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Sample records for adaptive meshing algorithms

  1. An Adaptive Mesh Algorithm: Mesh Structure and Generation

    SciTech Connect

    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 by 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

  2. 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.

  3. Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo

    NASA Astrophysics Data System (ADS)

    Garcia, Alejandro L.; Bell, John B.; Crutchfield, William Y.; Alder, Berni J.

    1999-09-01

    Adaptive mesh and algorithm refinement (AMAR) embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement (AMR) hierarchy. The coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of AMR. Direct simulation Monte Carlo (DSMC) is used as the particle algorithm embedded within a Godunov-type compressible Navier-Stokes solver. Several examples are presented and compared with purely continuum calculations.

  4. An Adaptive Mesh Algorithm: Mapping the Mesh Variables

    SciTech Connect

    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.

  5. Adaptive Mesh Refinement Algorithms for Parallel Unstructured Finite Element Codes

    SciTech Connect

    Parsons, I D; Solberg, J M

    2006-02-03

    This project produced algorithms for and software implementations of adaptive mesh refinement (AMR) methods for solving practical solid and thermal mechanics problems on multiprocessor parallel computers using unstructured finite element meshes. The overall goal is to provide computational solutions that are accurate to some prescribed tolerance, and adaptivity is the correct path toward this goal. These new tools will enable analysts to conduct more reliable simulations at reduced cost, both in terms of analyst and computer time. Previous academic research in the field of adaptive mesh refinement has produced a voluminous literature focused on error estimators and demonstration problems; relatively little progress has been made on producing efficient implementations suitable for large-scale problem solving on state-of-the-art computer systems. Research issues that were considered include: effective error estimators for nonlinear structural mechanics; local meshing at irregular geometric boundaries; and constructing efficient software for parallel computing environments.

  6. A structured multi-block solution-adaptive mesh algorithm with mesh quality assessment

    NASA Technical Reports Server (NTRS)

    Ingram, Clint L.; Laflin, Kelly R.; Mcrae, D. Scott

    1995-01-01

    The dynamic solution adaptive grid algorithm, DSAGA3D, is extended to automatically adapt 2-D structured multi-block grids, including adaption of the block boundaries. The extension is general, requiring only input data concerning block structure, connectivity, and boundary conditions. Imbedded grid singular points are permitted, but must be prevented from moving in space. Solutions for workshop cases 1 and 2 are obtained on multi-block grids and illustrate both increased resolution of and alignment with the solution. A mesh quality assessment criteria is proposed to determine how well a given mesh resolves and aligns with the solution obtained upon it. The criteria is used to evaluate the grid quality for solutions of workshop case 6 obtained on both static and dynamically adapted grids. The results indicate that this criteria shows promise as a means of evaluating resolution.

  7. An adaptive grid-based all hexahedral meshing algorithm based on 2-refinement.

    SciTech Connect

    Edgel, Jared; Benzley, Steven E.; Owen, Steven James

    2010-08-01

    Most adaptive mesh generation algorithms employ a 3-refinement method. This method, although easy to employ, provides a mesh that is often too coarse in some areas and over refined in other areas. Because this method generates 27 new hexes in place of a single hex, there is little control on mesh density. This paper presents an adaptive all-hexahedral grid-based meshing algorithm that employs a 2-refinement method. 2-refinement is based on dividing the hex to be refined into eight new hexes. This method allows a greater control on mesh density when compared to a 3-refinement procedure. This adaptive all-hexahedral meshing algorithm provides a mesh that is efficient for analysis by providing a high element density in specific locations and a reduced mesh density in other areas. In addition, this tool can be effectively used for inside-out hexahedral grid based schemes, using Cartesian structured grids for the base mesh, which have shown great promise in accommodating automatic all-hexahedral algorithms. This adaptive all-hexahedral grid-based meshing algorithm employs a 2-refinement insertion method. This allows greater control on mesh density when compared to 3-refinement methods. This algorithm uses a two layer transition zone to increase element quality and keeps transitions from lower to higher mesh densities smooth. Templates were introduced to allow both convex and concave refinement.

  8. Experiences with an adaptive mesh refinement algorithm in numerical relativity.

    NASA Astrophysics Data System (ADS)

    Choptuik, M. W.

    An implementation of the Berger/Oliger mesh refinement algorithm for a model problem in numerical relativity is described. The principles of operation of the method are reviewed and its use in conjunction with leap-frog schemes is considered. The performance of the algorithm is illustrated with results from a study of the Einstein/massless scalar field equations in spherical symmetry.

  9. Parallel paving: An algorithm for generating distributed, adaptive, all-quadrilateral meshes on parallel computers

    SciTech Connect

    Lober, R.R.; Tautges, T.J.; Vaughan, C.T.

    1997-03-01

    Paving is an automated mesh generation algorithm which produces all-quadrilateral elements. It can additionally generate these elements in varying sizes such that the resulting mesh adapts to a function distribution, such as an error function. While powerful, conventional paving is a very serial algorithm in its operation. Parallel paving is the extension of serial paving into parallel environments to perform the same meshing functions as conventional paving only on distributed, discretized models. This extension allows large, adaptive, parallel finite element simulations to take advantage of paving`s meshing capabilities for h-remap remeshing. A significantly modified version of the CUBIT mesh generation code has been developed to host the parallel paving algorithm and demonstrate its capabilities on both two dimensional and three dimensional surface geometries and compare the resulting parallel produced meshes to conventionally paved meshes for mesh quality and algorithm performance. Sandia`s {open_quotes}tiling{close_quotes} dynamic load balancing code has also been extended to work with the paving algorithm to retain parallel efficiency as subdomains undergo iterative mesh refinement.

  10. 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.

  11. An Adaptive Mesh Algorithm for Evolving Surfaces: Simulations of Drop Breakup and Coalescence

    NASA Astrophysics Data System (ADS)

    Cristini, Vittorio; Bławzdziewicz, Jerzy; Loewenberg, Michael

    2001-04-01

    An algorithm is presented for the adaptive restructuring of meshes on evolving surfaces. The resolution of the relevant local length scale is maintained everywhere with prescribed accuracy through the minimization of an appropriate mesh energy function by a sequence of local restructuring operations. The resulting discretization depends on the instantaneous configuration of the surface but is insensitive to the deformation history. Application of the adaptive discretization algorithm is illustrated with three-dimensional boundary-integral simulations of deformable drops in Stokes flow. The results show that the algorithm can accurately resolve detailed features of deformed fluid interfaces, including slender filaments associated with drop breakup and dimpled regions associated with drop coalescence. Our algorithm should be useful in a variety of fields, including computational fluid dynamics, image processing, geographical information systems, and biomedical engineering problems.

  12. Adaptive-mesh-based algorithm for fluorescence molecular tomography using an analytical solution

    NASA Astrophysics Data System (ADS)

    Wang, Daifa; Song, Xiaolei; Bai, Jing

    2007-07-01

    Fluorescence molecular tomography (FMT) has become an important method for in-vivo imaging of small animals. It has been widely used for tumor genesis, cancer detection, metastasis, drug discovery, and gene therapy. In this study, an algorithm for FMT is proposed to obtain accurate and fast reconstruction by combining an adaptive mesh refinement technique and an analytical solution of diffusion equation. Numerical studies have been performed on a parallel plate FMT system with matching fluid. The reconstructions obtained show that the algorithm is efficient in computation time, and they also maintain image quality.

  13. Parallel Adaptive Mesh Refinement

    SciTech Connect

    Diachin, L; Hornung, R; Plassmann, P; WIssink, A

    2005-03-04

    As large-scale, parallel computers have become more widely available and numerical models and algorithms have advanced, the range of physical phenomena that can be simulated has expanded dramatically. Many important science and engineering problems exhibit solutions with localized behavior where highly-detailed salient features or large gradients appear in certain regions which are separated by much larger regions where the solution is smooth. Examples include chemically-reacting flows with radiative heat transfer, high Reynolds number flows interacting with solid objects, and combustion problems where the flame front is essentially a two-dimensional sheet occupying a small part of a three-dimensional domain. Modeling such problems numerically requires approximating the governing partial differential equations on a discrete domain, or grid. Grid spacing is an important factor in determining the accuracy and cost of a computation. A fine grid may be needed to resolve key local features while a much coarser grid may suffice elsewhere. Employing a fine grid everywhere may be inefficient at best and, at worst, may make an adequately resolved simulation impractical. Moreover, the location and resolution of fine grid required for an accurate solution is a dynamic property of a problem's transient features and may not be known a priori. Adaptive mesh refinement (AMR) is a technique that can be used with both structured and unstructured meshes to adjust local grid spacing dynamically to capture solution features with an appropriate degree of resolution. Thus, computational resources can be focused where and when they are needed most to efficiently achieve an accurate solution without incurring the cost of a globally-fine grid. Figure 1.1 shows two example computations using AMR; on the left is a structured mesh calculation of a impulsively-sheared contact surface and on the right is the fuselage and volume discretization of an RAH-66 Comanche helicopter [35]. Note the

  14. 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.

  15. A 3-D adaptive mesh refinement algorithm for multimaterial gas dynamics

    SciTech Connect

    Puckett, E.G. ); Saltzman, J.S. )

    1991-08-12

    Adaptive Mesh Refinement (AMR) in conjunction with high order upwind finite difference methods has been used effectively on a variety of problems. In this paper we discuss an implementation of an AMR finite difference method that solves the equations of gas dynamics with two material species in three dimensions. An equation for the evolution of volume fractions augments the gas dynamics system. The material interface is preserved and tracked from the volume fractions using a piecewise linear reconstruction technique. 14 refs., 4 figs.

  16. TRIM: A finite-volume MHD algorithm for an unstructured adaptive mesh

    SciTech Connect

    Schnack, D.D.; Lottati, I.; Mikic, Z.

    1995-07-01

    The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.

  17. A solution-adaptive mesh algorithm for dynamic/static refinement of two and three dimensional grids

    NASA Technical Reports Server (NTRS)

    Benson, Rusty A.; Mcrae, D. S.

    1991-01-01

    An adaptive grid algorithm has been developed in two and three dimensions that can be used dynamically with a solver or as part of a grid refinement process. The algorithm employs a transformation from the Cartesian coordinate system to a general coordinate space, which is defined as a parallelepiped in three dimensions. A weighting function, independent for each coordinate direction, is developed that will provide the desired refinement criteria in regions of high solution gradient. The adaptation is performed in the general coordinate space and the new grid locations are returned to the Cartesian space via a simple, one-step inverse mapping. The algorithm for relocation of the mesh points in the parametric space is based on the center of mass for distributed weights. Dynamic solution-adaptive results are presented for laminar flows in two and three dimensions.

  18. 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.

  19. 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.

  20. 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.

  1. 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.

  2. A Parallel Second-Order Adaptive Mesh Algorithm for Incompressible Flow in Porous Media

    SciTech Connect

    Pau, George Shu Heng; Almgren, Ann S.; Bell, John B.; Lijewski, Michael J.

    2008-04-01

    In this paper we present a second-order accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase 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 areadvanced multiple steps to reach the same time as the coarse grids and the data atdifferent 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 behavior of the method.

  3. MPDATA error estimator for mesh adaptivity

    NASA Astrophysics Data System (ADS)

    Szmelter, Joanna; Smolarkiewicz, Piotr K.

    2006-04-01

    In multidimensional positive definite advection transport algorithm (MPDATA) the leading error as well as the first- and second-order solutions are known explicitly by design. This property is employed to construct refinement indicators for mesh adaptivity. Recent progress with the edge-based formulation of MPDATA facilitates the use of the method in an unstructured-mesh environment. In particular, the edge-based data structure allows for flow solvers to operate on arbitrary hybrid meshes, thereby lending itself to implementations of various mesh adaptivity techniques. A novel unstructured-mesh nonoscillatory forward-in-time (NFT) solver for compressible Euler equations is used to illustrate the benefits of adaptive remeshing as well as mesh movement and enrichment for the efficacy of MPDATA-based flow solvers. Validation against benchmark test cases demonstrates robustness and accuracy of the approach.

  4. Eutectic pattern transition under different temperature gradients: A phase field study coupled with the parallel adaptive-mesh-refinement algorithm

    NASA Astrophysics Data System (ADS)

    Zhang, A.; Guo, Z.; Xiong, S.-M.

    2017-03-01

    Eutectic pattern transition under an externally imposed temperature gradient was studied using the phase field method coupled with a novel parallel adaptive-mesh-refinement (Para-AMR) algorithm. Numerical tests revealed that the Para-AMR algorithm could improve the computational efficiency by two orders of magnitude and thus made it possible to perform large-scale simulations without any compromising accuracy. Results showed that the direction of the temperature gradient played a crucial role in determining the eutectic patterns during solidification, which agreed well with experimental observations. In particular, the presence of the transverse temperature gradient could tilt the eutectic patterns, and in 3D simulations, the eutectic microstructure would alter from lamellar to rod-like and/or from rod-like to dumbbell-shaped. Furthermore, under a radial temperature gradient, the eutectic would evolve from a dumbbell-shaped or clover-shaped pattern to an isolated rod-like pattern.

  5. Simulating Magnetohydrodynamical Flow with Constrained Transport and Adaptive Mesh Refinement: Algorithms and Tests of the AstroBEAR Code

    NASA Astrophysics Data System (ADS)

    Cunningham, Andrew J.; Frank, Adam; Varnière, Peggy; Mitran, Sorin; Jones, Thomas W.

    2009-06-01

    A description is given of the algorithms implemented in the AstroBEAR adaptive mesh-refinement code for ideal magnetohydrodynamics. The code provides several high-resolution shock-capturing schemes which are constructed to maintain conserved quantities of the flow in a finite-volume sense. Divergence-free magnetic field topologies are maintained to machine precision by collating the components of the magnetic field on a cell-interface staggered grid and utilizing the constrained transport approach for integrating the induction equations. The maintenance of magnetic field topologies on adaptive grids is achieved using prolongation and restriction operators which preserve the divergence and curl of the magnetic field across collocated grids of different resolutions. The robustness and correctness of the code is demonstrated by comparing the numerical solution of various tests with analytical solutions or previously published numerical solutions obtained by other codes.

  6. Hybrid Surface Mesh Adaptation for Climate Modeling

    SciTech Connect

    Ahmed Khamayseh; Valmor de Almeida; Glen Hansen

    2008-10-01

    Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications, such as climate modeling. Typically, spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest. A second, less-popular method of spatial adaptivity is called “mesh motion” (r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales. This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function, the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is produced by element subdivision alone. Further, in an attempt to support the requirements of a very general class of climate simulation applications, the proposed method is designed to accommodate unstructured, polygonal mesh topologies in addition to the most popular mesh types.

  7. Adaptive mesh refinement for storm surge

    NASA Astrophysics Data System (ADS)

    Mandli, Kyle T.; Dawson, Clint N.

