applies a big data analysis to the large-scale ground motion simulation data. The system uses ground-motion index values and earthquake scenario parameters as input. We used peak ground velocity value and velocity response spectra as the ground-motion index. The ground-motion index values are calculated from our simulation data. We used simulated long-period ground motion waveforms at about 80,000 meshes calculated by a three dimensional finite difference method based on 369 earthquake scenarios of a great earthquake in the Nankai Trough. These scenarios were constructed by considering the uncertainty of source model parameters such as source area, rupture starting point, asperity location, rupture velocity, fmax and slip function. We used these parameters as the earthquake scenario parameter. The system firstly carries out the clustering of the earthquake scenario in each mesh by the k-means method. The number of clusters is determined in advance using a hierarchical clustering by the Ward's method. The scenario clustering results are converted to the 1-D feature vector. The dimension of the feature vector is the number of scenario combination. If two scenarios belong to the same cluster the component of the feature vector is 1, and otherwise the component is 0. The feature vector shows a `response' of mesh to the assumed earthquake scenario group. Next, the system performs the clustering of the mesh by k-means method using the feature vector of each mesh previously obtained. Here the number of clusters is arbitrarily given. The clustering of scenarios and meshes are performed by parallel distributed processing with Hadoop and Spark, respectively. In this study, we divided the meshes into 20 clusters. The meshes in each cluster are geometrically concentrated. Thus this system can extract regions, in which the meshes have similar `response', as clusters. For each cluster, it is possible to determine particular scenario parameters which characterize the cluster. In other word, by utilizing this system, we can obtain critical scenario parameters of the ground-motion simulation for each evaluation point objectively. This research was supported by CREST, JST.

Parallel Simulation of Three-Dimensional Free-Surface Fluid Flow Problems

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

BAER,THOMAS A.; SUBIA,SAMUEL R.; SACKINGER,PHILIP A.

2000-01-18

We describe parallel simulations of viscous, incompressible, free surface, Newtonian fluid flow problems that include dynamic contact lines. The Galerlin finite element method was used to discretize the fully-coupled governing conservation equations and a ''pseudo-solid'' mesh mapping approach was used to determine the shape of the free surface. In this approach, the finite element mesh is allowed to deform to satisfy quasi-static solid mechanics equations subject to geometric or kinematic constraints on the boundaries. As a result, nodal displacements must be included in the set of problem unknowns. Issues concerning the proper constraints along the solid-fluid dynamic contact line inmore » three dimensions are discussed. Parallel computations are carried out for an example taken from the coating flow industry, flow in the vicinity of a slot coater edge. This is a three-dimensional free-surface problem possessing a contact line that advances at the web speed in one region but transitions to static behavior in another part of the flow domain. Discussion focuses on parallel speedups for fixed problem size, a class of problems of immediate practical importance.« less

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

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

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

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)

Particle-mesh techniques

NASA Technical Reports Server (NTRS)

Macneice, Peter

1995-01-01

This is an introduction to numerical Particle-Mesh techniques, which are commonly used to model plasmas, gravitational N-body systems, and both compressible and incompressible fluids. The theory behind this approach is presented, and its practical implementation, both for serial and parallel machines, is discussed. This document is based on a four-hour lecture course presented by the author at the NASA Summer School for High Performance Computational Physics, held at Goddard Space Flight Center.

PARALLEL HOP: A SCALABLE HALO FINDER FOR MASSIVE COSMOLOGICAL DATA SETS

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

Skory, Stephen; Turk, Matthew J.; Norman, Michael L.

2010-11-15

Modern N-body cosmological simulations contain billions (10{sup 9}) of dark matter particles. These simulations require hundreds to thousands of gigabytes of memory and employ hundreds to tens of thousands of processing cores on many compute nodes. In order to study the distribution of dark matter in a cosmological simulation, the dark matter halos must be identified using a halo finder, which establishes the halo membership of every particle in the simulation. The resources required for halo finding are similar to the requirements for the simulation itself. In particular, simulations have become too extensive to use commonly employed halo finders, suchmore » that the computational requirements to identify halos must now be spread across multiple nodes and cores. Here, we present a scalable-parallel halo finding method called Parallel HOP for large-scale cosmological simulation data. Based on the halo finder HOP, it utilizes message passing interface and domain decomposition to distribute the halo finding workload across multiple compute nodes, enabling analysis of much larger data sets than is possible with the strictly serial or previous parallel implementations of HOP. We provide a reference implementation of this method as a part of the toolkit {sup yt}, an analysis toolkit for adaptive mesh refinement data that include complementary analysis modules. Additionally, we discuss a suite of benchmarks that demonstrate that this method scales well up to several hundred tasks and data sets in excess of 2000{sup 3} particles. The Parallel HOP method and our implementation can be readily applied to any kind of N-body simulation data and is therefore widely applicable.« less

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 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.

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

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.

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.

ATHENA 3D: A finite element code for ultrasonic wave propagation

NASA Astrophysics Data System (ADS)

Rose, C.; Rupin, F.; Fouquet, T.; Chassignole, B.

2014-04-01

The understanding of wave propagation phenomena requires use of robust numerical models. 3D finite element (FE) models are generally prohibitively time consuming. However, advances in computing processor speed and memory allow them to be more and more competitive. In this context, EDF R&D developed the 3D version of the well-validated FE code ATHENA2D. The code is dedicated to the simulation of wave propagation in all kinds of elastic media and in particular, heterogeneous and anisotropic materials like welds. It is based on solving elastodynamic equations in the calculation zone expressed in terms of stress and particle velocities. The particularity of the code relies on the fact that the discretization of the calculation domain uses a Cartesian regular 3D mesh while the defect of complex geometry can be described using a separate (2D) mesh using the fictitious domains method. This allows combining the rapidity of regular meshes computation with the capability of modelling arbitrary shaped defects. Furthermore, the calculation domain is discretized with a quasi-explicit time evolution scheme. Thereby only local linear systems of small size have to be solved. The final step to reduce the computation time relies on the fact that ATHENA3D has been parallelized and adapted to the use of HPC resources. In this paper, the validation of the 3D FE model is discussed. A cross-validation of ATHENA 3D and CIVA is proposed for several inspection configurations. The performances in terms of calculation time are also presented in the cases of both local computer and computation cluster use.

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

Efficient parallelization for AMR MHD multiphysics calculations; implementation in AstroBEAR

NASA Astrophysics Data System (ADS)

Carroll-Nellenback, Jonathan J.; Shroyer, Brandon; Frank, Adam; Ding, Chen

2013-03-01

Current adaptive mesh refinement (AMR) simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient parallelization and memory management. We have attempted to employ new techniques to achieve both of these goals. Patch or grid based AMR often employs ghost cells to decouple the hyperbolic advances of each grid on a given refinement level. This decoupling allows each grid to be advanced independently. In AstroBEAR we utilize this independence by threading the grid advances on each level with preference going to the finer level grids. This allows for global load balancing instead of level by level load balancing and allows for greater parallelization across both physical space and AMR level. Threading of level advances can also improve performance by interleaving communication with computation, especially in deep simulations with many levels of refinement. While we see improvements of up to 30% on deep simulations run on a few cores, the speedup is typically more modest (5-20%) for larger scale simulations. To improve memory management we have employed a distributed tree algorithm that requires processors to only store and communicate local sections of the AMR tree structure with neighboring processors. Using this distributed approach we are able to get reasonable scaling efficiency (>80%) out to 12288 cores and up to 8 levels of AMR - independent of the use of threading.

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.

Validation of 3D RANS-SA Calculations on Strand/Cartesian Meshes

DTIC Science & Technology

2014-01-07

a parallel environment. This allows for significant gains in efficiency and scalability of domain connectiv- ity, effectively eliminating inter... equation of state , p = ρRT is used to close the equations . 4 of 22 American Institute of Aeronautics and Astronautics 6 III.A. Discretization and...Utah State University 1415 Old Main Hill - Room 64 Logan, UT 84322 -1415 1 ABSTRACT Validation of 3D RANS-SA Calculations on Strand/Cartesian Meshes

Development of 3D electromagnetic modeling tools for airborne vehicles

NASA Technical Reports Server (NTRS)

Volakis, John L.

1992-01-01

The main goal of this report is to advance the development of methodologies for scattering by airborne composite vehicles. Although the primary focus continues to be the development of a general purpose computer code for analyzing the entire structure as a single unit, a number of other tasks are also being pursued in parallel with this effort. One of these tasks discussed within is on new finite element formulations and mesh termination schemes. The goal here is to decrease computation time while retaining accuracy and geometric adaptability.The second task focuses on the application of wavelets to electromagnetics. Wavelet transformations are shown to be able to reduce a full matrix to a band matrix, thereby reducing the solutions memory requirements. Included within this document are two separate papers on finite element formulations and wavelets.

Comparison of DAC and MONACO DSMC Codes with Flat Plate Simulation

NASA Technical Reports Server (NTRS)

Padilla, Jose F.

2010-01-01

Various implementations of the direct simulation Monte Carlo (DSMC) method exist in academia, government and industry. By comparing implementations, deficiencies and merits of each can be discovered. This document reports comparisons between DSMC Analysis Code (DAC) and MONACO. DAC is NASA's standard DSMC production code and MONACO is a research DSMC code developed in academia. These codes have various differences; in particular, they employ distinct computational grid definitions. In this study, DAC and MONACO are compared by having each simulate a blunted flat plate wind tunnel test, using an identical volume mesh. Simulation expense and DSMC metrics are compared. In addition, flow results are compared with available laboratory data. Overall, this study revealed that both codes, excluding grid adaptation, performed similarly. For parallel processing, DAC was generally more efficient. As expected, code accuracy was mainly dependent on physical models employed.

Latency Hiding in Dynamic Partitioning and Load Balancing of Grid Computing Applications

NASA Technical Reports Server (NTRS)

Das, Sajal K.; Harvey, Daniel J.; Biswas, Rupak

2001-01-01

The Information Power Grid (IPG) concept developed by NASA is aimed to provide a metacomputing platform for large-scale distributed computations, by hiding the intricacies of highly heterogeneous environment and yet maintaining adequate security. In this paper, we propose a latency-tolerant partitioning scheme that dynamically balances processor workloads on the.IPG, and minimizes data movement and runtime communication. By simulating an unsteady adaptive mesh application on a wide area network, we study the performance of our load balancer under the Globus environment. The number of IPG nodes, the number of processors per node, and the interconnected speeds are parameterized to derive conditions under which the IPG would be suitable for parallel distributed processing of such applications. Experimental results demonstrate that effective solution are achieved when the IPG nodes are connected by a high-speed asynchronous interconnection network.

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.

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

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.

Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP

NASA Technical Reports Server (NTRS)

Vadyak, Joseph; Shrewsbury, George E.; Narramore, Jim C.; Montry, Gary; Holst, Terry; Kwak, Dochan (Technical Monitor)

1995-01-01

The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time, load balancing, and scalability will be provided.

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.

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.

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)

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.

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.

National Combustion Code: Parallel Performance

NASA Technical Reports Server (NTRS)

Babrauckas, Theresa

2001-01-01

This report discusses the National Combustion Code (NCC). The NCC is an integrated system of codes for the design and analysis of combustion systems. The advanced features of the NCC meet designers' requirements for model accuracy and turn-around time. The fundamental features at the inception of the NCC were parallel processing and unstructured mesh. The design and performance of the NCC are discussed.

Options for Parallelizing a Planning and Scheduling Algorithm

NASA Technical Reports Server (NTRS)

Clement, Bradley J.; Estlin, Tara A.; Bornstein, Benjamin D.

2011-01-01

Space missions have a growing interest in putting multi-core processors onboard spacecraft. For many missions processing power significantly slows operations. We investigate how continual planning and scheduling algorithms can exploit multi-core processing and outline different potential design decisions for a parallelized planning architecture. This organization of choices and challenges helps us with an initial design for parallelizing the CASPER planning system for a mesh multi-core processor. This work extends that presented at another workshop with some preliminary results.

Wakefield Simulation of CLIC PETS Structure Using Parallel 3D Finite Element Time-Domain Solver T3P

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

Candel, A.; Kabel, A.; Lee, L.

In recent years, SLAC's Advanced Computations Department (ACD) has developed the parallel 3D Finite Element electromagnetic time-domain code T3P. Higher-order Finite Element methods on conformal unstructured meshes and massively parallel processing allow unprecedented simulation accuracy for wakefield computations and simulations of transient effects in realistic accelerator structures. Applications include simulation of wakefield damping in the Compact Linear Collider (CLIC) power extraction and transfer structure (PETS).

Simulation of Locking Space Truss Deployments for a Large Deployable Sparse Aperture Reflector

DTIC Science & Technology

2015-03-01

Dr. Alan Jennings, for his unending patience with my struggles through this entire process . Without his expertise, guidance, and trust I would have...engineer since they are not automatically meshed. Fortunately, the mesh process is quite swift. Figure 13 shows both a linear hexahedral element as well...less than that of the serial process . Therefore, COMSOL’s partially parallelized algorithms will not be sped up as a function of cores added and is

IFCPT S-Duct Grid-Adapted FUN3D Computations for the Third Propulsion Aerodynamics Works

NASA Technical Reports Server (NTRS)

Davis, Zach S.; Park, M. A.

2017-01-01

Contributions of the unstructured Reynolds-averaged Navier-Stokes code, FUN3D, to the 3rd AIAA Propulsion Aerodynamics Workshop are described for the diffusing IFCPT S-Duct. Using workshop-supplied grids, results for the baseline S-Duct, baseline S-Duct with Aerodynamic Interface Plane (AIP) rake hardware, and baseline S-Duct with flow control devices are compared with experimental data and results computed with output-based, off-body grid adaptation in FUN3D. Due to the absence of influential geometry components, total pressure recovery is overpredicted on the baseline S-Duct and S-Duct with flow control vanes when compared to experimental values. An estimate for the exact value of total pressure recovery is derived for these cases given an infinitely refined mesh. When results from output-based mesh adaptation are compared with those computed on workshop-supplied grids, a considerable improvement in predicting total pressure recovery is observed. By including more representative geometry, output-based mesh adaptation compares very favorably with experimental data in terms of predicting the total pressure recovery cost-function; whereas, results computed using the workshop-supplied grids are underpredicted.

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.

An automatic generation of non-uniform mesh for CFD analyses of image-based multiscale human airway models

NASA Astrophysics Data System (ADS)

Miyawaki, Shinjiro; Tawhai, Merryn H.; Hoffman, Eric A.; Lin, Ching-Long

2014-11-01

The authors have developed a method to automatically generate non-uniform CFD mesh for image-based human airway models. The sizes of generated tetrahedral elements vary in both radial and longitudinal directions to account for boundary layer and multiscale nature of pulmonary airflow. The proposed method takes advantage of our previously developed centerline-based geometry reconstruction method. In order to generate the mesh branch by branch in parallel, we used the open-source programs Gmsh and TetGen for surface and volume meshes, respectively. Both programs can specify element sizes by means of background mesh. The size of an arbitrary element in the domain is a function of wall distance, element size on the wall, and element size at the center of airway lumen. The element sizes on the wall are computed based on local flow rate and airway diameter. The total number of elements in the non-uniform mesh (10 M) was about half of that in the uniform mesh, although the computational time for the non-uniform mesh was about twice longer (170 min). The proposed method generates CFD meshes with fine elements near the wall and smooth variation of element size in longitudinal direction, which are required, e.g., for simulations with high flow rate. NIH Grants R01-HL094315, U01-HL114494, and S10-RR022421. Computer time provided by XSEDE.

MeSH Now: automatic MeSH indexing at PubMed scale via learning to rank.

PubMed

Mao, Yuqing; Lu, Zhiyong

2017-04-17

MeSH indexing is the task of assigning relevant MeSH terms based on a manual reading of scholarly publications by human indexers. The task is highly important for improving literature retrieval and many other scientific investigations in biomedical research. Unfortunately, given its manual nature, the process of MeSH indexing is both time-consuming (new articles are not immediately indexed until 2 or 3 months later) and costly (approximately ten dollars per article). In response, automatic indexing by computers has been previously proposed and attempted but remains challenging. In order to advance the state of the art in automatic MeSH indexing, a community-wide shared task called BioASQ was recently organized. We propose MeSH Now, an integrated approach that first uses multiple strategies to generate a combined list of candidate MeSH terms for a target article. Through a novel learning-to-rank framework, MeSH Now then ranks the list of candidate terms based on their relevance to the target article. Finally, MeSH Now selects the highest-ranked MeSH terms via a post-processing module. We assessed MeSH Now on two separate benchmarking datasets using traditional precision, recall and F 1 -score metrics. In both evaluations, MeSH Now consistently achieved over 0.60 in F-score, ranging from 0.610 to 0.612. Furthermore, additional experiments show that MeSH Now can be optimized by parallel computing in order to process MEDLINE documents on a large scale. We conclude that MeSH Now is a robust approach with state-of-the-art performance for automatic MeSH indexing and that MeSH Now is capable of processing PubMed scale documents within a reasonable time frame. http://www.ncbi.nlm.nih.gov/CBBresearch/Lu/Demo/MeSHNow/ .

Effects of mesenchymal stem cell and fibroblast coating on immunogenic potential of prosthetic meshes in vitro.

PubMed

Gao, Yue; Krpata, David M; Criss, Cory N; Liu, Lijia; Posielski, Natasza; Rosen, Michael J; Novitsky, Yuri W

2014-08-01

The aim of this study was to reveal the effect of fibroblast or mesenchymal stem cell (MSC) coating on the mesh-induced production of IL-1β, IL-6, and VEGF by macrophages. Four commonly used surgical meshes were tested in this study, including Parietex, SoftMesh, TIGR, and Strattice. One-square-centimeter pieces of each mesh were placed on top of a monolayer of human fibroblasts or rat MSCs. The coating status was monitored with a light microscope. The human promonocytic cell line U937 was induced to differentiate into macrophages (MΦ). Three weeks later, meshes were transferred to new 24-well plates and cocultured with the MΦs for 72 h. Culture medium was collected and analyzed for IL-1β, IL-6, and VEGF production using standard ELISA essays. Parallel mesh samples were fixed with paraformaldehyde or glutaraldehyde for histology or transmission electronic microscopy (TEM) analyses, respectively. Uncoated meshes induced increased production of all three cytokines compared with macrophages cultured alone. HF coating further increased the production of both IL-6 and VEGF but reduced IL-1β production. Except for the SoftMesh group, MSC coating significantly blunted release of all cytokines to levels even lower than with MΦs cultured alone. MΦs tended to deteriorate in the presence of MSCs. Both histology and TEM revealed intimate interactions between cell-coated meshes and MΦs. Cytokine response to fibroblast coating varied, while MSC coating blunted the immunogenic effect of both synthetic and biologic meshes in vitro. Cell coating appears to affect mesh biocompatibility and may become a key process in mesh evolution.

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.

High-resolution coupled ice sheet-ocean modeling using the POPSICLES model

NASA Astrophysics Data System (ADS)

Ng, E. G.; Martin, D. F.; Asay-Davis, X.; Price, S. F.; Collins, W.

2014-12-01

It is expected that a primary driver of future change of the Antarctic ice sheet will be changes in submarine melting driven by incursions of warm ocean water into sub-ice shelf cavities. Correctly modeling this response on a continental scale will require high-resolution modeling of the coupled ice-ocean system. We describe the computational and modeling challenges in our simulations of the full Southern Ocean coupled to a continental-scale Antarctic ice sheet model at unprecedented spatial resolutions (0.1 degree for the ocean model and adaptive mesh refinement down to 500m in the ice sheet model). The POPSICLES model couples the POP2x ocean model, a modified version of the Parallel Ocean Program (Smith and Gent, 2002), with the BISICLES ice-sheet model (Cornford et al., 2012) using a synchronous offline-coupling scheme. Part of the PISCEES SciDAC project and built on the Chombo framework, BISICLES makes use of adaptive mesh refinement to fully resolve dynamically-important regions like grounding lines and employs a momentum balance similar to the vertically-integrated formulation of Schoof and Hindmarsh (2009). Results of BISICLES simulations have compared favorably to comparable simulations with a Stokes momentum balance in both idealized tests like MISMIP3D (Pattyn et al., 2013) and realistic configurations (Favier et al. 2014). POP2x includes sub-ice-shelf circulation using partial top cells (Losch, 2008) and boundary layer physics following Holland and Jenkins (1999), Jenkins (2001), and Jenkins et al. (2010). Standalone POP2x output compares well with standard ice-ocean test cases (e.g., ISOMIP; Losch, 2008) and other continental-scale simulations and melt-rate observations (Kimura et al., 2013; Rignot et al., 2013). For the POPSICLES Antarctic-Southern Ocean simulations, ice sheet and ocean models communicate at one-month coupling intervals.

Magnetohydrodynamics with GAMER

NASA Astrophysics Data System (ADS)

Zhang, Ui-Han; Schive, Hsi-Yu; Chiueh, Tzihong

2018-06-01

GAMER, a parallel Graphic-processing-unit-accelerated Adaptive-MEsh-Refinement (AMR) hydrodynamic code, has been extended to support magnetohydrodynamics (MHD) with both the corner-transport-upwind and MUSCL-Hancock schemes and the constraint transport technique. The divergent preserving operator for AMR has been applied to reinforce the divergence-free constraint on the magnetic field. GAMER-MHD has fully exploited the concurrent executions between the graphic process unit (GPU) MHD solver and other central processing unit computation pertinent to AMR. We perform various standard tests to demonstrate that GAMER-MHD is both second-order accurate and robust, producing results as accurate as those given by high-resolution uniform-grid runs. We also explore a new 3D MHD test, where the magnetic field assumes the Arnold–Beltrami–Childress configuration, temporarily becomes turbulent with current sheets, and finally settles to a lowest-energy equilibrium state. This 3D problem is adopted for the performance test of GAMER-MHD. The single-GPU performance reaches 1.2 × 108 and 5.5 × 107 cell updates per second for the single- and double-precision calculations, respectively, on Tesla P100. We also demonstrate a parallel efficiency of ∼70% for both weak and strong scaling using 1024 XK nodes on the Blue Waters supercomputers.