    2014-03-01

    An approach to utilizing adaptive mesh refinement algorithms for storm surge modeling is proposed. Currently numerical models exist that can resolve the details of coastal regions but are often too costly to be run in an ensemble forecasting framework without significant computing resources. The application of adaptive mesh refinement algorithms substantially lowers the computational cost of a storm surge model run while retaining much of the desired coastal resolution. The approach presented is implemented in the GEOCLAW framework and compared to ADCIRC for Hurricane Ike along with observed tide gauge data and the computational cost of each model run.

  8. Adaption of unstructured meshes using node movement

    SciTech Connect

    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.

  9. Parallel Adaptive Mesh Refinement Library

    NASA Technical Reports Server (NTRS)

    Mac-Neice, Peter; Olson, Kevin

    2005-01-01

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

  10. Parallel adaptive mesh refinement within the PUMAA3D Project

    NASA Technical Reports Server (NTRS)

    Freitag, Lori; Jones, Mark; Plassmann, Paul

    1995-01-01

    To enable the solution of large-scale applications on distributed memory architectures, we are designing and implementing parallel algorithms for the fundamental tasks of unstructured mesh computation. In this paper, we discuss efficient algorithms developed for two of these tasks: parallel adaptive mesh refinement and mesh partitioning. The algorithms are discussed in the context of two-dimensional finite element solution on triangular meshes, but are suitable for use with a variety of element types and with h- or p-refinement. Results demonstrating the scalability and efficiency of the refinement algorithm and the quality of the mesh partitioning are presented for several test problems on the Intel DELTA.

  11. A Mass Conservation Algorithm for Adaptive Unrefinement Meshes Used by Finite Element Methods

    DTIC Science & Technology

    2012-01-01

    is an adaptive finite element method to simulate three-dimensional Navier- Stokes flow, unsaturated and saturated groundwater flow, overland flow...variables of fluid-motion simulations and are often solved at various times. It is important for the numerical model to predict accurate water depth...remove others where they are no longer required during the simulation . The AMR is proven to optimize the performance of a computed solution. However, mass

  12. Adaptive Mesh Refinement in CTH

    SciTech Connect

    Crawford, David

    1999-05-04

    This paper reports progress on implementing a new capability of adaptive mesh refinement into the Eulerian multimaterial shock- physics code CTH. The adaptivity is block-based with refinement and unrefinement occurring in an isotropic 2:1 manner. The code is designed to run on serial, multiprocessor and massive parallel platforms. An approximate factor of three in memory and performance improvements over comparable resolution non-adaptive calculations has-been demonstrated for a number of problems.

  13. 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

  14. 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.

  15. Advanced numerical methods in mesh generation and mesh adaptation

    SciTech Connect

    Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A

    2010-01-01

    Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge

  16. 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.

  17. Adaptive mesh refinement for stochastic reaction-diffusion processes

    SciTech Connect

    Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros

    2011-01-01

    We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction-diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction-diffusion processes as described by the Fisher-Kolmogorov and Gray-Scott equations.

  18. Serial and parallel dynamic adaptation of general hybrid meshes

    NASA Astrophysics Data System (ADS)

    Kavouklis, Christos

    The Navier-Stokes equations are a standard mathematical representation of viscous fluid flow. Their numerical solution in three dimensions remains a computationally intensive and challenging task, despite recent advances in computer speed and memory. A strategy to increase accuracy of Navier-Stokes simulations, while maintaining computing resources to a minimum, is local refinement of the associated computational mesh in regions of large solution gradients and coarsening in regions where the solution does not vary appreciably. In this work we consider adaptation of general hybrid meshes for Computational Fluid Dynamics (CFD) applications. Hybrid meshes are composed of four types of elements; hexahedra, prisms, pyramids and tetrahedra, and have been proven a promising technology in accurately resolving fluid flow for complex geometries. The first part of this dissertation is concerned with the design and implementation of a serial scheme for the adaptation of general three dimensional hybrid meshes. We have defined 29 refinement types, for all four kinds of elements. The core of the present adaptation scheme is an iterative algorithm that flags mesh edges for refinement, so that the adapted mesh is conformal. Of primary importance is considered the design of a suitable dynamic data structure that facilitates refinement and coarsening operations and furthermore minimizes memory requirements. A special dynamic list is defined for mesh elements, in contrast with the usual tree structures. It contains only elements of the current adaptation step and minimal information that is utilized to reconstruct parent elements when the mesh is coarsened. In the second part of this work, a new parallel dynamic mesh adaptation and load balancing algorithm for general hybrid meshes is presented. Partitioning of a hybrid mesh reduces to partitioning of the corresponding dual graph. Communication among processors is based on the faces of the interpartition boundary. The distributed

  19. Adaptive mesh refinement in titanium

    SciTech Connect

    Colella, Phillip; Wen, Tong

    2005-01-21

    In this paper, we evaluate Titanium's usability as a high-level parallel programming language through a case study, where we implement a subset of Chombo's functionality in Titanium. Chombo is a software package applying the Adaptive Mesh Refinement methodology to numerical Partial Differential Equations at the production level. In Chombo, the library approach is used to parallel programming (C++ and Fortran, with MPI), whereas Titanium is a Java dialect designed for high-performance scientific computing. The performance of our implementation is studied and compared with that of Chombo in solving Poisson's equation based on two grid configurations from a real application. Also provided are the counts of lines of code from both sides.

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

    USGS Publications Warehouse

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

    2006-01-01

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

  1. Parallel adaptation of general three-dimensional hybrid meshes

    SciTech Connect

    Kavouklis, Christos Kallinderis, Yannis

    2010-05-01

    A new parallel dynamic mesh adaptation and load balancing algorithm for general hybrid grids has been developed. The meshes considered in this work are composed of four kinds of elements; tetrahedra, prisms, hexahedra and pyramids, which poses a challenge to parallel mesh adaptation. Additional complexity imposed by the presence of multiple types of elements affects especially data migration, updates of local data structures and interpartition data structures. Efficient partition of hybrid meshes has been accomplished by transforming them to suitable graphs and using serial graph partitioning algorithms. Communication among processors is based on the faces of the interpartition boundary and the termination detection algorithm of Dijkstra is employed to ensure proper flagging of edges for refinement. An inexpensive dynamic load balancing strategy is introduced to redistribute work load among processors after adaptation. In particular, only the initial coarse mesh, with proper weighting, is balanced which yields savings in computation time and relatively simple implementation of mesh quality preservation rules, while facilitating coarsening of refined elements. Special algorithms are employed for (i) data migration and dynamic updates of the local data structures, (ii) determination of the resulting interpartition boundary and (iii) identification of the communication pattern of processors. Several representative applications are included to evaluate the method.

  2. 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.

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

    DTIC Science & Technology

    2013-03-01

    applications [3, 21, 22], including antenna, microwave circuits , geophysics, optics, etc. The Ground Penetrating Radar (GPR) is a popular and...Räisänen. An efficient FDTD algorithm for the analysis of microstrip patch antennas printed on a general anisotropic dielectric substrate. IEEE...45, 1995. [17] S. Gedney, F. Lansing, and D. Rascoe. Full wave analysis of microwave monolithic circuit devices using a generalized Yee-algorithm

  4. Elliptic Solvers for Adaptive Mesh Refinement Grids

    SciTech Connect

    Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.

    1999-06-03

    We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.

  5. 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

  6. 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

  7. 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.

  8. 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.

  9. 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.

  10. AN ADAPTIVE PARTICLE-MESH GRAVITY SOLVER FOR ENZO

    SciTech Connect

    Passy, Jean-Claude; Bryan, Greg L.

    2014-11-01

    We describe and implement an adaptive particle-mesh algorithm to solve the Poisson equation for grid-based hydrodynamics codes with nested grids. The algorithm is implemented and extensively tested within the astrophysical code Enzo against the multigrid solver available by default. We find that while both algorithms show similar accuracy for smooth mass distributions, the adaptive particle-mesh algorithm is more accurate for the case of point masses, and is generally less noisy. We also demonstrate that the two-body problem can be solved accurately in a configuration with nested grids. In addition, we discuss the effect of subcycling, and demonstrate that evolving all the levels with the same timestep yields even greater precision.

  11. PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes

    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. Unfortunately, an efficient parallel implementation is difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. First, we present an efficient parallel implementation of a tetrahedral mesh adaption scheme. Extremely promising parallel performance is achieved for various refinement and coarsening strategies on a realistic-sized domain. Next we describe PLUM, a novel method for dynamically balancing the processor workloads in adaptive grid computations. This research includes interfacing the parallel mesh adaption procedure based on actual flow solutions to a data remapping module, and incorporating an efficient parallel mesh repartitioner. A significant runtime improvement is achieved by observing that data movement for a refinement step should be performed after the edge-marking phase but before the actual subdivision. We also present optimal and heuristic remapping cost metrics that can accurately predict the total overhead for data redistribution. Several experiments are performed to verify the effectiveness of PLUM on sequences of dynamically adapted unstructured grids. Portability is demonstrated by presenting results on the two vastly different architectures of the SP2 and the Origin2OOO. Additionally, we evaluate the performance of five state-of-the-art partitioning algorithms that can be used within PLUM. It is shown that for certain classes of unsteady adaption, globally repartitioning the computational mesh produces higher quality results than diffusive repartitioning schemes. We also demonstrate that a coarse starting mesh produces high quality load balancing, at

  12. Parallel tetrahedral mesh adaptation with dynamic load balancing

    SciTech Connect

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

    2000-06-28

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

  13. Parallel Tetrahedral Mesh Adaptation with Dynamic Load Balancing

    NASA Technical Reports Server (NTRS)

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

    1999-01-01

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

  14. 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 inmore » a 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

  15. Mesh saliency with adaptive local patches

    NASA Astrophysics Data System (ADS)

    Nouri, Anass; Charrier, Christophe; Lézoray, Olivier

    2015-03-01

    3D object shapes (represented by meshes) include both areas that attract the visual attention of human observers and others less or not attractive at all. This visual attention depends on the degree of saliency exposed by these areas. In this paper, we propose a technique for detecting salient regions in meshes. To do so, we define a local surface descriptor based on local patches of adaptive size and filled with a local height field. The saliency of mesh vertices is then defined as its degree measure with edges weights computed from adaptive patch similarities. Our approach is compared to the state-of-the-art and presents competitive results. A study evaluating the influence of the parameters establishing this approach is also carried out. The strength and the stability of our approach with respect to noise and simplification are also studied.

  16. Multigrid solution of the Euler equations on unstructured and adaptive meshes

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri; Jameson, Antony

    1987-01-01

    A multigrid algorithm has been developed for solving the steady-state Euler equations in two dimensions on unstructured triangular meshes. The method assumes the various coarse and fine grids of the multigrid sequence to be independent of one another, thus decoupling the grid generation procedure from the multigrid algorithm. The transfer of variables between the various meshes employs a tree-search algorithm which rapidly identifies regions of overlap between coarse and fine grid cells. Finer meshes are obtained either by regenerating new globally refined meshes, or by adaptively refining the previous coarser mesh. For both cases, the observed convergence rates are comparable to those obtained with structured multigrid Euler solvers. The adaptively generated meshes are shown to produce solutions of higher accuracy with fewer mesh points.

  17. Update on Development of Mesh Generation Algorithms in MeshKit

    SciTech Connect

    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 MeshKit 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.

  18. 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.

  19. 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.

  20. Cartesian-cell based grid generation and adaptive mesh refinement

    NASA Technical Reports Server (NTRS)

    Coirier, William J.; Powell, Kenneth G.

    1993-01-01

    Viewgraphs on Cartesian-cell based grid generation and adaptive mesh refinement are presented. Topics covered include: grid generation; cell cutting; data structures; flow solver formulation; adaptive mesh refinement; and viscous flow.

  1. GRChombo: Numerical relativity with adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Clough, Katy; Figueras, Pau; Finkel, Hal; Kunesch, Markus; Lim, Eugene A.; Tunyasuvunakool, Saran

    2015-12-01

    In this work, we introduce {\\mathtt{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. {\\mathtt{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. We show that {\\mathtt{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.

  2. GRChombo : Numerical Relativity with Adaptive Mesh Refinement

    SciTech Connect

    Clough, Katy; Figueras, Pau; Finkel, Hal; Kunesch, Markus; Lim, Eugene A.; Tunyasuvunakool, Saran

    2015-12-24

    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. We 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.

  3. 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

  4. Advances in Patch-Based Adaptive Mesh Refinement Scalability

    SciTech Connect

    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 extension 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.

  5. Details of tetrahedral anisotropic mesh adaptation

    NASA Astrophysics Data System (ADS)

    Jensen, Kristian Ejlebjerg; Gorman, Gerard

    2016-04-01

    We have implemented tetrahedral anisotropic mesh adaptation using the local operations of coarsening, swapping, refinement and smoothing in MATLAB without the use of any for- N loops, i.e. the script is fully vectorised. In the process of doing so, we have made three observations related to details of the implementation: 1. restricting refinement to a single edge split per element not only simplifies the code, it also improves mesh quality, 2. face to edge swapping is unnecessary, and 3. optimising for the Vassilevski functional tends to give a little higher value for the mean condition number functional than optimising for the condition number functional directly. These observations have been made for a uniform and a radial shock metric field, both starting from a structured mesh in a cube. Finally, we compare two coarsening techniques and demonstrate the importance of applying smoothing in the mesh adaptation loop. The results pertain to a unit cube geometry, but we also show the effect of corners and edges by applying the implementation in a spherical geometry.

  6. White Dwarf Mergers on Adaptive Meshes

    NASA Astrophysics Data System (ADS)

    Katz, Maximilian Peter

    The mergers of binary white dwarf systems are potential progenitors of astrophysical explosions such as Type Ia supernovae. These white dwarfs can merge either by orbital decay through the emission of gravitational waves or by direct collisions as a result of orbital perturbations. The coalescence of the stars may ignite nuclear fusion, resulting in the destruction of both stars through a thermonuclear runaway and ensuing detonation. The goal of this dissertation is to simulate binary white dwarf systems using the techniques of computational fluid dynamics and therefore to understand what numerical techniques are necessary to obtain accurate dynamical evolution of the system, as well as to learn what conditions are necessary to enable a realistic detonation. For this purpose I have used software that solves the relevant fluid equations, the Poisson equation for self-gravity, and the systems governing nuclear reactions between atomic species. These equations are modeled on a computational domain that uses the technique of adaptive mesh refinement to have the highest spatial resolution in the areas of the domain that are most sensitive to the need for accurate numerical evolution. I have identified that the most important obstacles to accurate evolution are the numerical violation of conservation of energy and angular momentum in the system, and the development of numerically seeded thermonuclear detonations that do not bear resemblance to physically correct detonations. I then developed methods for ameliorating these problems, and determined what metrics can be used for judging whether a given white dwarf merger simulation is trustworthy. This involved the development of a number of algorithmic improvements to the simulation software, which I describe. Finally, I performed high-resolution simulations of typical cases of white dwarf mergers and head-on collisions to demonstrate the impacts of these choices. The results of these simulations and the corresponding

  7. A geometry preserving, conservative, mesh-to-mesh isogeometric interpolation algorithm for spatial adaptivity of the multigroup, second-order even-parity form of the neutron transport equation

    NASA Astrophysics Data System (ADS)

    Welch, J. A.; Kópházi, J.; Owens, A. R.; Eaton, M. D.

    2017-10-01

    In this paper a method is presented for the application of energy-dependent spatial meshes applied to the multigroup, second-order, even-parity form of the neutron transport equation using Isogeometric Analysis (IGA). The computation of the inter-group regenerative source terms is based on conservative interpolation by Galerkin projection. The use of Non-Uniform Rational B-splines (NURBS) from the original computer-aided design (CAD) model allows for efficient implementation and calculation of the spatial projection operations while avoiding the complications of matching different geometric approximations faced by traditional finite element methods (FEM). The rate-of-convergence was verified using the method of manufactured solutions (MMS) and found to preserve the theoretical rates when interpolating between spatial meshes of different refinements. The scheme's numerical efficiency was then studied using a series of two-energy group pincell test cases where a significant saving in the number of degrees-of-freedom can be found if the energy group with a complex variation in the solution is refined more than an energy group with a simpler solution function. Finally, the method was applied to a heterogeneous, seven-group reactor pincell where the spatial meshes for each energy group were adaptively selected for refinement. It was observed that by refining selected energy groups a reduction in the total number of degrees-of-freedom for the same total L2 error can be obtained.

  8. Block-structured adaptive mesh refinement - theory, implementation and application

    SciTech Connect

    Deiterding, Ralf

    2011-01-01

    Structured adaptive mesh refinement (SAMR) techniques can enable cutting-edge simulations of problems governed by conservation laws. Focusing on the strictly hyperbolic case, these notes explain all algorithmic and mathematical details of a technically relevant implementation tailored for distributed memory computers. An overview of the background of commonly used finite volume discretizations for gas dynamics is included and typical benchmarks to quantify accuracy and performance of the dynamically adaptive code are discussed. Large-scale simulations of shock-induced realistic combustion in non-Cartesian geometry and shock-driven fluid-structure interaction with fully coupled dynamic boundary motion demonstrate the applicability of the discussed techniques for complex scenarios.

  9. Adaptive upscaling with the dual mesh method

    SciTech Connect

    Guerillot, D.; Verdiere, S.

    1997-08-01

    The objective of this paper is to demonstrate that upscaling should be calculated during the flow simulation instead of trying to enhance the a priori upscaling methods. Hence, counter-examples are given to motivate our approach, the so-called Dual Mesh Method. The main steps of this numerical algorithm are recalled. Applications illustrate the necessity to consider different average relative permeability values depending on the direction in space. Moreover, these values could be different for the same average saturation. This proves that an a priori upscaling cannot be the answer even in homogeneous cases because of the {open_quotes}dynamical heterogeneity{close_quotes} created by the saturation profile. Other examples show the efficiency of the Dual Mesh Method applied to heterogeneous medium and to an actual field case in South America.

  10. A New Approach to Parallel Dynamic Partitioning for Adaptive Unstructured Meshes

    NASA Technical Reports Server (NTRS)

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

    1999-01-01

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

  11. On Adaptive Mesh Generation in Two-Dimensions

    SciTech Connect

    D'Azevedo, E.

    1999-10-11

    This work considers the effectiveness of using anisotropic coordinate transformation in adaptive mesh generation. The anisotropic coordinate transformation is derived by interpreting the Hessian matrix of the data function as a metric tensor that measures the local approximation error. The Hessian matrix contains information about the local curvature of the surface and gives guidance in the aspect ratio and orientation for mesh generation. Since theoretically, an asymptotically optimally efficient mesh can be produced by transforming a regular mesh of optimal shape elements, it would be interesting to compare this approach with existing techniques in solution adaptive meshes. PLTMG , a general elliptic solver, is used to generate solution adapted triangular meshes for comparison. The solver has the capability of performing a posteriori error estimates in performing longest edge refinement, vertex unrefinement and mesh smoothing. Numerical experiments on three simple problems suggest the methodology employed in PLTMG is effective in generating near optimally efficient meshes.

  12. Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries

    SciTech Connect

    Phillip, B.

    2000-07-24

    Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.

  13. Development and Verification of Unstructured Adaptive Mesh Technique with Edge Compatibility

    NASA Astrophysics Data System (ADS)

    Ito, Kei; Kunugi, Tomoaki; Ohshima, Hiroyuki

    In the design study of the large-sized sodium-cooled fast reactor (JSFR), one key issue is suppression of gas entrainment (GE) phenomena at a gas-liquid interface. Therefore, the authors have been developed a high-precision CFD algorithm to evaluate the GE phenomena accurately. The CFD algorithm has been developed on unstructured meshes to establish an accurate modeling of JSFR system. For two-phase interfacial flow simulations, a high-precision volume-of-fluid algorithm is employed. It was confirmed that the developed CFD algorithm could reproduce the GE phenomena in a simple GE experiment. Recently, the authors have been developed an important technique for the simulation of the GE phenomena in JSFR. That is an unstructured adaptive mesh technique which can apply fine cells dynamically to the region where the GE occurs in JSFR. In this paper, as a part of the development, a two-dimensional unstructured adaptive mesh technique is discussed. In the two-dimensional adaptive mesh technique, each cell is refined isotropically to reduce distortions of the mesh. In addition, connection cells are formed to eliminate the edge incompatibility between refined and non-refined cells. The two-dimensional unstructured adaptive mesh technique is verified by solving well-known lid-driven cavity flow problem. As a result, the two-dimensional unstructured adaptive mesh technique succeeds in providing a high-precision solution, even though poor-quality distorted initial mesh is employed. In addition, the simulation error on the two-dimensional unstructured adaptive mesh is much less than the error on the structured mesh with a larger number of cells.

  14. Adaptive cockroach swarm algorithm

    NASA Astrophysics Data System (ADS)

    Obagbuwa, Ibidun C.; Abidoye, Ademola P.

    2017-07-01

    An adaptive cockroach swarm optimization (ACSO) algorithm is proposed in this paper to strengthen the existing cockroach swarm optimization (CSO) algorithm. The ruthless component of CSO algorithm is modified by the employment of blend crossover predator-prey evolution method which helps algorithm prevent any possible population collapse, maintain population diversity and create adaptive search in each iteration. The performance of the proposed algorithm on 16 global optimization benchmark function problems was evaluated and compared with the existing CSO, cuckoo search, differential evolution, particle swarm optimization and artificial bee colony algorithms.

  15. Adaptive Mesh Refinement for ICF Calculations

    NASA Astrophysics Data System (ADS)

    Fyfe, David

    2005-10-01

    This paper describes our use of the package PARAMESH to create an Adaptive Mesh Refinement (AMR) version of NRL's FASTRAD3D code. PARAMESH was designed to create an MPI-based AMR code from a block structured serial code such as FASTRAD3D. FASTRAD3D is a compressible hydrodynamics code containing the physical effects relevant for the simulation of high-temperature plasmas including inertial confinement fusion (ICF) Rayleigh-Taylor unstable direct drive laser targets. These effects include inverse bremmstrahlung laser energy absorption, classical flux-limited Spitzer thermal conduction, real (table look-up) equation-of-state with either separate or identical electron and ion temperatures, multi-group variable Eddington radiation transport, and multi-group alpha particle transport and thermonuclear burn. Numerically, this physics requires an elliptic solver and a ray tracing approach on the AMR grid, which is the main subject of this paper. A sample ICF calculation will be presented. MacNeice et al., ``PARAMESH: A parallel adaptive mesh refinement community tool,'' Computer Physics Communications, 126 (2000), pp. 330-354.

  16. Current sheets, reconnection and adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Marliani, Christiane

    1998-11-01

    Adaptive structured mesh refinement methods have proved to be an appropriate tool for the numerical study of a variety of problems where largely separated length scales are involved, e.g. [R. Grauer, C. Marliani, K. Germaschewski, PRL, 80, 4177, (1998)]. A typical example in plasma physics are the current sheets in magnetohydrodynamic flows. Their dynamics is investigated in the framework of incompressible MHD. We present simulations of the ideal and inviscid dynamics in two and three dimensions. In addition, we show numerical simulations for the resistive case in two dimensions. Specifically, we show simulations for the case of the doubly periodic coalescence instability. At the onset of the reconnection process the kinetic energy rises and drops rapidly and afterwards settles into an oscillatory phase. The timescale of the magnetic reconnection process is not affected by these fast events but consistent with the Sweet-Parker model of stationary reconnection. Taking into account the electron inertia terms in the generalized Ohm's law the electron skin depth is introduced as an additional parameter. The modified equations allow for magnetic reconnection in the collisionless regime. Current density and vorticity concentrate in extremely long and thin sheets. Their dynamics becomes numerically accessible by means of adaptive mesh refinement.

  17. 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.

  18. An Adaptive Mesh Refined Gradient-Augmented Level Set Method

    NASA Astrophysics Data System (ADS)

    Nave, Jean-Christophe; Seibold, Benjamin; Rosales, Ruben

    2010-11-01

    The Gradient-Augmented Level Set method (GA-LS) was introduced at the 62^nd annual APS-DFD meeting by Nave et al. (arXiv:0905.3409). Leveraging the optimal locality and unconditional stability of the method, we present a natural extension to adaptive quad-tree meshes. The new method possesses many desirable features such as improved mass conservation, reduced computational effort, and is, due to the optimal locality property of the underlying GA-LS, very easy to implement. Several key benchmark tests will be presented to help demonstrate the benefits of the approach, and the overall simplicity of the algorithm.

  19. 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

    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.

  20. AN ALGORITHM FOR PARALLEL SN SWEEPS ON UNSTRUCTURED MESHES

    SciTech Connect

    S. D. PAUTZ

    2000-12-01

    We develop a new algorithm for performing parallel S{sub n} sweeps on unstructured meshes. The algorithm uses a low-complexity list ordering heuristic to determine a sweep ordering on any partitioned mesh. For typical problems and with ''normal'' mesh partitionings we have observed nearly linear speedups on up to 126 processors. This is an important and desirable result, since although analyses of structured meshes indicate that parallel sweeps will not scale with normal partitioning approaches, we do not observe any severe asymptotic degradation in the parallel efficiency with modest ({le}100) levels of parallelism. This work is a fundamental step in the development of parallel S{sub n} methods.

  1. Content-Adaptive Finite Element Mesh Generation of 3-D Complex MR Volumes for Bioelectromagnetic Problems.

    PubMed

    Lee, W; Kim, T-S; Cho, M; Lee, S

    2005-01-01

    In studying bioelectromagnetic problems, finite element method offers several advantages over other conventional methods such as boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropy. Mesh generation is the first requirement in the finite element analysis and there are many different approaches in mesh generation. However conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes, resulting in numerous elements in the smaller volume regions, thereby increasing computational load and demand. In this work, we present an improved content-adaptive mesh generation scheme that is efficient and fast along with options to change the contents of meshes. For demonstration, mesh models of the head from a volume MRI are presented in 2-D and 3-D.

  2. Anisotropic Mesh Adaptivity for FE-simulation of cardiovascular flow

    NASA Astrophysics Data System (ADS)

    Mueller, Jens; Sahni, Onkar; Jansen, Kenneth E.; Shephard, Mark S.; Taylor, Charles A.

    2004-11-01

    In this study we present an adaptive anisotropic finite element method and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the weak SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretized by linear finite elements, both for the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptavity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical pipe and then to a pig artery with a stenosis bypassed by a graft. The efficiency of the method is measured in terms of computational savings when we compute the wall shear stresses, a quantity identified to be important to understanding arterial disease.

  3. Visualization of Scalar Adaptive Mesh Refinement Data

    SciTech Connect

    VACET; Weber, Gunther; Weber, Gunther H.; Beckner, Vince E.; Childs, Hank; Ligocki, Terry J.; Miller, Mark C.; Van Straalen, Brian; Bethel, E. Wes

    2007-12-06

    Adaptive Mesh Refinement (AMR) is a highly effective computation method for simulations that span a large range of spatiotemporal scales, such as astrophysical simulations, which must accommodate ranges from interstellar to sub-planetary. Most mainstream visualization tools still lack support for AMR grids as a first class data type and AMR code teams use custom built applications for AMR visualization. The Department of Energy's (DOE's) Science Discovery through Advanced Computing (SciDAC) Visualization and Analytics Center for Enabling Technologies (VACET) is currently working on extending VisIt, which is an open source visualization tool that accommodates AMR as a first-class data type. These efforts will bridge the gap between general-purpose visualization applications and highly specialized AMR visual analysis applications. Here, we give an overview of the state of the art in AMR scalar data visualization research.

  4. Split Bregman's algorithm for three-dimensional mesh segmentation

    NASA Astrophysics Data System (ADS)

    Habiba, Nabi; Ali, Douik

    2016-05-01

    Variational methods have attracted a lot of attention in the literature, especially for image and mesh segmentation. The methods aim at minimizing the energy to optimize both edge and region detections. We propose a spectral mesh decomposition algorithm to obtain disjoint but meaningful regions of an input mesh. The related optimization problem is nonconvex, and it is very difficult to find a good approximation or global optimum, which represents a challenge in computer vision. We propose an alternating split Bregman algorithm for mesh segmentation, where we extended the image-dedicated model to a three-dimensional (3-D) mesh one. By applying our scheme to 3-D mesh segmentation, we obtain fast solvers that can outperform various conventional ones, such as graph-cut and primal dual methods. A consistent evaluation of the proposed method on various public domain 3-D databases for different metrics is elaborated, and a comparison with the state-of-the-art is performed.

  5. Anisotropic mesh adaptivity for multi-scale ocean modelling.

    PubMed

    Piggott, M D; Farrell, P E; Wilson, C R; Gorman, G J; Pain, C C

    2009-11-28

    Research into the use of unstructured mesh methods in oceanography has been growing steadily over the past decade. The advantages of this approach for domain representation and non-uniform resolution are clear. However, a number of issues remain, in particular those related to the computational cost of models produced using unstructured mesh methods compared with their structured mesh counterparts. Mesh adaptivity represents an important means to improve the competitiveness of unstructured mesh models, where high resolution is only used when and where necessary. In this paper, an optimization-based approach to mesh adaptivity is described where emphasis is placed on capturing anisotropic solution characteristics. Comparisons are made between the results obtained with uniform isotropic resolution, isotropic adaptive resolution and fully anisotropic adaptive resolution.