Mesh refinement strategy for optimal control problems

NASA Astrophysics Data System (ADS)

Paiva, L. T.; Fontes, F. A. C. C.

2013-10-01

Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.

Parallel Element Agglomeration Algebraic Multigrid and Upscaling Library

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

Barker, Andrew T.; Benson, Thomas R.; Lee, Chak Shing

ParELAG is a parallel C++ library for numerical upscaling of finite element discretizations and element-based algebraic multigrid solvers. It provides optimal complexity algorithms to build multilevel hierarchies and solvers that can be used for solving a wide class of partial differential equations (elliptic, hyperbolic, saddle point problems) on general unstructured meshes. Additionally, a novel multilevel solver for saddle point problems with divergence constraint is implemented.

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.

OpenGl Visualization Tool and Library Version: 1.0

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

2010-06-22

GLVis is an OpenGL tool for visualization of finite element meshes and functions. When started without any options, GLVis starts a server, which waits for a socket connections and visualizes any recieved data. This way the results of simulations on a remote (parallel) machine can be visualized on the lical user desktop. GLVis can also be used to visualize a mesh with or without a finite element function (solution). It can run a batch sequence of commands (GLVis scripts), or display previously saved socket streams.

Practical Aerodynamic Design Optimization Based on the Navier-Stokes Equations and a Discrete Adjoint Method

NASA Technical Reports Server (NTRS)

Grossman, Bernard

1999-01-01

Compressible and incompressible versions of a three-dimensional unstructured mesh Reynolds-averaged Navier-Stokes flow solver have been differentiated and resulting derivatives have been verified by comparisons with finite differences and a complex-variable approach. In this implementation, the turbulence model is fully coupled with the flow equations in order to achieve this consistency. The accuracy demonstrated in the current work represents the first time that such an approach has been successfully implemented. The accuracy of a number of simplifying approximations to the linearizations of the residual have been examined. A first-order approximation to the dependent variables in both the adjoint and design equations has been investigated. The effects of a "frozen" eddy viscosity and the ramifications of neglecting some mesh sensitivity terms were also examined. It has been found that none of the approximations yielded derivatives of acceptable accuracy and were often of incorrect sign. However, numerical experiments indicate that an incomplete convergence of the adjoint system often yield sufficiently accurate derivatives, thereby significantly lowering the time required for computing sensitivity information. The convergence rate of the adjoint solver relative to the flow solver has been examined. Inviscid adjoint solutions typically require one to four times the cost of a flow solution, while for turbulent adjoint computations, this ratio can reach as high as eight to ten. Numerical experiments have shown that the adjoint solver can stall before converging the solution to machine accuracy, particularly for viscous cases. A possible remedy for this phenomenon would be to include the complete higher-order linearization in the preconditioning step, or to employ a simple form of mesh sequencing to obtain better approximations to the solution through the use of coarser meshes. An efficient surface parameterization based on a free-form deformation technique has been utilized and the resulting codes have been integrated with an optimization package. Lastly, sample optimizations have been shown for inviscid and turbulent flow over an ONERA M6 wing. Drag reductions have been demonstrated by reducing shock strengths across the span of the wing. In order for large scale optimization to become routine, the benefits of parallel architectures should be exploited. Although the flow solver has been parallelized using compiler directives. The parallel efficiency is under 50 percent. Clearly, parallel versions of the codes will have an immediate impact on the ability to design realistic configurations on fine meshes, and this effort is currently underway.

Underworld: What we set out to do, How far did we get, What did we Learn ? (Invited)

NASA Astrophysics Data System (ADS)

Moresi, L. N.

2013-12-01

Underworld was conceived as a tool for modelling 3D lithospheric deformation coupled with the underlying / surrounding mantle flow. The challenges involved were to find a method capable of representing the complicated, non-linear, history dependent rheology of the near surface as well as being able to model mantle convection, and, simultaneously, to be able to solve the numerical system efficiently. Underworld is a hybrid particle / mesh code reminiscent of the particle-in-cell techniques from the early 1960s. The Underworld team (*) was not the first to use this approach, nor the last, but the team does have considerable experience and much has been learned along the way. The use of a finite element method as the underlying "cell" in which the Lagrangian particles are embedded considerably reduces errors associated with mapping material properties to the cells. The particles are treated as moving quadrature points in computing the stiffness matrix integrals. The decoupling of deformation markers from computation points allows the use of structured meshes, efficient parallel decompositions, and simple-to-code geometric multigrid solution methods. For a 3D code such efficiencies are very important. The elegance of the method is that it can be completely described in a couple of sentences. However, there are some limitations: it is not obvious how to retain this elegance for unstructured or adaptive meshes, arbitrary element types are not sufficiently well integrated by the simple quadrature approach, and swarms of particles representing volumes are usually an inefficient representation of surfaces. This will be discussed ! (*) Although not formally constituted, my co-conspirators in this exercise are listed as the Underworld team and I will reveal their true identities on the day.

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 class of hybrid finite element methods for electromagnetics: A review

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Chatterjee, A.; Gong, J.

1993-01-01

Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.

The Space-Time Conservative Schemes for Large-Scale, Time-Accurate Flow Simulations with Tetrahedral Meshes

NASA Technical Reports Server (NTRS)

Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung

2016-01-01

Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.

Creation of parallel algorithms for the solution of problems of gas dynamics on multi-core computers and GPU

NASA Astrophysics Data System (ADS)

Rybakin, B.; Bogatencov, P.; Secrieru, G.; Iliuha, N.

2013-10-01

The paper deals with a parallel algorithm for calculations on multiprocessor computers and GPU accelerators. The calculations of shock waves interaction with low-density bubble results and the problem of the gas flow with the forces of gravity are presented. This algorithm combines a possibility to capture a high resolution of shock waves, the second-order accuracy for TVD schemes, and a possibility to observe a low-level diffusion of the advection scheme. Many complex problems of continuum mechanics are numerically solved on structured or unstructured grids. To improve the accuracy of the calculations is necessary to choose a sufficiently small grid (with a small cell size). This leads to the drawback of a substantial increase of computation time. Therefore, for the calculations of complex problems it is reasonable to use the method of Adaptive Mesh Refinement. That is, the grid refinement is performed only in the areas of interest of the structure, where, e.g., the shock waves are generated, or a complex geometry or other such features exist. Thus, the computing time is greatly reduced. In addition, the execution of the application on the resulting sequence of nested, decreasing nets can be parallelized. Proposed algorithm is based on the AMR method. Utilization of AMR method can significantly improve the resolution of the difference grid in areas of high interest, and from other side to accelerate the processes of the multi-dimensional problems calculating. Parallel algorithms of the analyzed difference models realized for the purpose of calculations on graphic processors using the CUDA technology [1].

3D unstructured-mesh radiation transport codes

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

Morel, J.

1997-12-31

Three unstructured-mesh radiation transport codes are currently being developed at Los Alamos National Laboratory. The first code is ATTILA, which uses an unstructured tetrahedral mesh in conjunction with standard Sn (discrete-ordinates) angular discretization, standard multigroup energy discretization, and linear-discontinuous spatial differencing. ATTILA solves the standard first-order form of the transport equation using source iteration in conjunction with diffusion-synthetic acceleration of the within-group source iterations. DANTE is designed to run primarily on workstations. The second code is DANTE, which uses a hybrid finite-element mesh consisting of arbitrary combinations of hexahedra, wedges, pyramids, and tetrahedra. DANTE solves several second-order self-adjoint forms of the transport equation including the even-parity equation, the odd-parity equation, and a new equation called the self-adjoint angular flux equation. DANTE also offers three angular discretization options:more » $$S{_}n$$ (discrete-ordinates), $$P{_}n$$ (spherical harmonics), and $$SP{_}n$$ (simplified spherical harmonics). DANTE is designed to run primarily on massively parallel message-passing machines, such as the ASCI-Blue machines at LANL and LLNL. The third code is PERICLES, which uses the same hybrid finite-element mesh as DANTE, but solves the standard first-order form of the transport equation rather than a second-order self-adjoint form. DANTE uses a standard $$S{_}n$$ discretization in angle in conjunction with trilinear-discontinuous spatial differencing, and diffusion-synthetic acceleration of the within-group source iterations. PERICLES was initially designed to run on workstations, but a version for massively parallel message-passing machines will be built. The three codes will be described in detail and computational results will be presented.« less

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.

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.

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.

Diffuse interface simulation of bubble rising process: a comparison of adaptive mesh refinement and arbitrary lagrange-euler methods

NASA Astrophysics Data System (ADS)

Wang, Ye; Cai, Jiejin; Li, Qiong; Yin, Huaqiang; Yang, Xingtuan

2018-06-01

Gas-liquid two phase flow exists in several industrial processes and light-water reactors (LWRs). A diffuse interface based finite element method with two different mesh generation methods namely, the Adaptive Mesh Refinement (AMR) and the Arbitrary Lagrange Euler (ALE) methods is used to model the shape and velocity changes in a rising bubble. Moreover, the calculating speed and mesh generation strategies of AMR and ALE are contrasted. The simulation results agree with the Bhagat's experiments, indicating that both mesh generation methods can simulate the characteristics of bubble accurately. We concluded that: the small bubble rises as elliptical with oscillation, whereas a larger bubble (11 mm > d > 7 mm) rises with a morphology between the elliptical and cap type with a larger oscillation. When the bubble is large (d > 11 mm), it rises up as a cap type, and the amplitude becomes smaller. Moreover, it takes longer to achieve the stable shape from the ellipsoid to the spherical cap type with the increase of the bubble diameter. The results also show that for smaller diameter case, the ALE method uses fewer grids and has a faster calculation speed, but the AMR method can solve the case of a large geometry deformation efficiently.

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.

The whole mesh deformation model: a fast image segmentation method suitable for effective parallelization

NASA Astrophysics Data System (ADS)

Lenkiewicz, Przemyslaw; Pereira, Manuela; Freire, Mário M.; Fernandes, José

2013-12-01

In this article, we propose a novel image segmentation method called the whole mesh deformation (WMD) model, which aims at addressing the problems of modern medical imaging. Such problems have raised from the combination of several factors: (1) significant growth of medical image volumes sizes due to increasing capabilities of medical acquisition devices; (2) the will to increase the complexity of image processing algorithms in order to explore new functionality; (3) change in processor development and turn towards multi processing units instead of growing bus speeds and the number of operations per second of a single processing unit. Our solution is based on the concept of deformable models and is characterized by a very effective and precise segmentation capability. The proposed WMD model uses a volumetric mesh instead of a contour or a surface to represent the segmented shapes of interest, which allows exploiting more information in the image and obtaining results in shorter times, independently of image contents. The model also offers a good ability for topology changes and allows effective parallelization of workflow, which makes it a very good choice for large datasets. We present a precise model description, followed by experiments on artificial images and real medical data.

Numerical aspects and implementation of a two-layer zonal wall model for LES of compressible turbulent flows on unstructured meshes

NASA Astrophysics Data System (ADS)

Park, George Ilhwan; Moin, Parviz

2016-01-01

This paper focuses on numerical and practical aspects associated with a parallel implementation of a two-layer zonal wall model for large-eddy simulation (LES) of compressible wall-bounded turbulent flows on unstructured meshes. A zonal wall model based on the solution of unsteady three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations on a separate near-wall grid is implemented in an unstructured, cell-centered finite-volume LES solver. The main challenge in its implementation is to couple two parallel, unstructured flow solvers for efficient boundary data communication and simultaneous time integrations. A coupling strategy with good load balancing and low processors underutilization is identified. Face mapping and interpolation procedures at the coupling interface are explained in detail. The method of manufactured solution is used for verifying the correct implementation of solver coupling, and parallel performance of the combined wall-modeled LES (WMLES) solver is investigated. The method has successfully been applied to several attached and separated flows, including a transitional flow over a flat plate and a separated flow over an airfoil at an angle of attack.

A coupled ALE-AMR method for shock hydrodynamics

DOE PAGES

Waltz, J.; Bakosi, J.

2018-03-05

We present a numerical method combining adaptive mesh refinement (AMR) with arbitrary Lagrangian-Eulerian (ALE) mesh motion for the simulation of shock hydrodynamics on unstructured grids. The primary goal of the coupled method is to use AMR to reduce numerical error in ALE simulations at reduced computational expense relative to uniform fine mesh calculations, in the same manner that AMR has been used in Eulerian simulations. We also identify deficiencies with ALE methods that AMR is able to mitigate, and discuss the unique coupling challenges. The coupled method is demonstrated using three-dimensional unstructured meshes of up to O(10 7) tetrahedral cells.more » Convergence of ALE-AMR solutions towards both uniform fine mesh ALE results and analytic solutions is demonstrated. Speed-ups of 5-10× for a given level of error are observed relative to uniform fine mesh calculations.« less

A coupled ALE-AMR method for shock hydrodynamics

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

Waltz, J.; Bakosi, J.

We present a numerical method combining adaptive mesh refinement (AMR) with arbitrary Lagrangian-Eulerian (ALE) mesh motion for the simulation of shock hydrodynamics on unstructured grids. The primary goal of the coupled method is to use AMR to reduce numerical error in ALE simulations at reduced computational expense relative to uniform fine mesh calculations, in the same manner that AMR has been used in Eulerian simulations. We also identify deficiencies with ALE methods that AMR is able to mitigate, and discuss the unique coupling challenges. The coupled method is demonstrated using three-dimensional unstructured meshes of up to O(10 7) tetrahedral cells.more » Convergence of ALE-AMR solutions towards both uniform fine mesh ALE results and analytic solutions is demonstrated. Speed-ups of 5-10× for a given level of error are observed relative to uniform fine mesh calculations.« less

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

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.

jInv: A Modular and Scalable Framework for Electromagnetic Inverse Problems

NASA Astrophysics Data System (ADS)

Belliveau, P. T.; Haber, E.

2016-12-01

Inversion is a key tool in the interpretation of geophysical electromagnetic (EM) data. Three-dimensional (3D) EM inversion is very computationally expensive and practical software for inverting large 3D EM surveys must be able to take advantage of high performance computing (HPC) resources. It has traditionally been difficult to achieve those goals in a high level dynamic programming environment that allows rapid development and testing of new algorithms, which is important in a research setting. With those goals in mind, we have developed jInv, a framework for PDE constrained parameter estimation problems. jInv provides optimization and regularization routines, a framework for user defined forward problems, and interfaces to several direct and iterative solvers for sparse linear systems. The forward modeling framework provides finite volume discretizations of differential operators on rectangular tensor product meshes and tetrahedral unstructured meshes that can be used to easily construct forward modeling and sensitivity routines for forward problems described by partial differential equations. jInv is written in the emerging programming language Julia. Julia is a dynamic language targeted at the computational science community with a focus on high performance and native support for parallel programming. We have developed frequency and time-domain EM forward modeling and sensitivity routines for jInv. We will illustrate its capabilities and performance with two synthetic time-domain EM inversion examples. First, in airborne surveys, which use many sources, we achieve distributed memory parallelism by decoupling the forward and inverse meshes and performing forward modeling for each source on small, locally refined meshes. Secondly, we invert grounded source time-domain data from a gradient array style induced polarization survey using a novel time-stepping technique that allows us to compute data from different time-steps in parallel. These examples both show that it is possible to invert large scale 3D time-domain EM datasets within a modular, extensible framework written in a high-level, easy to use programming language.

A Discontinuous Petrov-Galerkin Methodology for Adaptive Solutions to the Incompressible Navier-Stokes Equations

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

Roberts, Nathan V.; Demkowiz, Leszek; Moser, Robert

2015-11-15

The discontinuous Petrov-Galerkin methodology with optimal test functions (DPG) of Demkowicz and Gopalakrishnan [18, 20] guarantees the optimality of the solution in an energy norm, and provides several features facilitating adaptive schemes. Whereas Bubnov-Galerkin methods use identical trial and test spaces, Petrov-Galerkin methods allow these function spaces to differ. In DPG, test functions are computed on the fly and are chosen to realize the supremum in the inf-sup condition; the method is equivalent to a minimum residual method. For well-posed problems with sufficiently regular solutions, DPG can be shown to converge at optimal rates—the inf-sup constants governing the convergence aremore » mesh-independent, and of the same order as those governing the continuous problem [48]. DPG also provides an accurate mechanism for measuring the error, and this can be used to drive adaptive mesh refinements. We employ DPG to solve the steady incompressible Navier-Stokes equations in two dimensions, building on previous work on the Stokes equations, and focusing particularly on the usefulness of the approach for automatic adaptivity starting from a coarse mesh. We apply our approach to a manufactured solution due to Kovasznay as well as the lid-driven cavity flow, backward-facing step, and flow past a cylinder problems.« less

Fault-tolerant onboard digital information switching and routing for communications satellites

NASA Technical Reports Server (NTRS)

Shalkhauser, Mary JO; Quintana, Jorge A.; Soni, Nitin J.; Kim, Heechul

1993-01-01

The NASA Lewis Research Center is developing an information-switching processor for future meshed very-small-aperture terminal (VSAT) communications satellites. The information-switching processor will switch and route baseband user data onboard the VSAT satellite to connect thousands of Earth terminals. Fault tolerance is a critical issue in developing information-switching processor circuitry that will provide and maintain reliable communications services. In parallel with the conceptual development of the meshed VSAT satellite network architecture, NASA designed and built a simple test bed for developing and demonstrating baseband switch architectures and fault-tolerance techniques. The meshed VSAT architecture and the switching demonstration test bed are described, and the initial switching architecture and the fault-tolerance techniques that were developed and tested are discussed.

High-Performance Parallel Analysis of Coupled Problems for Aircraft Propulsion

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Gumaste, U.; Chen, P.-S.; Lesoinne, M.; Stern, P.

1997-01-01

Applications are described of high-performance computing methods to the numerical simulation of complete jet engines. The methodology focuses on the partitioned analysis of the interaction of the gas flow with a flexible structure and with the fluid mesh motion driven by structural displacements. The latter is treated by a ALE technique that models the fluid mesh motion as that of a fictitious mechanical network laid along the edges of near-field elements. New partitioned analysis procedures to treat this coupled three-component problem were developed. These procedures involved delayed corrections and subcycling, and have been successfully tested on several massively parallel computers, including the iPSC-860, Paragon XP/S and the IBM SP2. The NASA-sponsored ENG10 program was used for the global steady state analysis of the whole engine. This program uses a regular FV-multiblock-grid discretization in conjunction with circumferential averaging to include effects of blade forces, loss, combustor heat addition, blockage, bleeds and convective mixing. A load-balancing preprocessor for parallel versions of ENG10 was developed as well as the capability for the first full 3D aeroelastic simulation of a multirow engine stage. This capability was tested on the IBM SP2 parallel supercomputer at NASA Ames.

Cooled particle accelerator target

DOEpatents

Degtiarenko, Pavel V.

2005-06-14

A novel particle beam target comprising: a rotating target disc mounted on a retainer and thermally coupled to a first array of spaced-apart parallel plate fins that extend radially inwardly from the retainer and mesh without physical contact with a second array of spaced-apart parallel plate fins that extend radially outwardly from and are thermally coupled to a cooling mechanism capable of removing heat from said second array of spaced-apart fins and located within the first array of spaced-apart parallel fins. Radiant thermal exchange between the two arrays of parallel plate fins provides removal of heat from the rotating disc. A method of cooling the rotating target is also described.

SIAM Conference on Parallel Processing for Scientific Computing, 4th, Chicago, IL, Dec. 11-13, 1989, Proceedings

NASA Technical Reports Server (NTRS)

Dongarra, Jack (Editor); Messina, Paul (Editor); Sorensen, Danny C. (Editor); Voigt, Robert G. (Editor)

1990-01-01

Attention is given to such topics as an evaluation of block algorithm variants in LAPACK and presents a large-grain parallel sparse system solver, a multiprocessor method for the solution of the generalized Eigenvalue problem on an interval, and a parallel QR algorithm for iterative subspace methods on the CM2. A discussion of numerical methods includes the topics of asynchronous numerical solutions of PDEs on parallel computers, parallel homotopy curve tracking on a hypercube, and solving Navier-Stokes equations on the Cedar Multi-Cluster system. A section on differential equations includes a discussion of a six-color procedure for the parallel solution of elliptic systems using the finite quadtree structure, data parallel algorithms for the finite element method, and domain decomposition methods in aerodynamics. Topics dealing with massively parallel computing include hypercube vs. 2-dimensional meshes and massively parallel computation of conservation laws. Performance and tools are also discussed.

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.

Toward Automatic Verification of Goal-Oriented Flow Simulations

NASA Technical Reports Server (NTRS)

Nemec, Marian; Aftosmis, Michael J.

2014-01-01

We demonstrate the power of adaptive mesh refinement with adjoint-based error estimates in verification of simulations governed by the steady Euler equations. The flow equations are discretized using a finite volume scheme on a Cartesian mesh with cut cells at the wall boundaries. The discretization error in selected simulation outputs is estimated using the method of adjoint-weighted residuals. Practical aspects of the implementation are emphasized, particularly in the formulation of the refinement criterion and the mesh adaptation strategy. Following a thorough code verification example, we demonstrate simulation verification of two- and three-dimensional problems. These involve an airfoil performance database, a pressure signature of a body in supersonic flow and a launch abort with strong jet interactions. The results show reliable estimates and automatic control of discretization error in all simulations at an affordable computational cost. Moreover, the approach remains effective even when theoretical assumptions, e.g., steady-state and solution smoothness, are relaxed.