  6. Tetrahedral and Hexahedral Mesh Adaptation for CFD Problems

    NASA Technical Reports Server (NTRS)

    Biswas, Rupak; Strawn, Roger C.; Chancellor, Marisa K. (Technical Monitor)

    1997-01-01

    This paper presents two unstructured mesh adaptation schemes for problems in computational fluid dynamics. The procedures allow localized grid refinement and coarsening to efficiently capture aerodynamic flow features of interest. The first procedure is for purely tetrahedral grids; unfortunately, repeated anisotropic adaptation may significantly deteriorate the quality of the mesh. Hexahedral elements, on the other hand, can be subdivided anisotropically without mesh quality problems. Furthermore, hexahedral meshes yield more accurate solutions than their tetrahedral counterparts for the same number of edges. Both the tetrahedral and hexahedral mesh adaptation procedures use edge-based data structures that facilitate efficient subdivision by allowing individual edges to be marked for refinement or coarsening. However, for hexahedral adaptation, pyramids, prisms, and tetrahedra are used as buffer elements between refined and unrefined regions to eliminate hanging vertices. Computational results indicate that the hexahedral adaptation procedure is a viable alternative to adaptive tetrahedral schemes.

  7. Tetrahedral and Hexahedral Mesh Adaptation for CFD Problems

    NASA Technical Reports Server (NTRS)

    Biswas, Rupak; Strawn, Roger C.; Chancellor, Marisa K. (Technical Monitor)

    1997-01-01

    This paper presents two unstructured mesh adaptation schemes for problems in computational fluid dynamics. The procedures allow localized grid refinement and coarsening to efficiently capture aerodynamic flow features of interest. The first procedure is for purely tetrahedral grids; unfortunately, repeated anisotropic adaptation may significantly deteriorate the quality of the mesh. Hexahedral elements, on the other hand, can be subdivided anisotropically without mesh quality problems. Furthermore, hexahedral meshes yield more accurate solutions than their tetrahedral counterparts for the same number of edges. Both the tetrahedral and hexahedral mesh adaptation procedures use edge-based data structures that facilitate efficient subdivision by allowing individual edges to be marked for refinement or coarsening. However, for hexahedral adaptation, pyramids, prisms, and tetrahedra are used as buffer elements between refined and unrefined regions to eliminate hanging vertices. Computational results indicate that the hexahedral adaptation procedure is a viable alternative to adaptive tetrahedral schemes.

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

    NASA Technical Reports Server (NTRS)

    Biswas, Rupak; Oliker, Leonid; Sohn, Andrew

    1996-01-01

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

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

    NASA Technical Reports Server (NTRS)

    Biswas, Rupak; Oliker, Leonid; Sohn, Andrew

    1996-01-01

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

  10. Adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients

    PubMed Central

    Xia, Kelin; Zhan, Meng; Wan, Decheng; Wei, Guo-Wei

    2011-01-01

    Mesh deformation methods are a versatile strategy for solving partial differential equations (PDEs) with a vast variety of practical applications. However, these methods break down for elliptic PDEs with discontinuous coefficients, namely, elliptic interface problems. For this class of problems, the additional interface jump conditions are required to maintain the well-posedness of the governing equation. Consequently, in order to achieve high accuracy and high order convergence, additional numerical algorithms are required to enforce the interface jump conditions in solving elliptic interface problems. The present work introduces an interface technique based adaptively deformed mesh strategy for resolving elliptic interface problems. We take the advantages of the high accuracy, flexibility and robustness of the matched interface and boundary (MIB) method to construct an adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients. The proposed method generates deformed meshes in the physical domain and solves the transformed governed equations in the computational domain, which maintains regular Cartesian meshes. The mesh deformation is realized by a mesh transformation PDE, which controls the mesh redistribution by a source term. The source term consists of a monitor function, which builds in mesh contraction rules. Both interface geometry based deformed meshes and solution gradient based deformed meshes are constructed to reduce the L∞ and L2 errors in solving elliptic interface problems. The proposed adaptively deformed mesh based interface method is extensively validated by many numerical experiments. Numerical results indicate that the adaptively deformed mesh based interface method outperforms the original MIB method for dealing with elliptic interface problems. PMID:22586356

  11. Carpet: Adaptive Mesh Refinement for the Cactus Framework

    NASA Astrophysics Data System (ADS)

    Schnetter, Erik; Hawley, Scott; Hawke, Ian

    2016-11-01

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

  12. Adaptive superposition of finite element meshes in linear and nonlinear dynamic analysis

    NASA Astrophysics Data System (ADS)

    Yue, Zhihua

    2005-11-01

    The numerical analysis of transient phenomena in solids, for instance, wave propagation and structural dynamics, is a very important and active area of study in engineering. Despite the current evolutionary state of modern computer hardware, practical analysis of large scale, nonlinear transient problems requires the use of adaptive methods where computational resources are locally allocated according to the interpolation requirements of the solution form. Adaptive analysis of transient problems involves obtaining solutions at many different time steps, each of which requires a sequence of adaptive meshes. Therefore, the execution speed of the adaptive algorithm is of paramount importance. In addition, transient problems require that the solution must be passed from one adaptive mesh to the next adaptive mesh with a bare minimum of solution-transfer error since this form of error compromises the initial conditions used for the next time step. A new adaptive finite element procedure (s-adaptive) is developed in this study for modeling transient phenomena in both linear elastic solids and nonlinear elastic solids caused by progressive damage. The adaptive procedure automatically updates the time step size and the spatial mesh discretization in transient analysis, achieving the accuracy and the efficiency requirements simultaneously. The novel feature of the s-adaptive procedure is the original use of finite element mesh superposition to produce spatial refinement in transient problems. The use of mesh superposition enables the s-adaptive procedure to completely avoid the need for cumbersome multipoint constraint algorithms and mesh generators, which makes the s-adaptive procedure extremely fast. Moreover, the use of mesh superposition enables the s-adaptive procedure to minimize the solution-transfer error. In a series of different solid mechanics problem types including 2-D and 3-D linear elastic quasi-static problems, 2-D material nonlinear quasi-static problems

  13. Novel biomedical tetrahedral mesh methods: algorithms and applications

    NASA Astrophysics Data System (ADS)

    Yu, Xiao; Jin, Yanfeng; Chen, Weitao; Huang, Pengfei; Gu, Lixu

    2007-12-01

    Tetrahedral mesh generation algorithm, as a prerequisite of many soft tissue simulation methods, becomes very important in the virtual surgery programs because of the real-time requirement. Aiming to speed up the computation in the simulation, we propose a revised Delaunay algorithm which makes a good balance of quality of tetrahedra, boundary preservation and time complexity, with many improved methods. Another mesh algorithm named Space-Disassembling is also presented in this paper, and a comparison of Space-Disassembling, traditional Delaunay algorithm and the revised Delaunay algorithm is processed based on clinical soft-tissue simulation projects, including craniofacial plastic surgery and breast reconstruction plastic surgery.

  14. 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).

  15. 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.

  16. Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees

    PubMed Central

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

    2014-01-01

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

  17. Anisotropic Mesh Adaptivity for Turbulent Flows with Boundary Layers

    NASA Astrophysics Data System (ADS)

    Chitale, Kedar C.

    Turbulent flows are found everywhere in nature and are studied, analyzed and simulated using various experimental and numerical tools. For computational analysis, a variety of turbulence models are available and the accuracy of these models in capturing the phenomenon depends largely on the mesh spacings, especially near the walls, in the boundary layer region. Special semi-structured meshes called "mesh boundary layers" are widely used in the CFD community in simulations of turbulent flows, because of their graded and orthogonal layered structure. They provide an efficient way to achieve very fine and highly anisotropic mesh spacings without introducing poorly shaped elements. Since usually the required mesh spacings to accurately resolve the flow are not known a priori to the simulations, an adaptive approach based on a posteriori error indicators is used to achieve an appropriate mesh. In this study, we apply the adaptive meshing techniques to turbulent flows with a focus on boundary layers. We construct a framework to calculate the critical wall normal mesh spacings inside the boundary layers based on the flow physics and the knowledge of the turbulence model. This approach is combined with numerical error indicators to adapt the entire flow region. We illustrate the effectiveness of this hybrid approach by applying it to three aerodynamic flows and studying their superior performance in capturing the flow structures in detail. We also demonstrate the capabilities of the current developments in parallel boundary layer mesh adaptation by applying them to two internal flow problems. We also study the application of adaptive boundary layer meshes to complex geometries like multi element wings. We highlight the advantage of using such techniques for superior wake and tip region resolution by showcasing flow results. We also outline the future direction for the adaptive meshing techniques to be useful to the large scale flow computations.

  18. 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.

  19. Generation of multi-million element meshes for solid model-based geometries: The Dicer algorithm

    SciTech Connect

    Melander, D.J.; Benzley, S.E.; Tautges, T.J.

    1997-06-01

    The Dicer algorithm generates a fine mesh by refining each element in a coarse all-hexahedral mesh generated by any existing all-hexahedral mesh generation algorithm. The fine mesh is geometry-conforming. Using existing all-hexahedral meshing algorithms to define the initial coarse mesh simplifies the overall meshing process and allows dicing to take advantage of improvements in other meshing algorithms immediately. The Dicer algorithm will be used to generate large meshes in support of the ASCI program. The authors also plan to use dicing as the basis for parallel mesh generation. Dicing strikes a careful balance between the interactive mesh generation and multi-million element mesh generation processes for complex 3D geometries, providing an efficient means for producing meshes of varying refinement once the coarse mesh is obtained.

  20. Efficient texture mapping by adaptive mesh division in mesh-based computer generated hologram.

    PubMed

    Ji, Yeong-Min; Yeom, Hanju-; Park, Jae-Hyeung

    2016-11-28

    We propose a method that achieves efficient texture mapping in fully-analytic computer generated holograms based on triangular meshes. In computer graphics, the texture mapping is commonly used to represent the details of objects without increasing the number of the triangular meshes. In fully-analytic triangular-mesh-based computer generated holograms, however, those methods cannot be directly applied because each mesh cannot have arbitrary amplitude distribution inside the triangular mesh area in order to keep the analytic representation. In this paper, we propose an efficient texture mapping method for fully-analytic mesh-based computer generated hologram. The proposed method uses an adaptive triangular mesh division to minimize the increase of the number of the triangular meshes for the given texture image data. The geometrical similarity relationship between the original triangular mesh and the divided one is also exploited to obtain the angular spectrum of the divided mesh from pre-calculated data for the original one. As a result, the proposed method enables to obtain the computer generated hologram of high details with much smaller computation time in comparison with the brute-force approach. The feasibility of the proposed method is confirmed by simulations and optical experiments.

  1. GAMER: GPU-accelerated Adaptive MEsh Refinement code

    NASA Astrophysics Data System (ADS)

    Schive, Hsi-Yu; Tsai, Yu-Chih; Chiueh, Tzihong

    2016-12-01

    GAMER (GPU-accelerated Adaptive MEsh Refinement) serves as a general-purpose adaptive mesh refinement + GPU framework and solves hydrodynamics with self-gravity. The code supports adaptive mesh refinement (AMR), hydrodynamics with self-gravity, and a variety of GPU-accelerated hydrodynamic and Poisson solvers. It also supports hybrid OpenMP/MPI/GPU parallelization, concurrent CPU/GPU execution for performance optimization, and Hilbert space-filling curve for load balance. Although the code is designed for simulating galaxy formation, it can be easily modified to solve a variety of applications with different governing equations. All optimization strategies implemented in the code can be inherited straightforwardly.

  2. Methods and evaluations of MRI content-adaptive finite element mesh generation for bioelectromagnetic problems.

    PubMed

    Lee, W H; Kim, T-S; Cho, M H; Ahn, Y B; Lee, S Y

    2006-12-07

    In studying bioelectromagnetic problems, finite element analysis (FEA) offers several advantages over conventional methods such as the boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropic conductivity. For FEA, mesh generation is the first critical requirement and there exist many different approaches. However, conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes (cMeshes), resulting in numerous nodes and elements in modelling the conducting domain, and thereby increasing computational load and demand. In this work, we present efficient content-adaptive mesh generation schemes for complex biological volumes of MR images. The presented methodology is fully automatic and generates FE meshes that are adaptive to the geometrical contents of MR images, allowing optimal representation of conducting domain for FEA. We have also evaluated the effect of cMeshes on FEA in three dimensions by comparing the forward solutions from various cMesh head models to the solutions from the reference FE head model in which fine and equidistant FEs constitute the model. The results show that there is a significant gain in computation time with minor loss in numerical accuracy. We believe that cMeshes should be useful in the FEA of bioelectromagnetic problems.

  3. Methods and evaluations of MRI content-adaptive finite element mesh generation for bioelectromagnetic problems

    NASA Astrophysics Data System (ADS)

    Lee, W. H.; Kim, T.-S.; Cho, M. H.; Ahn, Y. B.; Lee, S. Y.

    2006-12-01

    In studying bioelectromagnetic problems, finite element analysis (FEA) offers several advantages over conventional methods such as the boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropic conductivity. For FEA, mesh generation is the first critical requirement and there exist many different approaches. However, conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes (cMeshes), resulting in numerous nodes and elements in modelling the conducting domain, and thereby increasing computational load and demand. In this work, we present efficient content-adaptive mesh generation schemes for complex biological volumes of MR images. The presented methodology is fully automatic and generates FE meshes that are adaptive to the geometrical contents of MR images, allowing optimal representation of conducting domain for FEA. We have also evaluated the effect of cMeshes on FEA in three dimensions by comparing the forward solutions from various cMesh head models to the solutions from the reference FE head model in which fine and equidistant FEs constitute the model. The results show that there is a significant gain in computation time with minor loss in numerical accuracy. We believe that cMeshes should be useful in the FEA of bioelectromagnetic problems.

  4. 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

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

    SciTech Connect

    Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; Mahadevan, Vijay; Jiao, Xiangmin

    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 to 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.

  6. 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

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

    SciTech Connect

    Ibrahim, Ahmad M.; Wilson, Paul P.H.; Sawan, Mohamed E.; Mosher, Scott W.; Peplow, Douglas E.; Wagner, John C.; Evans, Thomas M.; Grove, Robert 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 much 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.

  8. A two-dimensional adaptive mesh generation method

    NASA Astrophysics Data System (ADS)

    Altas, Irfan; Stephenson, John W.

    1991-05-01

    The present, two-dimensional adaptive mesh-generation method allows selective modification of a small portion of the mesh without affecting large areas of adjacent mesh-points, and is applicable with or without boundary-fitted coordinate-generation procedures. The cases of differential equation discretization by, on the one hand, classical difference formulas designed for uniform meshes, and on the other the present difference formulas, are illustrated through the application of the method to the Hiemenz flow for which the Navier-Stokes equation's exact solution is known, as well as to a two-dimensional viscous internal flow problem.