Large Eddy simulation of compressible flows with a low-numerical dissipation patch-based adaptive mesh refinement method

NASA Astrophysics Data System (ADS)

Pantano, Carlos

2005-11-01

We describe a hybrid finite difference method for large-eddy simulation (LES) of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). Numerical experiments and validation calculations are presented including a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability. The approach is a conservative flux-based SAMR formulation and as such, it utilizes refinement to computational advantage. The numerical method for the resolved scale terms encompasses the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered scheme that is consistent with a skew-symmetric finite difference formulation is used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. The subgrid stresses and transports are calculated by means of the streched-vortex model, Misra & Pullin (1997)

Ordering Unstructured Meshes for Sparse Matrix Computations on Leading Parallel Systems

NASA Technical Reports Server (NTRS)

Oliker, Leonid; Li, Xiaoye; Heber, Gerd; Biswas, Rupak

2000-01-01

The ability of computers to solve hitherto intractable problems and simulate complex processes using mathematical models makes them an indispensable part of modern science and engineering. Computer simulations of large-scale realistic applications usually require solving a set of non-linear partial differential equations (PDES) over a finite region. For example, one thrust area in the DOE Grand Challenge projects is to design future accelerators such as the SpaHation Neutron Source (SNS). Our colleagues at SLAC need to model complex RFQ cavities with large aspect ratios. Unstructured grids are currently used to resolve the small features in a large computational domain; dynamic mesh adaptation will be added in the future for additional efficiency. The PDEs for electromagnetics are discretized by the FEM method, which leads to a generalized eigenvalue problem Kx = AMx, where K and M are the stiffness and mass matrices, and are very sparse. In a typical cavity model, the number of degrees of freedom is about one million. For such large eigenproblems, direct solution techniques quickly reach the memory limits. Instead, the most widely-used methods are Krylov subspace methods, such as Lanczos or Jacobi-Davidson. In all the Krylov-based algorithms, sparse matrix-vector multiplication (SPMV) must be performed repeatedly. Therefore, the efficiency of SPMV usually determines the eigensolver speed. SPMV is also one of the most heavily used kernels in large-scale numerical simulations.

A Coupled Earthquake-Tsunami Simulation Framework Applied to the Sumatra 2004 Event

NASA Astrophysics Data System (ADS)

Vater, Stefan; Bader, Michael; Behrens, Jörn; van Dinther, Ylona; Gabriel, Alice-Agnes; Madden, Elizabeth H.; Ulrich, Thomas; Uphoff, Carsten; Wollherr, Stephanie; van Zelst, Iris

2017-04-01

Large earthquakes along subduction zone interfaces have generated destructive tsunamis near Chile in 1960, Sumatra in 2004, and northeast Japan in 2011. In order to better understand these extreme events, we have developed tools for physics-based, coupled earthquake-tsunami simulations. This simulation framework is applied to the 2004 Indian Ocean M 9.1-9.3 earthquake and tsunami, a devastating event that resulted in the loss of more than 230,000 lives. The earthquake rupture simulation is performed using an ADER discontinuous Galerkin discretization on an unstructured tetrahedral mesh with the software SeisSol. Advantages of this approach include accurate representation of complex fault and sea floor geometries and a parallelized and efficient workflow in high-performance computing environments. Accurate and efficient representation of the tsunami evolution and inundation at the coast is achieved with an adaptive mesh discretizing the shallow water equations with a second-order Runge-Kutta discontinuous Galerkin (RKDG) scheme. With the application of the framework to this historic event, we aim to better understand the involved mechanisms between the dynamic earthquake within the earth's crust, the resulting tsunami wave within the ocean, and the final coastal inundation process. Earthquake model results are constrained by GPS surface displacements and tsunami model results are compared with buoy and inundation data. This research is part of the ASCETE Project, "Advanced Simulation of Coupled Earthquake and Tsunami Events", funded by the Volkswagen Foundation.

MPI-AMRVAC 2.0 for Solar and Astrophysical Applications

NASA Astrophysics Data System (ADS)

Xia, C.; Teunissen, J.; El Mellah, I.; Chané, E.; Keppens, R.

2018-02-01

We report on the development of MPI-AMRVAC version 2.0, which is an open-source framework for parallel, grid-adaptive simulations of hydrodynamic and magnetohydrodynamic (MHD) astrophysical applications. The framework now supports radial grid stretching in combination with adaptive mesh refinement (AMR). The advantages of this combined approach are demonstrated with one-dimensional, two-dimensional, and three-dimensional examples of spherically symmetric Bondi accretion, steady planar Bondi–Hoyle–Lyttleton flows, and wind accretion in supergiant X-ray binaries. Another improvement is support for the generic splitting of any background magnetic field. We present several tests relevant for solar physics applications to demonstrate the advantages of field splitting on accuracy and robustness in extremely low-plasma β environments: a static magnetic flux rope, a magnetic null-point, and magnetic reconnection in a current sheet with either uniform or anomalous resistivity. Our implementation for treating anisotropic thermal conduction in multi-dimensional MHD applications is also described, which generalizes the original slope-limited symmetric scheme from two to three dimensions. We perform ring diffusion tests that demonstrate its accuracy and robustness, and show that it prevents the unphysical thermal flux present in traditional schemes. The improved parallel scaling of the code is demonstrated with three-dimensional AMR simulations of solar coronal rain, which show satisfactory strong scaling up to 2000 cores. Other framework improvements are also reported: the modernization and reorganization into a library, the handling of automatic regression tests, the use of inline/online Doxygen documentation, and a new future-proof data format for input/output.

Adaptive, Tactical Mesh Networking: Control Base MANET Model

DTIC Science & Technology

2010-09-01

pp. 316–320 Available: IEEE Xplore , http://ieeexplore.ieee.org [Accessed: June 9, 2010]. [5] N. Sidiropoulos, “Multiuser Transmit Beamforming...Mobile Mesh Segments of TNT Testbed .......... 11 Figure 5. Infrastructure and Ad Hoc Mode of IEEE 802.11................................ 13 Figure...6. The Power Spectral Density of OFDM................................................ 14 Figure 7. A Typical IEEE 802.16 Network

A manual for PARTI runtime primitives

NASA Technical Reports Server (NTRS)

Berryman, Harry; Saltz, Joel

1990-01-01

Primitives are presented that are designed to help users efficiently program irregular problems (e.g., unstructured mesh sweeps, sparse matrix codes, adaptive mesh partial differential equations solvers) on distributed memory machines. These primitives are also designed for use in compilers for distributed memory multiprocessors. Communications patterns are captured at runtime, and the appropriate send and receive messages are automatically generated.

An hp-adaptivity and error estimation for hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Bey, Kim S.

1995-01-01

This paper presents an hp-adaptive discontinuous Galerkin method for linear hyperbolic conservation laws. A priori and a posteriori error estimates are derived in mesh-dependent norms which reflect the dependence of the approximate solution on the element size (h) and the degree (p) of the local polynomial approximation. The a posteriori error estimate, based on the element residual method, provides bounds on the actual global error in the approximate solution. The adaptive strategy is designed to deliver an approximate solution with the specified level of error in three steps. The a posteriori estimate is used to assess the accuracy of a given approximate solution and the a priori estimate is used to predict the mesh refinements and polynomial enrichment needed to deliver the desired solution. Numerical examples demonstrate the reliability of the a posteriori error estimates and the effectiveness of the hp-adaptive strategy.

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

Analysis of Adaptive Mesh Refinement for IMEX Discontinuous Galerkin Solutions of the Compressible Euler Equations with Application to Atmospheric Simulations

DTIC Science & Technology

2013-01-01

ξi be the Legendre -Gauss-Lobatto (LGL) points defined as the roots of (1 − ξ2)P ′N (ξ) = 0, where PN (ξ) is the N th order Legendre polynomial . The...mesh refinement. By expanding the solution in a basis of high order polynomials in each element, one can dynamically adjust the order of these basis...on refining the mesh while keeping the polynomial order constant across the elements. If we choose to allow non-conforming elements, the challenge in

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.

Local error estimates for adaptive simulation of the Reaction–Diffusion Master Equation via operator splitting

PubMed Central

Hellander, Andreas; Lawson, Michael J; Drawert, Brian; Petzold, Linda

2015-01-01

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity. PMID:26865735

Local error estimates for adaptive simulation of the Reaction-Diffusion Master Equation via operator splitting.

PubMed

Hellander, Andreas; Lawson, Michael J; Drawert, Brian; Petzold, Linda

2014-06-01

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity.

Numerical modeling of landslide-generated tsunami using adaptive unstructured meshes

NASA Astrophysics Data System (ADS)

Wilson, Cian; Collins, Gareth; Desousa Costa, Patrick; Piggott, Matthew

2010-05-01

Landslides impacting into or occurring under water generate waves, which can have devastating environmental consequences. Depending on the characteristics of the landslide the waves can have significant amplitude and potentially propagate over large distances. Linear models of classical earthquake-generated tsunamis cannot reproduce the highly nonlinear generation mechanisms required to accurately predict the consequences of landslide-generated tsunamis. Also, laboratory-scale experimental investigation is limited to simple geometries and short time-scales before wave reflections contaminate the data. Computational fluid dynamics models based on the nonlinear Navier-Stokes equations can simulate landslide-tsunami generation at realistic scales. However, traditional chessboard-like structured meshes introduce superfluous resolution and hence the computing power required for such a simulation can be prohibitively high, especially in three dimensions. Unstructured meshes allow the grid spacing to vary rapidly from high resolution in the vicinity of small scale features to much coarser, lower resolution in other areas. Combining this variable resolution with dynamic mesh adaptivity allows such high resolution zones to follow features like the interface between the landslide and the water whilst minimising the computational costs. Unstructured meshes are also better suited to representing complex geometries and bathymetries allowing more realistic domains to be simulated. Modelling multiple materials, like water, air and a landslide, on an unstructured adaptive mesh poses significant numerical challenges. Novel methods of interface preservation must be considered and coupled to a flow model in such a way that ensures conservation of the different materials. Furthermore this conservation property must be maintained during successive stages of mesh optimisation and interpolation. In this paper we validate a new multi-material adaptive unstructured fluid dynamics model against the well-known Lituya Bay landslide-generated wave experiment and case study [1]. In addition, we explore the effect of physical parameters, such as the shape, velocity and viscosity of the landslide, on wave amplitude and run-up, to quantify their influence on the landslide-tsunami hazard. As well as reproducing the experimental results, the model is shown to have excellent conservation and bounding properties. It also requires fewer nodes than an equivalent resolution fixed mesh simulation, therefore minimising at least one aspect of the computational cost. These computational savings are directly transferable to higher dimensions and some initial three dimensional results are also presented. These reproduce the experiments of DiRisio et al. [2], where an 80cm long landslide analogue was released from the side of an 8.9m diameter conical island in a 50 × 30m tank of water. The resulting impact between the landslide and the water generated waves with an amplitude of 1cm at wave gauges around the island. The range of scales that must be considered in any attempt to numerically reproduce this experiment makes it an ideal case study for our multi-material adaptive unstructured fluid dynamics model. [1] FRITZ, H. M., MOHAMMED, F., & YOO, J. 2009. Lituya Bay Landslide Impact Generated Mega-Tsunami 50th Anniversary. Pure and Applied Geophysics, 166(1), 153-175. [2] DIRISIO, M., DEGIROLAMO, P., BELLOTTI, G., PANIZZO, A., ARISTODEMO, F.,

Parallel Simulation of Three-Dimensional Free Surface Fluid Flow Problems

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

BAER,THOMAS A.; SACKINGER,PHILIP A.; SUBIA,SAMUEL R.