  9. Numerical Differentiation for Adaptively Refined Finite Element Meshes

    NASA Technical Reports Server (NTRS)

    Borgioli, Andrea; Cwik, Tom

    1998-01-01

    Postprocessing of point-wise data is a fundamental process in many fields of research. Numerical differentiation is a key operation in computational electromagnetics. In the case of data obtained from a finite element method with automatic mesh refinement much work needs still to be done. This paper addresses some issues in differentiating data obtained from a finite element electromagnetic code with adaptive mesh refinement, and it proposes a methodology for deriving the electric field given the magnetic field on a mesh of linear triangular elements. The procedure itself is nevertheless more general and might be extended for numerically differentiating any point-wise solution based on triangular meshes.

  10. ENZO: AN ADAPTIVE MESH REFINEMENT CODE FOR ASTROPHYSICS

    SciTech Connect

    Bryan, Greg L.; Turk, Matthew J.; Norman, Michael L.; Bordner, James; Xu, Hao; Kritsuk, Alexei G.; O'Shea, Brian W.; Smith, Britton; Abel, Tom; Wang, Peng; Skillman, Samuel W.; Wise, John H.; Reynolds, Daniel R.; Collins, David C.; Harkness, Robert P.; Kim, Ji-hoon; Kuhlen, Michael; Goldbaum, Nathan; Hummels, Cameron; Collaboration: Enzo Collaboration; and others

    2014-04-01

    This paper describes the open-source code Enzo, which uses block-structured adaptive mesh refinement to provide high spatial and temporal resolution for modeling astrophysical fluid flows. The code is Cartesian, can be run in one, two, and three dimensions, and supports a wide variety of physics including hydrodynamics, ideal and non-ideal magnetohydrodynamics, N-body dynamics (and, more broadly, self-gravity of fluids and particles), primordial gas chemistry, optically thin radiative cooling of primordial and metal-enriched plasmas (as well as some optically-thick cooling models), radiation transport, cosmological expansion, and models for star formation and feedback in a cosmological context. In addition to explaining the algorithms implemented, we present solutions for a wide range of test problems, demonstrate the code's parallel performance, and discuss the Enzo collaboration's code development methodology.

  11. PARAMESH: A Parallel Adaptive Mesh Refinement Community Toolkit

    NASA Technical Reports Server (NTRS)

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

    1999-01-01

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

  12. Unstructured mesh quality assessment and upwind Euler solution algorithm validation

    NASA Astrophysics Data System (ADS)

    Woodard, Paul R.; Batina, John T.; Yang, Henry T. Y.

    1994-05-01

    Quality assessment procedures are described for two and three dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of the Euler equations for these meshes are obtained at low angle of attack, transonic conditions. Results for these cases, obtained as part of a validation study, investigate accuracy of an implicit upwind Euler solution algorithm.

  13. Parallel adaptive mesh refinement for electronic structure calculations

    SciTech Connect

    Kohn, S.; Weare, J.; Ong, E.; Baden, S.

    1996-12-01

    We have applied structured adaptive mesh refinement techniques to the solution of the LDA equations for electronic structure calculations. Local spatial refinement concentrates memory resources and numerical effort where it is most needed, near the atomic centers and in regions of rapidly varying charge density. The structured grid representation enables us to employ efficient iterative solver techniques such as conjugate gradients with multigrid preconditioning. We have parallelized our solver using an object-oriented adaptive mesh refinement framework.

  14. Zonal multigrid solution of compressible flow problems on unstructured and adaptive meshes

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri J.

    1989-01-01

    The simultaneous use of adaptive meshing techniques with a multigrid strategy for solving the 2-D Euler equations in the context of unstructured meshes is studied. To obtain optimal efficiency, methods capable of computing locally improved solutions without recourse to global recalculations are pursued. A method for locally refining an existing unstructured mesh, without regenerating a new global mesh is employed, and the domain is automatically partitioned into refined and unrefined regions. Two multigrid strategies are developed. In the first, time-stepping is performed on a global fine mesh covering the entire domain, and convergence acceleration is achieved through the use of zonal coarse grid accelerator meshes, which lie under the adaptively refined regions of the global fine mesh. Both schemes are shown to produce similar convergence rates to each other, and also with respect to a previously developed global multigrid algorithm, which performs time-stepping throughout the entire domain, on each mesh level. However, the present schemes exhibit higher computational efficiency due to the smaller number of operations on each level.

  15. Spatial and temporal adaptive procedures for the unsteady aerodynamic analysis of airfoils using unstructured meshes

    NASA Technical Reports Server (NTRS)

    Hooker, John R.; Batina, John T.; Williams, Marc H.

    1992-01-01

    An algorithm which combines spatial and temporal adaption for the time integration of the two-dimensional Euler equations on unstructured meshes of triangles is presented. Spatial adaption involves mesh enrichment to add elements in high gradient regions of the flow and mesh coarsening to remove elements where they are no longer needed. Temporal adaption is a time accurate, local time stepping procedure which integrates the flow equations in each cell according to the local numerical stability constraint. The flow solver utilizes a four-stage Runge-Kutta time integration scheme with an upwind flux-split spatial discretization. Results obtained using spatial and temporal adaption indicate that highly accurate solutions can be obtained with a significant savings of computing time over global time stepping.

  16. A conforming to interface structured adaptive mesh refinement technique for modeling fracture problems

    NASA Astrophysics Data System (ADS)

    Soghrati, Soheil; Xiao, Fei; Nagarajan, Anand

    2016-12-01

    A Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique is introduced for the automated transformation of a structured grid into a conforming mesh with appropriate element aspect ratios. The CISAMR algorithm is composed of three main phases: (i) Structured Adaptive Mesh Refinement (SAMR) of the background grid; (ii) r-adaptivity of the nodes of elements cut by the crack; (iii) sub-triangulation of the elements deformed during the r-adaptivity process and those with hanging nodes generated during the SAMR process. The required considerations for the treatment of crack tips and branching cracks are also discussed in this manuscript. Regardless of the complexity of the problem geometry and without using iterative smoothing or optimization techniques, CISAMR ensures that aspect ratios of conforming elements are lower than three. Multiple numerical examples are presented to demonstrate the application of CISAMR for modeling linear elastic fracture problems with intricate morphologies.

  17. A conforming to interface structured adaptive mesh refinement technique for modeling fracture problems

    NASA Astrophysics Data System (ADS)

    Soghrati, Soheil; Xiao, Fei; Nagarajan, Anand

    2017-04-01

    A Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique is introduced for the automated transformation of a structured grid into a conforming mesh with appropriate element aspect ratios. The CISAMR algorithm is composed of three main phases: (i) Structured Adaptive Mesh Refinement (SAMR) of the background grid; (ii) r-adaptivity of the nodes of elements cut by the crack; (iii) sub-triangulation of the elements deformed during the r-adaptivity process and those with hanging nodes generated during the SAMR process. The required considerations for the treatment of crack tips and branching cracks are also discussed in this manuscript. Regardless of the complexity of the problem geometry and without using iterative smoothing or optimization techniques, CISAMR ensures that aspect ratios of conforming elements are lower than three. Multiple numerical examples are presented to demonstrate the application of CISAMR for modeling linear elastic fracture problems with intricate morphologies.

  18. CONSTRAINED-TRANSPORT MAGNETOHYDRODYNAMICS WITH ADAPTIVE MESH REFINEMENT IN CHARM

    SciTech Connect

    Miniati, Francesco; Martin, Daniel F. E-mail: DFMartin@lbl.gov

    2011-07-01

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

  19. Time-accurate anisotropic mesh adaptation for three-dimensional time-dependent problems with body-fitted moving geometries

    NASA Astrophysics Data System (ADS)

    Barral, N.; Olivier, G.; Alauzet, F.

    2017-02-01

    Anisotropic metric-based mesh adaptation has proved its efficiency to reduce the CPU time of steady and unsteady simulations while improving their accuracy. However, its extension to time-dependent problems with body-fitted moving geometries is far from straightforward. This paper establishes a well-founded framework for multiscale mesh adaptation of unsteady problems with moving boundaries. This framework is based on a novel space-time analysis of the interpolation error, within the continuous mesh theory. An optimal metric field, called ALE metric field, is derived, which takes into account the movement of the mesh during the adaptation. Based on this analysis, the global fixed-point adaptation algorithm for time-dependent simulations is extended to moving boundary problems, within the range of body-fitted moving meshes and ALE simulations. Finally, three dimensional adaptive simulations with moving boundaries are presented to validate the proposed approach.

  20. Adaptive mesh refinement and adjoint methods in geophysics simulations

    NASA Astrophysics Data System (ADS)

    Burstedde, Carsten

    2013-04-01

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

  1. Adaptive continuous twisting algorithm

    NASA Astrophysics Data System (ADS)

    Moreno, Jaime A.; Negrete, Daniel Y.; Torres-González, Victor; Fridman, Leonid

    2016-09-01

    In this paper, an adaptive continuous twisting algorithm (ACTA) is presented. For double integrator, ACTA produces a continuous control signal ensuring finite time convergence of the states to zero. Moreover, the control signal generated by ACTA compensates the Lipschitz perturbation in finite time, i.e. its value converges to the opposite value of the perturbation. ACTA also keeps its convergence properties, even in the case that the upper bound of the derivative of the perturbation exists, but it is unknown.

  2. Adaptive time-step with anisotropic meshing for incompressible flows

    NASA Astrophysics Data System (ADS)

    Coupez, T.; Jannoun, G.; Nassif, N.; Nguyen, H. C.; Digonnet, H.; Hachem, E.

    2013-05-01

    This paper presents a method of combining anisotropic mesh adaptation and adaptive time-stepping for Computational Fluid Dynamics (CFD). First, we recall important features of the anisotropic meshing approach using a posteriori estimates relying on the length distribution tensor approach and the associated edge based error analysis. Then we extend the proposed technique to contain adaptive time advancing based on a newly developed time error estimator. The objective of this paper is to show that the combination of time and space anisotropic adaptations with highly stretched elements can be used to compute high Reynolds number flows within reasonable computational and storage costs. In particular, it will be shown that boundary layers, flow detachments and all vortices are well captured automatically by the mesh. The time-step is controlled by the interpolation error and preserves the accuracy of the mesh adapted solution. A Variational MultiScale (VMS) method is employed for the discretization of the Navier-Stokes equations. Numerical solutions of some benchmark problems demonstrate the applicability of the proposed space-time error estimator. An important feature of the proposed method is its conceptual and computational simplicity as it only requires from the user a number of nodes according to which the mesh and the time-steps are automatically adapted.

  3. Structured Adaptive Mesh Refinement Application Infrastructure

    SciTech Connect

    2010-07-15

    SAMRAI is an object-oriented support library for structured adaptice mesh refinement (SAMR) simulation of computational science problems, modeled by systems of partial differential equations (PDEs). SAMRAI is developed and maintained in the Center for Applied Scientific Computing (CASC) under ASCI ITS and PSE support. SAMRAI is used in a variety of application research efforts at LLNL and in academia. These applications are developed in collaboration with SAMRAI development team members.

  4. Adaptive mesh generation for viscous flows using Delaunay triangulation

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri J.

    1990-01-01

    A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.

  5. Adaptive mesh generation for viscous flows using Delaunay triangulation

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri J.

    1988-01-01

    A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.

  6. Automatic off-body overset adaptive Cartesian mesh method based on an octree approach

    NASA Astrophysics Data System (ADS)

    Péron, Stéphanie; Benoit, Christophe

    2013-01-01

    This paper describes a method for generating adaptive structured Cartesian grids within a near-body/off-body mesh partitioning framework for the flow simulation around complex geometries. The off-body Cartesian mesh generation derives from an octree structure, assuming each octree leaf node defines a structured Cartesian block. This enables one to take into account the large scale discrepancies in terms of resolution between the different bodies involved in the simulation, with minimum memory requirements. Two different conversions from the octree to Cartesian grids are proposed: the first one generates Adaptive Mesh Refinement (AMR) type grid systems, and the second one generates abutting or minimally overlapping Cartesian grid set. We also introduce an algorithm to control the number of points at each adaptation, that automatically determines relevant values of the refinement indicator driving the grid refinement and coarsening. An application to a wing tip vortex computation assesses the capability of the method to capture accurately the flow features.

  7. Relativistic Vlasov-Maxwell modelling using finite volumes and adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Wettervik, Benjamin Svedung; DuBois, Timothy C.; Siminos, Evangelos; Fülöp, Tünde

    2017-06-01

    The dynamics of collisionless plasmas can be modelled by the Vlasov-Maxwell system of equations. An Eulerian approach is needed to accurately describe processes that are governed by high energy tails in the distribution function, but is of limited efficiency for high dimensional problems. The use of an adaptive mesh can reduce the scaling of the computational cost with the dimension of the problem. Here, we present a relativistic Eulerian Vlasov-Maxwell solver with block-structured adaptive mesh refinement in one spatial and one momentum dimension. The discretization of the Vlasov equation is based on a high-order finite volume method. A flux corrected transport algorithm is applied to limit spurious oscillations and ensure the physical character of the distribution function. We demonstrate a speed-up by a factor of 7 × in a typical scenario involving laser pulse interaction with an underdense plasma due to the use of an adaptive mesh.

  8. Patch-based Adaptive Mesh Refinement for Multimaterial Hydrodynamics

    SciTech Connect

    Lomov, I; Pember, R; Greenough, J; Liu, B

    2005-10-18

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

  9. 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.

  10. Conservative Patch Algorithm and Mesh Sequencing for PAB3D

    NASA Technical Reports Server (NTRS)

    Pao, S. P.; Abdol-Hamid, K. S.

    2005-01-01

    A mesh-sequencing algorithm and a conservative patched-grid-interface algorithm (hereafter Patch Algorithm ) have been incorporated into the PAB3D code, which is a computer program that solves the Navier-Stokes equations for the simulation of subsonic, transonic, or supersonic flows surrounding an aircraft or other complex aerodynamic shapes. These algorithms are efficient, flexible, and have added tremendously to the capabilities of PAB3D. The mesh-sequencing algorithm makes it possible to perform preliminary computations using only a fraction of the grid cells (provided the original cell count is divisible by an integer) along any grid coordinate axis, independently of the other axes. The patch algorithm addresses another critical need in multi-block grid situation where the cell faces of adjacent grid blocks may not coincide, leading to errors in calculating fluxes of conserved physical quantities across interfaces between the blocks. The patch algorithm, based on the Stokes integral formulation of the applicable conservation laws, effectively matches each of the interfacial cells on one side of the block interface to the corresponding fractional cell area pieces on the other side. This approach is comprehensive and unified such that all interface topology is automatically processed without user intervention. This algorithm is implemented in a preprocessing code that creates a cell-by-cell database that will maintain flux conservation at any level of full or reduced grid density as the user may choose by way of the mesh-sequencing algorithm. These two algorithms have enhanced the numerical accuracy of the code, reduced the time and effort for grid preprocessing, and provided users with the flexibility of performing computations at any desired full or reduced grid resolution to suit their specific computational requirements.