1999-10-14

Simulation of viscous three-dimensional fluid flow typically involves a large number of unknowns. When free surfaces are included, the number of unknowns increases dramatically. Consequently, this class of problem is an obvious application of parallel high performance computing. We describe parallel computation of viscous, incompressible, free surface, Newtonian fluid flow problems that include dynamic contact fines. The Galerkin finite element method was used to discretize the fully-coupled governing conservation equations and a ''pseudo-solid'' mesh mapping approach was used to determine the shape of the free surface. In this approach, the finite element mesh is allowed to deform to satisfy quasi-staticmore » solid mechanics equations subject to geometric or kinematic constraints on the boundaries. As a result, nodal displacements must be included in the set of unknowns. Other issues discussed are the proper constraints appearing along the dynamic contact line in three dimensions. Issues affecting efficient parallel simulations include problem decomposition to equally distribute computational work among a SPMD computer and determination of robust, scalable preconditioners for the distributed matrix systems that must be solved. Solution continuation strategies important for serial simulations have an enhanced relevance in a parallel coquting environment due to the difficulty of solving large scale systems. Parallel computations will be demonstrated on an example taken from the coating flow industry: flow in the vicinity of a slot coater edge. This is a three dimensional free surface problem possessing a contact line that advances at the web speed in one region but transitions to static behavior in another region. As such, a significant fraction of the computational time is devoted to processing boundary data. Discussion focuses on parallel speed ups for fixed problem size, a class of problems of immediate practical importance.« less

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

Supercomputer modeling of flow past hypersonic flight vehicles

NASA Astrophysics Data System (ADS)

Ermakov, M. K.; Kryukov, I. A.

2017-02-01

A software platform for MPI-based parallel solution of the Navier-Stokes (Euler) equations for viscous heat-conductive compressible perfect gas on 3-D unstructured meshes is developed. The discretization and solution of the Navier-Stokes equations are constructed on generalized S.K. Godunov’s method and the second order approximation in space and time. Developed software platform allows to carry out effectively flow past hypersonic flight vehicles simulations for the Mach numbers 6 and higher, and numerical meshes with up to 1 billion numerical cells and with up to 128 processors.

ATDM LANL FleCSI: Topology and Execution Framework

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

Bergen, Benjamin Karl

FleCSI is a compile-time configurable C++ framework designed to support multi-physics application development. As such, FleCSI attempts to provide a very general set of infrastructure design patterns that can be specialized and extended to suit the needs of a broad variety of solver and data requirements. This means that FleCSI is potentially useful to many different ECP projects. Current support includes multidimensional mesh topology, mesh geometry, and mesh adjacency information, n-dimensional hashed-tree data structures, graph partitioning interfaces, and dependency closures (to identify data dependencies between distributed-memory address spaces). FleCSI introduces a functional programming model with control, execution, and data abstractionsmore » that are consistent with state-of-the-art task-based runtimes such as Legion and Charm++. The model also provides support for fine-grained, data-parallel execution with backend support for runtimes such as OpenMP and C++17. The FleCSI abstraction layer provides the developer with insulation from the underlying runtimes, while allowing support for multiple runtime systems, including conventional models like asynchronous MPI. The intent is to give developers a concrete set of user-friendly programming tools that can be used now, while allowing flexibility in choosing runtime implementations and optimizations that can be applied to architectures and runtimes that arise in the future. This project is essential to the ECP Ristra Next-Generation Code project, part of ASC ATDM, because it provides a hierarchically parallel programming model that is consistent with the design of modern system architectures, but which allows for the straightforward expression of algorithmic parallelism in a portably performant manner.« less

Application of CHAD hydrodynamics to shock-wave problems

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

Trease, H.E.; O`Rourke, P.J.; Sahota, M.S.

1997-12-31

CHAD is the latest in a sequence of continually evolving computer codes written to effectively utilize massively parallel computer architectures and the latest grid generators for unstructured meshes. Its applications range from automotive design issues such as in-cylinder and manifold flows of internal combustion engines, vehicle aerodynamics, underhood cooling and passenger compartment heating, ventilation, and air conditioning to shock hydrodynamics and materials modeling. CHAD solves the full unsteady Navier-Stoke equations with the k-epsilon turbulence model in three space dimensions. The code has four major features that distinguish it from the earlier KIVA code, also developed at Los Alamos. First, itmore » is based on a node-centered, finite-volume method in which, like finite element methods, all fluid variables are located at computational nodes. The computational mesh efficiently and accurately handles all element shapes ranging from tetrahedra to hexahedra. Second, it is written in standard Fortran 90 and relies on automatic domain decomposition and a universal communication library written in standard C and MPI for unstructured grids to effectively exploit distributed-memory parallel architectures. Thus the code is fully portable to a variety of computing platforms such as uniprocessor workstations, symmetric multiprocessors, clusters of workstations, and massively parallel platforms. Third, CHAD utilizes a variable explicit/implicit upwind method for convection that improves computational efficiency in flows that have large velocity Courant number variations due to velocity of mesh size variations. Fourth, CHAD is designed to also simulate shock hydrodynamics involving multimaterial anisotropic behavior under high shear. The authors will discuss CHAD capabilities and show several sample calculations showing the strengths and weaknesses of CHAD.« less

A scalable PC-based parallel computer for lattice QCD

NASA Astrophysics Data System (ADS)

Fodor, Z.; Katz, S. D.; Pappa, G.

2003-05-01

A PC-based parallel computer for medium/large scale lattice QCD simulations is suggested. The Eo¨tvo¨s Univ., Inst. Theor. Phys. cluster consists of 137 Intel P4-1.7GHz nodes. Gigabit Ethernet cards are used for nearest neighbor communication in a two-dimensional mesh. The sustained performance for dynamical staggered (wilson) quarks on large lattices is around 70(110) GFlops. The exceptional price/performance ratio is below $1/Mflop.

Moving and adaptive grid methods for compressible flows

NASA Technical Reports Server (NTRS)

Trepanier, Jean-Yves; Camarero, Ricardo

1995-01-01

This paper describes adaptive grid methods developed specifically for compressible flow computations. The basic flow solver is a finite-volume implementation of Roe's flux difference splitting scheme or arbitrarily moving unstructured triangular meshes. The grid adaptation is performed according to geometric and flow requirements. Some results are included to illustrate the potential of the methodology.

The Data Transfer Kit: A geometric rendezvous-based tool for multiphysics data transfer

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

Slattery, S. R.; Wilson, P. P. H.; Pawlowski, R. P.

2013-07-01

The Data Transfer Kit (DTK) is a software library designed to provide parallel data transfer services for arbitrary physics components based on the concept of geometric rendezvous. The rendezvous algorithm provides a means to geometrically correlate two geometric domains that may be arbitrarily decomposed in a parallel simulation. By repartitioning both domains such that they have the same geometric domain on each parallel process, efficient and load balanced search operations and data transfer can be performed at a desirable algorithmic time complexity with low communication overhead relative to other types of mapping algorithms. With the increased development efforts in multiphysicsmore » simulation and other multiple mesh and geometry problems, generating parallel topology maps for transferring fields and other data between geometric domains is a common operation. The algorithms used to generate parallel topology maps based on the concept of geometric rendezvous as implemented in DTK are described with an example using a conjugate heat transfer calculation and thermal coupling with a neutronics code. In addition, we provide the results of initial scaling studies performed on the Jaguar Cray XK6 system at Oak Ridge National Laboratory for a worse-case-scenario problem in terms of algorithmic complexity that shows good scaling on 0(1 x 104) cores for topology map generation and excellent scaling on 0(1 x 105) cores for the data transfer operation with meshes of O(1 x 109) elements. (authors)« less

Full-Carpet Design of a Low-Boom Demonstrator Concept

NASA Technical Reports Server (NTRS)

Ordaz, Irian; Wintzer, Mathias; Rallabhandi, Sriram K.

2015-01-01

The Cart3D adjoint-based design framework is used to mitigate the undesirable o -track sonic boom properties of a demonstrator concept designed for low-boom directly under the flight path. First, the requirements of a Cart3D design mesh are determined using a high-fidelity mesh adapted to minimize the discretization error of the CFD analysis. Low-boom equivalent area targets are then generated at the under-track and one off-track azimuthal position for the baseline configuration. The under-track target is generated using a trim- feasible low-boom target generation process, ensuring that the final design is not only low-boom, but also trimmed at the specified flight condition. The o -track equivalent area target is generated by minimizing the A-weighted loudness using an efficient adjoint-based approach. The configuration outer mold line is then parameterized and optimized to match the off-body pressure distributions prescribed by the low-boom targets. The numerical optimizer uses design gradients which are calculated using the Cart3D adjoint- based design capability. Optimization constraints are placed on the geometry to satisfy structural feasibility. The low-boom properties of the final design are verified using the adaptive meshing approach. This analysis quantifies the error associated with the CFD mesh that is used for design. Finally, an alternate mesh construction and target positioning approach offering greater computational efficiency is demonstrated and verified.

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

Koniges, A.E.; Craddock, G.G.; Schnack, D.D.

The purpose of the workshop was to assemble workers, both within and outside of the fusion-related computations areas, for discussion regarding the issues of dynamically adaptive gridding. There were three invited talks related to adaptive gridding application experiences in various related fields of computational fluid dynamics (CFD), and nine short talks reporting on the progress of adaptive techniques in the specific areas of scrape-off-layer (SOL) modeling and magnetohydrodynamic (MHD) stability. Adaptive mesh methods have been successful in a number of diverse fields of CFD for over a decade. The method involves dynamic refinement of computed field profiles in a waymore » that disperses uniformly the numerical errors associated with discrete approximations. Because the process optimizes computational effort, adaptive mesh methods can be used to study otherwise the intractable physical problems that involve complex boundary shapes or multiple spatial/temporal scales. Recent results indicate that these adaptive techniques will be required for tokamak fluid-based simulations involving the diverted tokamak SOL modeling and MHD simulations problems related to the highest priority ITER relevant issues.Individual papers are indexed separately on the energy data bases.« less

RICH: OPEN-SOURCE HYDRODYNAMIC SIMULATION ON A MOVING VORONOI MESH

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

Yalinewich, Almog; Steinberg, Elad; Sari, Re’em

2015-02-01

We present here RICH, a state-of-the-art two-dimensional hydrodynamic code based on Godunov’s method, on an unstructured moving mesh (the acronym stands for Racah Institute Computational Hydrodynamics). This code is largely based on the code AREPO. It differs from AREPO in the interpolation and time-advancement schemeS as well as a novel parallelization scheme based on Voronoi tessellation. Using our code, we study the pros and cons of a moving mesh (in comparison to a static mesh). We also compare its accuracy to other codes. Specifically, we show that our implementation of external sources and time-advancement scheme is more accurate and robustmore » than is AREPO when the mesh is allowed to move. We performed a parameter study of the cell rounding mechanism (Lloyd iterations) and its effects. We find that in most cases a moving mesh gives better results than a static mesh, but it is not universally true. In the case where matter moves in one way and a sound wave is traveling in the other way (such that relative to the grid the wave is not moving) a static mesh gives better results than a moving mesh. We perform an analytic analysis for finite difference schemes that reveals that a Lagrangian simulation is better than a Eulerian simulation in the case of a highly supersonic flow. Moreover, we show that Voronoi-based moving mesh schemes suffer from an error, which is resolution independent, due to inconsistencies between the flux calculation and the change in the area of a cell. Our code is publicly available as open source and designed in an object-oriented, user-friendly way that facilitates incorporation of new algorithms and physical processes.« less

Center for Efficient Exascale Discretizations Software Suite

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

Kolev, Tzanio; Dobrev, Veselin; Tomov, Vladimir

The CEED Software suite is a collection of generally applicable software tools focusing on the following computational motives: PDE discretizations on unstructured meshes, high-order finite element and spectral element methods and unstructured adaptive mesh refinement. All of this software is being developed as part of CEED, a co-design Center for Efficient Exascale Discretizations, within DOE's Exascale Computing Project (ECP) program.

Toward automatic finite element analysis

NASA Technical Reports Server (NTRS)

Kela, Ajay; Perucchio, Renato; Voelcker, Herbert

1987-01-01

Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.

A manual for PARTI runtime primitives, revision 1

NASA Technical Reports Server (NTRS)

Das, Raja; Saltz, Joel; Berryman, Harry

1991-01-01

Primitives are presented that are designed to help users efficiently program irregular problems (e.g., unstructured mesh sweeps, sparse matrix codes, adaptive mesh partial differential equations solvers) on distributed memory machines. These primitives are also designed for use in compilers for distributed memory multiprocessors. Communications patterns are captured at runtime, and the appropriate send and receive messages are automatically generated.

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.

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

Selecting criteria for the right prosthesis in defect of the abdominal wall surgery.

PubMed

Mohamed, H; Ion, D; Serban, M B; Ciurea, M

2009-01-01

The article is debating a theme of great interest for the defect of the abdominal wall surgery--the use of biocompatible prosthesis. The surgeon is often confused by the avalanche of offers made by the mesh producers, making it mandatory for him to know very well the behavior of these alloplastic structures in the tissue environment. From this point of view, we have discussed both the physicochemical properties and the histological reaction brought by the most common type of meshes: polypropylene, polyethylene - tereftalat, polytetrafluorideethylene. This presentation brings out the minimal but mandatory criteria for any mesh to be accepted, but also the criteria that need to be taken into consideration when we try to improve the qualities of the mesh closer to the desideratum of the "ideal mesh". The main conclusion of this review is that we have to change the myth of the "ideal mesh" with "the right chosen mesh", that based on its chemical, physical, structural and biological qualities will adapt perfectly first to the patient's needs and second to the surgeon's needs.

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.

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

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.

An Efficient Radial Basis Function Mesh Deformation Scheme within an Adjoint-Based Aerodynamic Optimization Framework

NASA Astrophysics Data System (ADS)

Poirier, Vincent

Mesh deformation schemes play an important role in numerical aerodynamic optimization. As the aerodynamic shape changes, the computational mesh must adapt to conform to the deformed geometry. In this work, an extension to an existing fast and robust Radial Basis Function (RBF) mesh movement scheme is presented. Using a reduced set of surface points to define the mesh deformation increases the efficiency of the RBF method; however, at the cost of introducing errors into the parameterization by not recovering the exact displacement of all surface points. A secondary mesh movement is implemented, within an adjoint-based optimization framework, to eliminate these errors. The proposed scheme is tested within a 3D Euler flow by reducing the pressure drag while maintaining lift of a wing-body configured Boeing-747 and an Onera-M6 wing. As well, an inverse pressure design is executed on the Onera-M6 wing and an inverse span loading case is presented for a wing-body configured DLR-F6 aircraft.

Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2012-01-01

The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

Evolution of the mandibular mesh implant.

PubMed

Salyer, K E; Johns, D F; Holmes, R E; Layton, J G

1977-07-01

Between 1960 and 1972, the Dallas Veterans Administration Hospital Maxillofacial Research Laboratory developed and made over 150 cast-mesh implants. Successive designs were ovoid, circular, and double-lumened in cross section to improve implant strength, surface area for bioattachment, and adjustability. Sleeves, collars, and bows were employed in the assembly of these implants, with an acrylic condylar head attached when indicated. In 1972, our laboratory developed a mandibular mesh tray, cast in one piece on a single sprue, with preservation of the vertically adjustable ramus. Stainless steel replaced Vitallium because of its greater malleability. Essentially, a lost-wax technique is used to cast the mesh tray. The model of a mandibular segment is duplicated as a refractory model. Mesh wax, made in our own custom-made die, is adapted to the refractory model. The unit is then sprued and invested. The wax is fired our of the mold in a gas furnace. Casting is done by the transferral of molten stainless steel from the crucible to the mold by centrifugal force in an electro-induction casting machine. Other mesh implants that have been developed are made from wire mesh, Dacron mesh, cast Ticonium, and hydroformed titanium.

Characterizing mesh size distributions (MSDs) in thermosetting materials using a high-pressure system.

PubMed

Larché, J-F; Seynaeve, J-M; Voyard, G; Bussière, P-O; Gardette, J-L

2011-04-21

The thermoporosimetry method was adapted to determine the mesh size distribution of an acrylate thermoset clearcoat. This goal was achieved by increasing the solvent rate transfer by increasing the pressure and temperature. A comparison of the results obtained using this approach with those obtained by DMA (dynamic mechanical analysis) underlined the accuracy of thermoporosimetry in characterizing the macromolecular architecture of thermosets. The thermoporosimetry method was also used to analyze the effects of photoaging on cross-linking, which result from the photodegradation of the acrylate thermoset. It was found that the formation of a three-dimensional network followed by densification generates a modification of the average mesh size that leads to a dramatic decrease of the meshes of the polymer.

Monte Carlo charged-particle tracking and energy deposition on a Lagrangian mesh.

PubMed

Yuan, J; Moses, G A; McKenty, P W

2005-10-01

A Monte Carlo algorithm for alpha particle tracking and energy deposition on a cylindrical computational mesh in a Lagrangian hydrodynamics code used for inertial confinement fusion (ICF) simulations is presented. The straight line approximation is used to follow propagation of "Monte Carlo particles" which represent collections of alpha particles generated from thermonuclear deuterium-tritium (DT) reactions. Energy deposition in the plasma is modeled by the continuous slowing down approximation. The scheme addresses various aspects arising in the coupling of Monte Carlo tracking with Lagrangian hydrodynamics; such as non-orthogonal severely distorted mesh cells, particle relocation on the moving mesh and particle relocation after rezoning. A comparison with the flux-limited multi-group diffusion transport method is presented for a polar direct drive target design for the National Ignition Facility. Simulations show the Monte Carlo transport method predicts about earlier ignition than predicted by the diffusion method, and generates higher hot spot temperature. Nearly linear speed-up is achieved for multi-processor parallel simulations.

In situ visualization and data analysis for turbidity currents simulation

NASA Astrophysics Data System (ADS)

Camata, Jose J.; Silva, Vítor; Valduriez, Patrick; Mattoso, Marta; Coutinho, Alvaro L. G. A.

2018-01-01

Turbidity currents are underflows responsible for sediment deposits that generate geological formations of interest for the oil and gas industry. LibMesh-sedimentation is an application built upon the libMesh library to simulate turbidity currents. In this work, we present the integration of libMesh-sedimentation with in situ visualization and in transit data analysis tools. DfAnalyzer is a solution based on provenance data to extract and relate strategic simulation data in transit from multiple data for online queries. We integrate libMesh-sedimentation and ParaView Catalyst to perform in situ data analysis and visualization. We present a parallel performance analysis for two turbidity currents simulations showing that the overhead for both in situ visualization and in transit data analysis is negligible. We show that our tools enable monitoring the sediments appearance at runtime and steer the simulation based on the solver convergence and visual information on the sediment deposits, thus enhancing the analytical power of turbidity currents simulations.

Quasi-Optimal Elimination Trees for 2D Grids with Singularities

DOE PAGES

Paszyńska, A.; Paszyński, M.; Jopek, K.; ...

2015-01-01

We consmore » truct quasi-optimal elimination trees for 2D finite element meshes with singularities. These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination process model the execution of the multifrontal algorithms in serial and in parallel shared-memory executions. Since the meshes considered are a subspace of all possible mesh partitions, we call these minimizers quasi-optimal. We minimize the cost functionals using dynamic programming. Finding these minimizers is more computationally expensive than solving the original algebraic system. Nevertheless, from the insights provided by the analysis of the dynamic programming minima, we propose a heuristic construction of the elimination trees that has cost O N e log ⁡ N e , where N e is the number of elements in the mesh. We show that this heuristic ordering has similar computational cost to the quasi-optimal elimination trees found with dynamic programming and outperforms state-of-the-art alternatives in our numerical experiments.« less

Quasi-Optimal Elimination Trees for 2D Grids with Singularities

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

Paszyńska, A.; Paszyński, M.; Jopek, K.

We consmore » truct quasi-optimal elimination trees for 2D finite element meshes with singularities. These trees minimize the complexity of the solution of the discrete system. The computational cost estimates of the elimination process model the execution of the multifrontal algorithms in serial and in parallel shared-memory executions. Since the meshes considered are a subspace of all possible mesh partitions, we call these minimizers quasi-optimal. We minimize the cost functionals using dynamic programming. Finding these minimizers is more computationally expensive than solving the original algebraic system. Nevertheless, from the insights provided by the analysis of the dynamic programming minima, we propose a heuristic construction of the elimination trees that has cost O N e log ⁡ N e , where N e is the number of elements in the mesh. We show that this heuristic ordering has similar computational cost to the quasi-optimal elimination trees found with dynamic programming and outperforms state-of-the-art alternatives in our numerical experiments.« less

Simulation of geothermal water extraction in heterogeneous reservoirs using dynamic unstructured mesh optimisation

NASA Astrophysics Data System (ADS)

Salinas, P.; Pavlidis, D.; Jacquemyn, C.; Lei, Q.; Xie, Z.; Pain, C.; Jackson, M.

2017-12-01

It is well known that the pressure gradient into a production well increases with decreasing distance to the well. To properly capture the local pressure drawdown into the well a high grid or mesh resolution is required; moreover, the location of the well must be captured accurately. In conventional simulation models, the user must interact with the model to modify grid resolution around wells of interest, and the well location is approximated on a grid defined early in the modelling process.We report a new approach for improved simulation of near wellbore flow in reservoir scale models through the use of dynamic mesh optimisation and the recently presented double control volume finite element method. Time is discretized using an adaptive, implicit approach. Heterogeneous geologic features are represented as volumes bounded by surfaces. Within these volumes, termed geologic domains, the material properties are constant. Up-, cross- or down-scaling of material properties during dynamic mesh optimization is not required, as the properties are uniform within each geologic domain. A given model typically contains numerous such geologic domains. Wells are implicitly coupled with the domain, and the fluid flows is modelled inside the wells. The method is novel for two reasons. First, a fully unstructured tetrahedral mesh is used to discretize space, and the spatial location of the well is specified via a line vector, ensuring its location even if the mesh is modified during the simulation. The well location is therefore accurately captured, the approach allows complex well trajectories and wells with many laterals to be modelled. Second, computational efficiency is increased by use of dynamic mesh optimization, in which an unstructured mesh adapts in space and time to key solution fields (preserving the geometry of the geologic domains), such as pressure, velocity or temperature, this also increases the quality of the solutions by placing higher resolution where required to reduce an error metric based on the Hessian of the field. This allows the local pressure drawdown to be captured without user¬ driven modification of the mesh. We demonstrate that the method has wide application in reservoir ¬scale models of geothermal fields, and regional models of groundwater resources.