  11. 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.

  12. Using Adaptive Mesh Refinment to Simulate Storm Surge

    NASA Astrophysics Data System (ADS)

    Mandli, K. T.; Dawson, C.

    2012-12-01

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

  13. Parallelization of an Adaptive Multigrid Algorithm for Fast Solution of Finite Element Structural Problems

    SciTech Connect

    Crane, N K; Parsons, I D; Hjelmstad, K D

    2002-03-21

    Adaptive mesh refinement selectively subdivides the elements of a coarse user supplied mesh to produce a fine mesh with reduced discretization error. Effective use of adaptive mesh refinement coupled with an a posteriori error estimator can produce a mesh that solves a problem to a given discretization error using far fewer elements than uniform refinement. A geometric multigrid solver uses increasingly finer discretizations of the same geometry to produce a very fast and numerically scalable solution to a set of linear equations. Adaptive mesh refinement is a natural method for creating the different meshes required by the multigrid solver. This paper describes the implementation of a scalable adaptive multigrid method on a distributed memory parallel computer. Results are presented that demonstrate the parallel performance of the methodology by solving a linear elastic rocket fuel deformation problem on an SGI Origin 3000. Two challenges must be met when implementing adaptive multigrid algorithms on massively parallel computing platforms. First, although the fine mesh for which the solution is desired may be large and scaled to the number of processors, the multigrid algorithm must also operate on much smaller fixed-size data sets on the coarse levels. Second, the mesh must be repartitioned as it is adapted to maintain good load balancing. In an adaptive multigrid algorithm, separate mesh levels may require separate partitioning, further complicating the load balance problem. This paper shows that, when the proper optimizations are made, parallel adaptive multigrid algorithms perform well on machines with several hundreds of processors.

  14. Adaptive mesh refinement and multilevel iteration for multiphase, multicomponent flow in porous media

    SciTech Connect

    Hornung, R.D.

    1996-12-31

    An adaptive local mesh refinement (AMR) algorithm originally developed for unsteady gas dynamics is extended to multi-phase flow in porous media. Within the AMR framework, we combine specialized numerical methods to treat the different aspects of the partial differential equations. Multi-level iteration and domain decomposition techniques are incorporated to accommodate elliptic/parabolic behavior. High-resolution shock capturing schemes are used in the time integration of the hyperbolic mass conservation equations. When combined with AMR, these numerical schemes provide high resolution locally in a more efficient manner than if they were applied on a uniformly fine computational mesh. We will discuss the interplay of physical, mathematical, and numerical concerns in the application of adaptive mesh refinement to flow in porous media problems of practical interest.

  15. An adaptive mesh magneto-hydrodynamic analysis of interstellar clouds

    NASA Astrophysics Data System (ADS)

    Kominsky, Paul J.

    Interstellar clouds play a key role in many astrophysical events. The interactions of dense interstellar clouds with shock waves and interstellar wind were investigated using an adaptive three-dimensional Cartesian mesh approach to the magneto-hydrodynamic equations. The mixing of the cloud material with the post-shock material results in complex layers of current density. In both the shock and wind interactions, a tail develops similar to the tail found with comets due to the solar wind. The orientation of this tail structure changes with the direction of the magnetic field, and may be useful to observationally determining the orientation of magnetic fields in the interstellar medium. The octree data structure was analyzed in regard to parallel work units. Larger block sizes have a higher volume to surface ratio and support a higher percentage of computational cells to non-computational cells, but require more cells at the finest grid resolution. Keeping the minimum resolution of the grid fixed, and averaging over all possible grids, the analysis confirms experience that block sizes larger than 8 × 8 × 8 cells do not improve storage efficiency. A novel algorithm was developed to implement rotationally periodic boundary conditions on quadtree and octree data, structures. Astrophysical flows wit h symmetric circulation, such as accretion disks, or periodic instabilities, such supernova remnants, may be able to take advantage of such boundary conditions while maintaining the other benefits of a Cartesian grid.

  16. Numerical study of Taylor bubbles with adaptive unstructured meshes

    NASA Astrophysics Data System (ADS)

    Xie, Zhihua; Pavlidis, Dimitrios; Percival, James; Pain, Chris; Matar, Omar; Hasan, Abbas; Azzopardi, Barry

    2014-11-01

    The Taylor bubble is a single long bubble which nearly fills the entire cross section of a liquid-filled circular tube. This type of bubble flow regime often occurs in gas-liquid slug flows in many industrial applications, including oil-and-gas production, chemical and nuclear reactors, and heat exchangers. The objective of this study is to investigate the fluid dynamics of Taylor bubbles rising in a vertical pipe filled with oils of extremely high viscosity (mimicking the ``heavy oils'' found in the oil-and-gas industry). A modelling and simulation framework is presented here which can modify and adapt anisotropic unstructured meshes to better represent the underlying physics of bubble rise and reduce the computational effort without sacrificing accuracy. The numerical framework consists of a mixed control-volume and finite-element formulation, a ``volume of fluid''-type method for the interface capturing based on a compressive control volume advection method, and a force-balanced algorithm for the surface tension implementation. Numerical examples of some benchmark tests and the dynamics of Taylor bubbles are presented to show the capability of this method. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.

  17. Parallel adaptive mesh refinement techniques for plasticity problems

    NASA Technical Reports Server (NTRS)

    Barry, W. J.; Jones, M. T.; Plassmann, P. E.

    1997-01-01

    The accurate modeling of the nonlinear properties of materials can be computationally expensive. Parallel computing offers an attractive way for solving such problems; however, the efficient use of these systems requires the vertical integration of a number of very different software components, we explore the solution of two- and three-dimensional, small-strain plasticity problems. We consider a finite-element formulation of the problem with adaptive refinement of an unstructured mesh to accurately model plastic transition zones. We present a framework for the parallel implementation of such complex algorithms. This framework, using libraries from the SUMAA3d project, allows a user to build a parallel finite-element application without writing any parallel code. To demonstrate the effectiveness of this approach on widely varying parallel architectures, we present experimental results from an IBM SP parallel computer and an ATM-connected network of Sun UltraSparc workstations. The results detail the parallel performance of the computational phases of the application during the process while the material is incrementally loaded.

  18. Parallel adaptive mesh refinement techniques for plasticity problems

    NASA Technical Reports Server (NTRS)

    Barry, W. J.; Jones, M. T.; Plassmann, P. E.

    1997-01-01

    The accurate modeling of the nonlinear properties of materials can be computationally expensive. Parallel computing offers an attractive way for solving such problems; however, the efficient use of these systems requires the vertical integration of a number of very different software components, we explore the solution of two- and three-dimensional, small-strain plasticity problems. We consider a finite-element formulation of the problem with adaptive refinement of an unstructured mesh to accurately model plastic transition zones. We present a framework for the parallel implementation of such complex algorithms. This framework, using libraries from the SUMAA3d project, allows a user to build a parallel finite-element application without writing any parallel code. To demonstrate the effectiveness of this approach on widely varying parallel architectures, we present experimental results from an IBM SP parallel computer and an ATM-connected network of Sun UltraSparc workstations. The results detail the parallel performance of the computational phases of the application during the process while the material is incrementally loaded.

  19. Parallel adaptive mesh refinement techniques for plasticity problems

    SciTech Connect

    Barry, W.J.; Jones, M.T. |; Plassmann, P.E.

    1997-12-31

    The accurate modeling of the nonlinear properties of materials can be computationally expensive. Parallel computing offers an attractive way for solving such problems; however, the efficient use of these systems requires the vertical integration of a number of very different software components, we explore the solution of two- and three-dimensional, small-strain plasticity problems. We consider a finite-element formulation of the problem with adaptive refinement of an unstructured mesh to accurately model plastic transition zones. We present a framework for the parallel implementation of such complex algorithms. This framework, using libraries from the SUMAA3d project, allows a user to build a parallel finite-element application without writing any parallel code. To demonstrate the effectiveness of this approach on widely varying parallel architectures, we present experimental results from an IBM SP parallel computer and an ATM-connected network of Sun UltraSparc workstations. The results detail the parallel performance of the computational phases of the application during the process while the material is incrementally loaded.

  20. Adaptive mesh refinement for shocks and material interfaces

    SciTech Connect

    Dai, William Wenlong

    2010-01-01

    There are three kinds of adaptive mesh refinement (AMR) in structured meshes. Block-based AMR sometimes over refines meshes. Cell-based AMR treats cells cell by cell and thus loses the advantage of the nature of structured meshes. Patch-based AMR is intended to combine advantages of block- and cell-based AMR, i.e., the nature of structured meshes and sharp regions of refinement. But, patch-based AMR has its own difficulties. For example, patch-based AMR typically cannot preserve symmetries of physics problems. In this paper, we will present an approach for a patch-based AMR for hydrodynamics simulations. The approach consists of clustering, symmetry preserving, mesh continuity, flux correction, communications, management of patches, and load balance. The special features of this patch-based AMR include symmetry preserving, efficiency of refinement across shock fronts and material interfaces, special implementation of flux correction, and patch management in parallel computing environments. To demonstrate the capability of the AMR framework, we will show both two- and three-dimensional hydrodynamics simulations with many levels of refinement.

  1. 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.

  2. 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.

  3. Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling

    NASA Astrophysics Data System (ADS)

    Davis, B. N.; LeVeque, R. J.

    2016-12-01

    One difficulty in developing numerical methods for tsunami modeling is the fact that solutions contain time-varying regions where much higher resolution is required than elsewhere in the domain, particularly when tracking a tsunami propagating across the ocean. The open source GeoClaw software deals with this issue by using block-structured adaptive mesh refinement to selectively refine around propagating waves. For problems where only a target area of the total solution is of interest (e.g., one coastal community), a method that allows identifying and refining the grid only in regions that influence this target area would significantly reduce the computational cost of finding a solution. In this work, we show that solving the time-dependent adjoint equation and using a suitable inner product with the forward solution allows more precise refinement of the relevant waves. We present the adjoint methodology first in one space dimension for illustration and in a broad context since it could also be used in other adaptive software, and potentially for other tsunami applications beyond adaptive refinement. We then show how this adjoint method has been integrated into the adaptive mesh refinement strategy of the open source GeoClaw software and present tsunami modeling results showing that the accuracy of the solution is maintained and the computational time required is significantly reduced through the integration of the adjoint method into adaptive mesh refinement.

  4. 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.

  5. Parallel Block Structured Adaptive Mesh Refinement on Graphics Processing Units

    SciTech Connect

    Beckingsale, D. A.; Gaudin, W. P.; Hornung, R. D.; Gunney, B. T.; Gamblin, T.; Herdman, J. A.; Jarvis, S. A.

    2014-11-17

    Block-structured adaptive mesh refinement is a technique that can be used when solving partial differential equations to reduce the number of zones necessary to achieve the required accuracy in areas of interest. These areas (shock fronts, material interfaces, etc.) are recursively covered with finer mesh patches that are grouped into a hierarchy of refinement levels. Despite the potential for large savings in computational requirements and memory usage without a corresponding reduction in accuracy, AMR adds overhead in managing the mesh hierarchy, adding complex communication and data movement requirements to a simulation. In this paper, we describe the design and implementation of a native GPU-based AMR library, including: the classes used to manage data on a mesh patch, the routines used for transferring data between GPUs on different nodes, and the data-parallel operators developed to coarsen and refine mesh data. We validate the performance and accuracy of our implementation using three test problems and two architectures: an eight-node cluster, and over four thousand nodes of Oak Ridge National Laboratory’s Titan supercomputer. Our GPU-based AMR hydrodynamics code performs up to 4.87× faster than the CPU-based implementation, and has been scaled to over four thousand GPUs using a combination of MPI and CUDA.

  6. 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

  7. 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

  8. 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.

  9. Model-Based Nonrigid Motion Analysis Using Natural Feature Adaptive Mesh

    SciTech Connect

    Zhang, Y.; Goldgof, D.B.; Sarkar, S.; Tsap, L.V.

    2000-04-25

    The success of nonrigid motion analysis using physical finite element model is dependent on the mesh that characterizes the object's geometric structure. We suggest a deformable mesh adapted to the natural features of images. The adaptive mesh requires much fewer number of nodes than the fixed mesh which was used in our previous work. We demonstrate the higher efficiency of the adaptive mesh in the context of estimating burn scar elasticity relative to normal skin elasticity using the observed 2D image sequence. Our results show that the scar assessment method based on the physical model using natural feature adaptive mesh can be applied to images which do not have artificial markers.

  10. 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

  11. A fourth order accurate adaptive mesh refinement method forpoisson's equation

    SciTech Connect

    Barad, Michael; Colella, Phillip

    2004-08-20

    We present a block-structured adaptive mesh refinement (AMR) method for computing solutions to Poisson's equation in two and three dimensions. It is based on a conservative, finite-volume formulation of the classical Mehrstellen methods. This is combined with finite volume AMR discretizations to obtain a method that is fourth-order accurate in solution error, and with easily verifiable solvability conditions for Neumann and periodic boundary conditions.

  12. Boltzmann Solver with Adaptive Mesh in Velocity Space

    SciTech Connect

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

    2011-05-20

    We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.

  13. 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

  14. 3D level set methods for evolving fronts on tetrahedral meshes with adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Morgan, Nathaniel R.; Waltz, Jacob I.

    2017-05-01

    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. The details of these level set and reinitialization methods are discussed. Results from a range of numerical test problems are presented.

  15. AMR++: Object-Oriented Parallel Adaptive Mesh Refinement

    SciTech Connect

    Quinlan, D.; Philip, B.

    2000-02-02

    Adaptive mesh refinement (AMR) computations are complicated by their dynamic nature. The development of solvers for realistic applications is complicated by both the complexity of the AMR and the geometry of realistic problem domains. The additional complexity of distributed memory parallelism within such AMR applications most commonly exceeds the level of complexity that can be reasonable maintained with traditional approaches toward software development. This paper will present the details of our object-oriented work on the simplification of the use of adaptive mesh refinement on applications with complex geometries for both serial and distributed memory parallel computation. We will present an independent set of object-oriented abstractions (C++ libraries) well suited to the development of such seemingly intractable scientific computations. As an example of the use of this object-oriented approach we will present recent results of an application modeling fluid flow in the eye. Within this example, the geometry is too complicated for a single curvilinear coordinate grid and so a set of overlapping curvilinear coordinate grids' are used. Adaptive mesh refinement and the required grid generation work to support the refinement process is coupled together in the solution of essentially elliptic equations within this domain. This paper will focus on the management of complexity within development of the AMR++ library which forms a part of the Overture object-oriented framework for the solution of partial differential equations within scientific computing.

  16. A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency

    NASA Astrophysics Data System (ADS)

    Bajc, Iztok; Hecht, Frédéric; Žumer, Slobodan

    2016-09-01

    This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics derived from the Hessian of a solution. The study is made on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in. Aspects relating the driving of mesh adaptivity within the nonlinear scheme are considered. The algorithmic performance is found to depend on at least two factors: when to trigger each single mesh adaptation, and the precision of the correlated remeshing. Each factor is represented by a parameter, with its values possibly varying for every new mesh adaptation. We empirically show that the time of the overall algorithm convergence can vary considerably when different sequences of parameters are used, thus posing a question about optimality. The extensive testings and debugging done within this work on the simulation of systems of nematic colloids substantially contributed to the upgrade of an open source finite element-oriented programming language to its 3D meshing possibilities, as also to an outer 3D remeshing module.

  17. Fast autodidactic adaptive equalization algorithms

    NASA Astrophysics Data System (ADS)

    Hilal, Katia

    Autodidactic equalization by adaptive filtering is addressed in a mobile radio communication context. A general method, using an adaptive stochastic gradient Bussgang type algorithm, to deduce two low cost computation algorithms is given: one equivalent to the initial algorithm and the other having improved convergence properties thanks to a block criteria minimization. Two start algorithms are reworked: the Godard algorithm and the decision controlled algorithm. Using a normalization procedure, and block normalization, the performances are improved, and their common points are evaluated. These common points are used to propose an algorithm retaining the advantages of the two initial algorithms. This thus inherits the robustness of the Godard algorithm and the precision and phase correction of the decision control algorithm. The work is completed by a study of the stable states of Bussgang type algorithms and of the stability of the Godard algorithms, initial and normalized. The simulation of these algorithms, carried out in a mobile radio communications context, and under severe conditions on the propagation channel, gave a 75% reduction in the number of samples required for the processing in relation with the initial algorithms. The improvement of the residual error was of a much lower return. These performances are close to making possible the use of autodidactic equalization in the mobile radio system.

  18. ADER-WENO finite volume schemes with space-time adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Dumbser, Michael; Zanotti, Olindo; Hidalgo, Arturo; Balsara, Dinshaw S.

    2013-09-01

    We present the first high order one-step ADER-WENO finite volume scheme with adaptive mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resulting algorithm is particularly well suited for an AMR strategy on space-time adaptive meshes, i.e. with time-accurate local time stepping. The AMR property has been implemented 'cell-by-cell', with a standard tree-type algorithm, while the scheme has been parallelized via the message passing interface (MPI) paradigm. The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations of magnetohydrodynamics (MHD). High order in space and time have been confirmed via a numerical convergence study and a detailed analysis of the computational speed-up with respect to highly refined uniform meshes is also presented. We also show test problems where the presented high order AMR scheme behaves clearly better than traditional second order AMR methods. The proposed scheme that combines for the first time high order ADER methods with space-time adaptive grids in two and three space dimensions is likely to become a useful tool in several fields of computational physics, applied mathematics and mechanics.

  19. 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.

  20. High-Performance Reactive Fluid Flow Simulations Using Adaptive Mesh Refinement on Thousands of Processors

    NASA Astrophysics Data System (ADS)

    Calder, A. C.; Curtis, B. C.; Dursi, L. J.; Fryxell, B.; Henry, G.; MacNeice, P.; Olson, K.; Ricker, P.; Rosner, R.; Timmes, F. X.; Tufo, H. M.; Truran, J. W.; Zingale, M.

    We present simulations and performance results of nuclear burning fronts in supernovae on the largest domain and at the finest spatial resolution studied to date. These simulations were performed on the Intel ASCI-Red machine at Sandia National Laboratories using FLASH, a code developed at the Center for Astrophysical Thermonuclear Flashes at the University of Chicago. FLASH is a modular, adaptive mesh, parallel simulation code capable of handling compressible, reactive fluid flows in astrophysical environments. FLASH is written primarily in Fortran 90, uses the Message-Passing Interface library for inter-processor communication and portability, and employs the PARAMESH package to manage a block-structured adaptive mesh that places blocks only where the resolution is required and tracks rapidly changing flow features, such as detonation fronts, with ease. We describe the key algorithms and their implementation as well as the optimizations required to achieve sustained performance of 238 GLOPS on 6420 processors of ASCI-Red in 64-bit arithmetic.

  1. Mesh adaption for efficient multiscale implementation of one-dimensional turbulence

    NASA Astrophysics Data System (ADS)

    Lignell, D. O.; Kerstein, A. R.; Sun, G.; Monson, E. I.

    2013-06-01

    One-Dimensional Turbulence (ODT) is a stochastic model for turbulent flow simulation. In an atmospheric context, it is analogous to single-column modeling (SCM) in that it lives on a 1D spatial domain, but different in that it time advances individual flow realizations rather than ensemble-averaged quantities. The lack of averaging enables a physically sound multiscale treatment, which is useful for resolving sporadic localized phenomena, as seen in stably stratified regimes, and sharp interfaces, as observed where a convective layer encounters a stable overlying zone. In such flows, the relevant scale range is so large that it is beneficial to enhance model performance by introducing an adaptive mesh. An adaptive-mesh algorithm that provides the desired performance characteristics is described and demonstrated, and its implications for the ODT advancement scheme are explained.

  2. Output-based space-time mesh adaptation for the compressible Navier-Stokes equations

    NASA Astrophysics Data System (ADS)

    Fidkowski, Krzysztof J.; Luo, Yuxing

    2011-06-01

    This paper presents an output-based adaptive algorithm for unsteady simulations of convection-dominated flows. A space-time discontinuous Galerkin discretization is used in which the spatial meshes remain static in both position and resolution, and in which all elements advance by the same time step. Error estimates are computed using an adjoint-weighted residual, where the discrete adjoint is computed on a finer space obtained by order enrichment of the primal space. An iterative method based on an approximate factorization is used to solve both the forward and adjoint problems. The output error estimate drives a fixed-growth adaptive strategy that employs hanging-node refinement in the spatial domain and slab bisection in the temporal domain. Detection of space-time anisotropy in the localization of the output error is found to be important for efficiency of the adaptive algorithm, and two anisotropy measures are presented: one based on inter-element solution jumps, and one based on projection of the adjoint. Adaptive results are shown for several two-dimensional convection-dominated flows, including the compressible Navier-Stokes equations. For sufficiently-low accuracy levels, output-based adaptation is shown to be advantageous in terms of degrees of freedom when compared to uniform refinement and to adaptive indicators based on approximation error and the unweighted residual. Time integral quantities are used for the outputs of interest, but entire time histories of the integrands are also compared and found to converge rapidly under the proposed scheme. In addition, the final output-adapted space-time meshes are shown to be relatively insensitive to the starting mesh.

  3. Spatial and temporal adaptive procedures for the unsteady aerodynamic analysis of airfoils using unstructured meshes. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Hooker, John R.; Batina, John T.; Williams, Marc H.

    1992-01-01

    An algorithm which combines spatial and temporal adaption for the time integration of the two dimensional Euler equations on unstructured meshes of triangles is presented. Spatial adaption involves mesh enrichment to add elements in high gradient regions of the flow and mesh coarsening to remove elements where they are no longer needed. Temporal adaption is a time accurate, local time stepping procedure which integrates the flow equations in each cell according to the local numerical stability constraint. The flow solver utilizes a four stage Runge-Kutta time integration scheme with an upwind flux-split spatial discretization. Results obtained using spatial and temporal adaption indicate that highly accurate solutions can be obtained with a significant savings of computing time over global time stepping.

  4. 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

  5. New Capabilities for Adaptive Mesh Simulation Use within FORWARD

    NASA Astrophysics Data System (ADS)

    Mathews, N.; Flyer, N.; Gibson, S. E.; Kucera, T. A.; Manchester, W.

    2016-12-01

    The multiscale nature of the solar corona can pose challenges to numerical simulations. Adaptive meshes are often used to resolve fine-scale structures, such as the chromospheric-coronal interface found in prominences and the transition region as a whole. FORWARD is a SolarSoft IDL package designed as a community resource for creating a broad range of synthetic coronal observables from numerical models and comparing them to data. However, to date its interface with numerical simulations has been limited to regular grids. We will present a new adaptive-grid interface to FORWARD that will enable efficient synthesis of solar observations. This is accomplished through the use of hierarchical IDL structures designed to enable finding nearest-neighbor points quickly for non-uniform grids. This facilitates line-of-sight integrations that can adapt to the unequally spaced mesh. We will demonstrate this capability for the Alfven-Wave driven SOlar wind Model (AWSOM), part of the Space Weather Modeling Framework (SWMF). In addition, we will use it in the context of a prominence-cavity model, highlighting new capabilities in FORWARD that allow treatment of continuum absorbtion as well as EUV line emission via dual populations (chromosphere-corona).

  6. 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.

  7. 3D Finite Element Trajectory Code with Adaptive Meshing

    NASA Astrophysics Data System (ADS)

    Ives, Lawrence; Bui, Thuc; Vogler, William; Bauer, Andy; Shephard, Mark; Beal, Mark; Tran, Hien

    2004-11-01

    Beam Optics Analysis, a new, 3D charged particle program is available and in use for the design of complex, 3D electron guns and charged particle devices. The code reads files directly from most CAD and solid modeling programs, includes an intuitive Graphical User Interface (GUI), and a robust mesh generator that is fully automatic. Complex problems can be set up, and analysis initiated in minutes. The program includes a user-friendly post processor for displaying field and trajectory data using 3D plots and images. The electrostatic solver is based on the standard nodal finite element method. The magnetostatic field solver is based on the vector finite element method and is also called during the trajectory simulation process to solve for self magnetic fields. The user imports the geometry from essentially any commercial CAD program and uses the GUI to assign parameters (voltages, currents, dielectric constant) and designate emitters (including work function, emitter temperature, and number of trajectories). The the mesh is generated automatically and analysis is performed, including mesh adaptation to improve accuracy and optimize computational resources. This presentation will provide information on the basic structure of the code, its operation, and it's capabilities.

  8. Cartesian based grid generation/adaptive mesh refinement

    NASA Technical Reports Server (NTRS)

    Coirier, William J.

    1992-01-01

    Grid adaptation has recently received attention in the computational fluid dynamics (CFD) community as a means to capture the salient features of a flowfield by either moving grid points of a structured or by adding cells in an unstructured manner. An approach based on a background cartesian mesh is investigated from which the geometry is 'cut' out of the mesh. Once the mesh is obtained, a solution on this coarse grid is found, that indicates which cells need to be refined. This process of refining/solving continues until the flow is grid refined in terms of a user specified global parameter (such as drag coefficient etc.). The advantages of this approach are twofold: the generation of the base grid is independent of the topology of the bodies or surfaces around/through which the flow is to be computed, and the resulting grid (in uncut regions) is highly isotropic, so that the truncation error is low. The flow solver (which, along with the grid generation is still under development) uses a completely unstructured data base, and is a finite volume, upwinding scheme. Current and future work will address generating Navier-Stokes suitable grids by using locally aligned and normal face/cell refining. The attached plot shows a simple grid about two turbine blades.

  9. FLY: a Tree Code for Adaptive Mesh Refinement

    NASA Astrophysics Data System (ADS)

    Becciani, U.; Antonuccio-Delogu, V.; Costa, A.; Ferro, D.

    FLY is a public domain parallel treecode, which makes heavy use of the one-sided communication paradigm to handle the management of the tree structure. It implements the equations for cosmological evolution and can be run for different cosmological models. This paper shows an example of the integration of a tree N-body code with an adaptive mesh, following the PARAMESH scheme. This new implementation will allow the FLY output, and more generally any binary output, to be used with any hydrodynamics code that adopts the PARAMESH data structure, to study compressible flow problems.

  10. Adaptive Mesh Refinement in Curvilinear Body-Fitted Grid Systems

    NASA Technical Reports Server (NTRS)

    Steinthorsson, Erlendur; Modiano, David; Colella, Phillip

    1995-01-01

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

  11. 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.

  12. Efficient simulation of three-dimensional anisotropic cardiac tissue using an adaptive mesh refinement method

    NASA Astrophysics Data System (ADS)

    Cherry, Elizabeth M.; Greenside, Henry S.; Henriquez, Craig S.

    2003-09-01

    A recently developed space-time adaptive mesh refinement algorithm (AMRA) for simulating isotropic one- and two-dimensional excitable media is generalized to simulate three-dimensional anisotropic media. The accuracy and efficiency of the algorithm is investigated for anisotropic and inhomogeneous 2D and 3D domains using the Luo-Rudy 1 (LR1) and FitzHugh-Nagumo models. For a propagating wave in a 3D slab of tissue with LR1 membrane kinetics and rotational anisotropy comparable to that found in the human heart, factors of 50 and 30 are found, respectively, for the speedup and for the savings in memory compared to an algorithm using a uniform space-time mesh at the finest resolution of the AMRA method. For anisotropic 2D and 3D media, we find no reduction in accuracy compared to a uniform space-time mesh. These results suggest that the AMRA will be able to simulate the 3D electrical dynamics of canine ventricles quantitatively for 1 s using 32 1-GHz Alpha processors in approximately 9 h.

  13. Thermal-chemical Mantle Convection Models With Adaptive Mesh Refinement

    NASA Astrophysics Data System (ADS)

    Leng, W.; Zhong, S.

    2008-12-01

    In numerical modeling of mantle convection, resolution is often crucial for resolving small-scale features. New techniques, adaptive mesh refinement (AMR), allow local mesh refinement wherever high resolution is needed, while leaving other regions with relatively low resolution. Both computational efficiency for large- scale simulation and accuracy for small-scale features can thus be achieved with AMR. Based on the octree data structure [Tu et al. 2005], we implement the AMR techniques into the 2-D mantle convection models. For pure thermal convection models, benchmark tests show that our code can achieve high accuracy with relatively small number of elements both for isoviscous cases (i.e. 7492 AMR elements v.s. 65536 uniform elements) and for temperature-dependent viscosity cases (i.e. 14620 AMR elements v.s. 65536 uniform elements). We further implement tracer-method into the models for simulating thermal-chemical convection. By appropriately adding and removing tracers according to the refinement of the meshes, our code successfully reproduces the benchmark results in van Keken et al. [1997] with much fewer elements and tracers compared with uniform-mesh models (i.e. 7552 AMR elements v.s. 16384 uniform elements, and ~83000 tracers v.s. ~410000 tracers). The boundaries of the chemical piles in our AMR code can be easily refined to the scales of a few kilometers for the Earth's mantle and the tracers are concentrated near the chemical boundaries to precisely trace the evolvement of the boundaries. It is thus very suitable for our AMR code to study the thermal-chemical convection problems which need high resolution to resolve the evolvement of chemical boundaries, such as the entrainment problems [Sleep, 1988].