A taxonomy and comparison of parallel block multi-level preconditioners for the incompressible Navier-Stokes equations.

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

Shadid, John Nicolas; Elman, Howard; Shuttleworth, Robert R.

2007-04-01

In recent years, considerable effort has been placed on developing efficient and robust solution algorithms for the incompressible Navier-Stokes equations based on preconditioned Krylov methods. These include physics-based methods, such as SIMPLE, and purely algebraic preconditioners based on the approximation of the Schur complement. All these techniques can be represented as approximate block factorization (ABF) type preconditioners. The goal is to decompose the application of the preconditioner into simplified sub-systems in which scalable multi-level type solvers can be applied. In this paper we develop a taxonomy of these ideas based on an adaptation of a generalized approximate factorization of themore » Navier-Stokes system first presented in [25]. This taxonomy illuminates the similarities and differences among these preconditioners and the central role played by efficient approximation of certain Schur complement operators. We then present a parallel computational study that examines the performance of these methods and compares them to an additive Schwarz domain decomposition (DD) algorithm. Results are presented for two and three-dimensional steady state problems for enclosed domains and inflow/outflow systems on both structured and unstructured meshes. The numerical experiments are performed using MPSalsa, a stabilized finite element code.« less

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

DOE PAGES

Ferguson, Jared O.; Jablonowski, Christiane; Johansen, Hans; ...

2016-11-09

Adaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This study aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interactionmore » of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the best accuracy for cost. The simulations show that the model can accurately resolve key local features without requiring global high-resolution grids. The adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse–fine interfaces. Finally and furthermore, the AMR grids keep any degradations of the large-scale smooth flows to a minimum.« less

Analyzing the Adaptive Mesh Refinement (AMR) Characteristics of a High-Order 2D Cubed-Sphere Shallow-Water Model

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

Ferguson, Jared O.; Jablonowski, Christiane; Johansen, Hans

Adaptive mesh refinement (AMR) is a technique that has been featured only sporadically in atmospheric science literature. This study aims to demonstrate the utility of AMR for simulating atmospheric flows. Several test cases are implemented in a 2D shallow-water model on the sphere using the Chombo-AMR dynamical core. This high-order finite-volume model implements adaptive refinement in both space and time on a cubed-sphere grid using a mapped-multiblock mesh technique. The tests consist of the passive advection of a tracer around moving vortices, a steady-state geostrophic flow, an unsteady solid-body rotation, a gravity wave impinging on a mountain, and the interactionmore » of binary vortices. Both static and dynamic refinements are analyzed to determine the strengths and weaknesses of AMR in both complex flows with small-scale features and large-scale smooth flows. The different test cases required different AMR criteria, such as vorticity or height-gradient based thresholds, in order to achieve the best accuracy for cost. The simulations show that the model can accurately resolve key local features without requiring global high-resolution grids. The adaptive grids are able to track features of interest reliably without inducing noise or visible distortions at the coarse–fine interfaces. Finally and furthermore, the AMR grids keep any degradations of the large-scale smooth flows to a minimum.« less

Unstructured Grid Adaptation: Status, Potential Impacts, and Recommended Investments Toward CFD Vision 2030

NASA Technical Reports Server (NTRS)

Park, Michael A.; Krakos, Joshua A.; Michal, Todd; Loseille, Adrien; Alonso, Juan J.

2016-01-01

Unstructured grid adaptation is a powerful tool to control discretization error for Computational Fluid Dynamics (CFD). It has enabled key increases in the accuracy, automation, and capacity of some fluid simulation applications. Slotnick et al. provides a number of case studies in the CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences to illustrate the current state of CFD capability and capacity. The authors forecast the potential impact of emerging High Performance Computing (HPC) environments forecast in the year 2030 and identify that mesh generation and adaptivity continue to be significant bottlenecks in the CFD work flow. These bottlenecks may persist because very little government investment has been targeted in these areas. To motivate investment, the impacts of improved grid adaptation technologies are identified. The CFD Vision 2030 Study roadmap and anticipated capabilities in complementary disciplines are quoted to provide context for the progress made in grid adaptation in the past fifteen years, current status, and a forecast for the next fifteen years with recommended investments. These investments are specific to mesh adaptation and impact other aspects of the CFD process. Finally, a strategy is identified to diffuse grid adaptation technology into production CFD work flows.

On Multi-Dimensional Unstructured Mesh Adaption

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1999-01-01

Anisotropic unstructured mesh adaption is developed for a truly multi-dimensional upwind fluctuation splitting scheme, as applied to scalar advection-diffusion. The adaption is performed locally using edge swapping, point insertion/deletion, and nodal displacements. Comparisons are made versus the current state of the art for aggressive anisotropic unstructured adaption, which is based on a posteriori error estimates. Demonstration of both schemes to model problems, with features representative of compressible gas dynamics, show the present method to be superior to the a posteriori adaption for linear advection. The performance of the two methods is more similar when applied to nonlinear advection, with a difference in the treatment of shocks. The a posteriori adaption can excessively cluster points to a shock, while the present multi-dimensional scheme tends to merely align with a shock, using fewer nodes. As a consequence of this alignment tendency, an implementation of eigenvalue limiting for the suppression of expansion shocks is developed for the multi-dimensional distribution scheme. The differences in the treatment of shocks by the adaption schemes, along with the inherently low levels of artificial dissipation in the fluctuation splitting solver, suggest the present method is a strong candidate for applications to compressible gas dynamics.

Reactive Transport Modeling of Induced Calcite Precipitation Reaction Fronts in Porous Media Using A Parallel, Fully Coupled, Fully Implicit Approach

NASA Astrophysics Data System (ADS)

Guo, L.; Huang, H.; Gaston, D.; Redden, G. D.; Fox, D. T.; Fujita, Y.

2010-12-01

Inducing mineral precipitation in the subsurface is one potential strategy for immobilizing trace metal and radionuclide contaminants. Generating mineral precipitates in situ can be achieved by manipulating chemical conditions, typically through injection or in situ generation of reactants. How these reactants transport, mix and react within the medium controls the spatial distribution and composition of the resulting mineral phases. Multiple processes, including fluid flow, dispersive/diffusive transport of reactants, biogeochemical reactions and changes in porosity-permeability, are tightly coupled over a number of scales. Numerical modeling can be used to investigate the nonlinear coupling effects of these processes which are quite challenging to explore experimentally. Many subsurface reactive transport simulators employ a de-coupled or operator-splitting approach where transport equations and batch chemistry reactions are solved sequentially. However, such an approach has limited applicability for biogeochemical systems with fast kinetics and strong coupling between chemical reactions and medium properties. A massively parallel, fully coupled, fully implicit Reactive Transport simulator (referred to as “RAT”) based on a parallel multi-physics object-oriented simulation framework (MOOSE) has been developed at the Idaho National Laboratory. Within this simulator, systems of transport and reaction equations can be solved simultaneously in a fully coupled, fully implicit manner using the Jacobian Free Newton-Krylov (JFNK) method with additional advanced computing capabilities such as (1) physics-based preconditioning for solution convergence acceleration, (2) massively parallel computing and scalability, and (3) adaptive mesh refinements for 2D and 3D structured and unstructured mesh. The simulator was first tested against analytical solutions, then applied to simulating induced calcium carbonate mineral precipitation in 1D columns and 2D flow cells as analogs to homogeneous and heterogeneous porous media, respectively. In 1D columns, calcium carbonate mineral precipitation was driven by urea hydrolysis catalyzed by urease enzyme, and in 2D flow cells, calcium carbonate mineral forming reactants were injected sequentially, forming migrating reaction fronts that are typically highly nonuniform. The RAT simulation results for the spatial and temporal distributions of precipitates, reaction rates and major species in the system, and also for changes in porosity and permeability, were compared to both laboratory experimental data and computational results obtained using other reactive transport simulators. The comparisons demonstrate the ability of RAT to simulate complex nonlinear systems and the advantages of fully coupled approaches, over de-coupled methods, for accurate simulation of complex, dynamic processes such as engineered mineral precipitation in subsurface environments.

A 3D front tracking method on a CPU/GPU system

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

Bo, Wurigen; Grove, John

2011-01-21

We describe the method to port a sequential 3D interface tracking code to a GPU with CUDA. The interface is represented as a triangular mesh. Interface geometry properties and point propagation are performed on a GPU. Interface mesh adaptation is performed on a CPU. The convergence of the method is assessed from the test problems with given velocity fields. Performance results show overall speedups from 11 to 14 for the test problems under mesh refinement. We also briefly describe our ongoing work to couple the interface tracking method with a hydro solver.

3-D Electromagnetic field analysis of wireless power transfer system using K computer

NASA Astrophysics Data System (ADS)

Kawase, Yoshihiro; Yamaguchi, Tadashi; Murashita, Masaya; Tsukada, Shota; Ota, Tomohiro; Yamamoto, Takeshi

2018-05-01

We analyze the electromagnetic field of a wireless power transfer system using the 3-D parallel finite element method on K computer, which is a super computer in Japan. It is clarified that the electromagnetic field of the wireless power transfer system can be analyzed in a practical time using the parallel computation on K computer, moreover, the accuracy of the loss calculation becomes better as the mesh division of the shield becomes fine.

A multilevel correction adaptive finite element method for Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

Modeling of heterogeneous elastic materials by the multiscale hp-adaptive finite element method

NASA Astrophysics Data System (ADS)

Klimczak, Marek; Cecot, Witold

2018-01-01

We present an enhancement of the multiscale finite element method (MsFEM) by combining it with the hp-adaptive FEM. Such a discretization-based homogenization technique is a versatile tool for modeling heterogeneous materials with fast oscillating elasticity coefficients. No assumption on periodicity of the domain is required. In order to avoid direct, so-called overkill mesh computations, a coarse mesh with effective stiffness matrices is used and special shape functions are constructed to account for the local heterogeneities at the micro resolution. The automatic adaptivity (hp-type at the macro resolution and h-type at the micro resolution) increases efficiency of computation. In this paper details of the modified MsFEM are presented and a numerical test performed on a Fichera corner domain is presented in order to validate the proposed approach.

Adaptive reconnection-based arbitrary Lagrangian Eulerian method

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

Bo, Wurigen; Shashkov, Mikhail

We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less

Adaptive reconnection-based arbitrary Lagrangian Eulerian method

DOE PAGES

Bo, Wurigen; Shashkov, Mikhail

2015-07-21

We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less