  14. Simulation of nonpoint source contamination based on adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Kourakos, G.; Harter, T.

    2014-12-01

    Contamination of groundwater aquifers from nonpoint sources is a worldwide problem. Typical agricultural groundwater basins receive contamination from a large array (in the order of ~10^5-6) of spatially and temporally heterogeneous sources such as fields, crops, dairies etc, while the received contaminants emerge at significantly uncertain time lags to a large array of discharge surfaces such as public supply, domestic and irrigation wells and streams. To support decision making in such complex regimes several approaches have been developed, which can be grouped into 3 categories: i) Index methods, ii)regression methods and iii) physically based methods. Among the three, physically based methods are considered more accurate, but at the cost of computational demand. In this work we present a physically based simulation framework which exploits the latest hardware and software developments to simulate large (>>1,000 km2) groundwater basins. First we simulate groundwater flow using a sufficiently detailed mesh to capture the spatial heterogeneity. To achieve optimal mesh quality we combine adaptive mesh refinement with the nonlinear solution for unconfined flow. Starting from a coarse grid the mesh is refined iteratively in the parts of the domain where the flow heterogeneity appears higher resulting in optimal grid. Secondly we simulate the nonpoint source pollution based on the detailed velocity field computed from the previous step. In our approach we use the streamline model where the 3D transport problem is decomposed into multiple 1D transport problems. The proposed framework is applied to simulate nonpoint source pollution in the Central Valley aquifer system, California.

  15. Nonhydrostatic adaptive mesh dynamics for multiscale climate models (Invited)

    NASA Astrophysics Data System (ADS)

    Collins, W.; Johansen, H.; McCorquodale, P.; Colella, P.; Ullrich, P. A.

    2013-12-01

    Many of the atmospheric phenomena with the greatest potential impact in future warmer climates are inherently multiscale. Such meteorological systems include hurricanes and tropical cyclones, atmospheric rivers, and other types of hydrometeorological extremes. These phenomena are challenging to simulate in conventional climate models due to the relatively coarse uniform model resolutions relative to the native nonhydrostatic scales of the phenomonological dynamics. To enable studies of these systems with sufficient local resolution for the multiscale dynamics yet with sufficient speed for climate-change studies, we have adapted existing adaptive mesh dynamics for the DOE-NSF Community Atmosphere Model (CAM). In this talk, we present an adaptive, conservative finite volume approach for moist non-hydrostatic atmospheric dynamics. The approach is based on the compressible Euler equations on 3D thin spherical shells, where the radial direction is treated implicitly (using a fourth-order Runga-Kutta IMEX scheme) to eliminate time step constraints from vertical acoustic waves. Refinement is performed only in the horizontal directions. The spatial discretization is the equiangular cubed-sphere mapping, with a fourth-order accurate discretization to compute flux averages on faces. By using both space-and time-adaptive mesh refinement, the solver allocates computational effort only where greater accuracy is needed. The resulting method is demonstrated to be fourth-order accurate for model problems, and robust at solution discontinuities and stable for large aspect ratios. We present comparisons using a simplified physics package for dycore comparisons of moist physics. Hadley cell lifting an advected tracer into upper atmosphere, with horizontal adaptivity

  16. 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.

  17. Dynamic Load Balancing for Adaptive Meshes using Symmetric Broadcast Networks

    NASA Technical Reports Server (NTRS)

    Das, Sajal K.; Harvey, Daniel J.; Biswas, Rupak; Saini, Subhash (Technical Monitor)

    1998-01-01

    Many scientific applications involve grids that lack a uniform underlying structure. These applications are often dynamic in the sense that the grid structure significantly changes between successive phases of execution. In parallel computing environments, mesh adaptation of grids through selective refinement/coarsening has proven to be an effective approach. However, achieving load balance while minimizing inter-processor communication and redistribution costs is a difficult problem. Traditional dynamic load balancers are mostly inadequate because they lack a global view across processors. In this paper, we compare a novel load balancer that utilizes symmetric broadcast networks (SBN) to a successful global load balancing environment (PLUM) created to handle adaptive unstructured applications. Our experimental results on the IBM SP2 demonstrate that performance of the proposed SBN load balancer is comparable to results achieved under PLUM.

  18. AMRSim: an object-oriented performance simulator for parallel adaptive mesh refinement

    SciTech Connect

    Miller, B; Philip, B; Quinlan, D; Wissink, A

    2001-01-08

    Adaptive mesh refinement is complicated by both the algorithms and the dynamic nature of the computations. In parallel the complexity of getting good performance is dependent upon the architecture and the application. Most attempts to address the complexity of AMR have lead to the development of library solutions, most have developed object-oriented libraries or frameworks. All attempts to date have made numerous and sometimes conflicting assumptions which make the evaluation of performance of AMR across different applications and architectures difficult or impracticable. The evaluation of different approaches can alternatively be accomplished through simulation of the different AMR processes. In this paper we outline our research work to simulate the processing of adaptive mesh refinement grids using a distributed array class library (P++). This paper presents a combined analytic and empirical approach, since details of the algorithms can be readily predicted (separated into specific phases), while the performance associated with the dynamic behavior must be studied empirically. The result, AMRSim, provides a simple way to develop bounds on the expected performance of AMR calculations subject to constraints given by the algorithms, frameworks, and architecture.

  19. 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.

  20. 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.

  1. 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.

  2. A Predictive Model of Fragmentation using Adaptive Mesh Refinement and a Hierarchical Material Model

    SciTech Connect

    Koniges, A E; Masters, N D; Fisher, A C; Anderson, R W; Eder, D C; Benson, D; Kaiser, T B; Gunney, B T; Wang, P; Maddox, B R; Hansen, J F; Kalantar, D H; Dixit, P; Jarmakani, H; Meyers, M A

    2009-03-03

    Fragmentation is a fundamental material process that naturally spans spatial scales from microscopic to macroscopic. We developed a mathematical framework using an innovative combination of hierarchical material modeling (HMM) and adaptive mesh refinement (AMR) to connect the continuum to microstructural regimes. This framework has been implemented in a new multi-physics, multi-scale, 3D simulation code, NIF ALE-AMR. New multi-material volume fraction and interface reconstruction algorithms were developed for this new code, which is leading the world effort in hydrodynamic simulations that combine AMR with ALE (Arbitrary Lagrangian-Eulerian) techniques. The interface reconstruction algorithm is also used to produce fragments following material failure. In general, the material strength and failure models have history vector components that must be advected along with other properties of the mesh during remap stage of the ALE hydrodynamics. The fragmentation models are validated against an electromagnetically driven expanding ring experiment and dedicated laser-based fragmentation experiments conducted at the Jupiter Laser Facility. As part of the exit plan, the NIF ALE-AMR code was applied to a number of fragmentation problems of interest to the National Ignition Facility (NIF). One example shows the added benefit of multi-material ALE-AMR that relaxes the requirement that material boundaries must be along mesh boundaries.

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

    SciTech Connect

    Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett; Ibanez, Daniel; Sahni, Onkar; Jansen, Kenneth E.; Shephard, Mark S.

    2017-01-01

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

  4. Patched based methods for adaptive mesh refinement solutions of partial differential equations

    SciTech Connect

    Saltzman, J.

    1997-09-02

    This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year`s school which is ``Multiscale Methods and Wavelets in Numerical Simulation.`` The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.

  5. Adaptive protection algorithm and system

    DOEpatents

    Hedrick, Paul [Pittsburgh, PA; Toms, Helen L [Irwin, PA; Miller, Roger M [Mars, PA

    2009-04-28

    An adaptive protection algorithm and system for protecting electrical distribution systems traces the flow of power through a distribution system, assigns a value (or rank) to each circuit breaker in the system and then determines the appropriate trip set points based on the assigned rank.

  6. Production-quality Tools for Adaptive Mesh RefinementVisualization

    SciTech Connect

    Weber, Gunther H.; Childs, Hank; Bonnell, Kathleen; Meredith,Jeremy; Miller, Mark; Whitlock, Brad; Bethel, E. Wes

    2007-10-25

    Adaptive Mesh Refinement (AMR) is a highly effectivesimulation method for spanning a large range of spatiotemporal scales,such as astrophysical simulations that must accommodate ranges frominterstellar to sub-planetary. Most mainstream visualization tools stilllack support for AMR as a first class data type and AMR code teams usecustom built applications for AMR visualization. The Department ofEnergy's (DOE's) Science Discovery through Advanced Computing (SciDAC)Visualization and Analytics Center for Enabling Technologies (VACET) isextending and deploying VisIt, an open source visualization tool thataccommodates AMR as a first-class data type, for use asproduction-quality, parallel-capable AMR visual data analysisinfrastructure. This effort will help science teams that use AMR-basedsimulations and who develop their own AMR visual data analysis softwareto realize cost and labor savings.

  7. Efficient Plasma Ion Source Modeling With Adaptive Mesh Refinement (Abstract)

    SciTech Connect

    Kim, J.S.; Vay, J.L.; Friedman, A.; Grote, D.P.

    2005-03-15

    Ion beam drivers for high energy density physics and inertial fusion energy research require high brightness beams, so there is little margin of error allowed for aberration at the emitter. Thus, accurate plasma ion source computer modeling is required to model the plasma sheath region and time-dependent effects correctly.A computer plasma source simulation module that can be used with a powerful heavy ion fusion code, WARP, or as a standalone code, is being developed. In order to treat the plasma sheath region accurately and efficiently, the module will have the capability of handling multiple spatial scale problems by using Adaptive Mesh Refinement (AMR). We will report on our progress on the project.

  8. Adaptive Mesh Refinement in Computational Astrophysics -- Methods and Applications

    NASA Astrophysics Data System (ADS)

    Balsara, D.

    2001-12-01

    The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so because the physics associated with astrophysical phenomena evolves in multi-scale fashion and we wish to arrive at a multi-scale simulational capability to represent the physics. Because astrophysical systems have magnetic fields, multi-scale magnetohydrodynamics (MHD) is of especial interest. In this paper we first discuss general issues in adaptive mesh refinement (AMR). We then focus on the important issues in carrying out divergence-free AMR-MHD and catalogue the progress we have made in that area. We show that AMR methods lend themselves to easy parallelization. We then discuss applications of the RIEMANN framework for AMR-MHD to problems in computational astophysics.

  9. 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.

  10. Novel adaptation of the demodulation technology for gear damage detection to variable amplitudes of mesh harmonics

    NASA Astrophysics Data System (ADS)

    Combet, F.; Gelman, L.

    2011-04-01

    In this paper, a novel adaptive demodulation technique including a new diagnostic feature is proposed for gear diagnosis in conditions of variable amplitudes of the mesh harmonics. This vibration technique employs the time synchronous average (TSA) of vibration signals. The new adaptive diagnostic feature is defined as the ratio of the sum of the sideband components of the envelope spectrum of a mesh harmonic to the measured power of the mesh harmonic. The proposed adaptation of the technique is justified theoretically and experimentally by the high level of the positive covariance between amplitudes of the mesh harmonics and the sidebands in conditions of variable amplitudes of the mesh harmonics. It is shown that the adaptive demodulation technique preserves effectiveness of local fault detection of gears operating in conditions of variable mesh amplitudes.

  11. 3D Compressible Melt Transport with Adaptive Mesh Refinement

    NASA Astrophysics Data System (ADS)

    Dannberg, Juliane; Heister, Timo

    2015-04-01

    Melt generation and migration have been the subject of numerous investigations, but their typical time and length-scales are vastly different from mantle convection, which makes it difficult to study these processes in a unified framework. The equations that describe coupled Stokes-Darcy flow have been derived a long time ago and they have been successfully implemented and applied in numerical models (Keller et al., 2013). However, modelling magma dynamics poses the challenge of highly non-linear and spatially variable material properties, in particular the viscosity. Applying adaptive mesh refinement to this type of problems is particularly advantageous, 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. In addition, previous models neglect the compressibility of both the solid and the fluid phase. However, experiments have shown that the melt density change from the depth of melt generation to the surface leads to a volume increase of up to 20%. Considering these volume changes in both phases also ensures self-consistency of models that strive to link melt generation to processes in the deeper mantle, where the compressibility of the solid phase becomes more important. We describe our extension of the finite-element mantle convection code ASPECT (Kronbichler et al., 2012) that allows for solving additional 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. We evaluate the functionality and potential of this method using a series of simple model setups and benchmarks, comparing results of the compressible and incompressible formulation and

  12. Adaptive FEM with coarse initial mesh guarantees optimal convergence rates for compactly perturbed elliptic problems

    NASA Astrophysics Data System (ADS)

    Bespalov, Alex; Haberl, Alexander; Praetorius, Dirk

    2017-04-01

    We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Garding inequality, adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence with optimal algebraic rates. As an important consequence of our analysis, one does not have to deal with the a-priori assumption that the underlying meshes are sufficiently fine. Hence, the overall conclusion of our results is that adaptivity has stabilizing effects and can overcome possibly pessimistic restrictions on the meshes. In particular, our analysis covers adaptive mesh-refinement for the finite element discretization of the Helmholtz equation from where our interest originated.

  13. Adaptivity techniques for the computation of two-dimensional viscous flows using structured meshes

    NASA Astrophysics Data System (ADS)

    Szmelter, J.; Evans, A.; Weatherill, N. P.

    In this paper three different adaptivity techniques have been investigated on the base of structured meshes. All the techniques indicate the significance of using adaptivity for improving computational results. In particular, the technique of combining point enrichment and node movement strategies offers the best compromise. Although, the work presented here used two-dimensional structured meshes, the techniques can be readily applied to hybrid and unstructured meshes. Also, preliminary three-dimensional numerical results have been already obtained by coauthors.

  14. Adaptive Mesh Expansion Model (AMEM) for Liver Segmentation from CT Image

    PubMed Central

    Wang, Xuehu; Yang, Jian; Ai, Danni; Zheng, Yongchang; Tang, Songyuan; Wang, Yongtian

    2015-01-01

    This study proposes a novel adaptive mesh expansion model (AMEM) for liver segmentation from computed tomography images. The virtual deformable simplex model (DSM) is introduced to represent the mesh, in which the motion of each vertex can be easily manipulated. The balloon, edge, and gradient forces are combined with the binary image to construct the external force of the deformable model, which can rapidly drive the DSM to approach the target liver boundaries. Moreover, tangential and normal forces are combined with the gradient image to control the internal force, such that the DSM degree of smoothness can be precisely controlled. The triangular facet of the DSM is adaptively decomposed into smaller triangular components, which can significantly improve the segmentation accuracy of the irregularly sharp corners of the liver. The proposed method is evaluated on the basis of different criteria applied to 10 clinical data sets. Experiments demonstrate that the proposed AMEM algorithm is effective and robust and thus outperforms six other up-to-date algorithms. Moreover, AMEM can achieve a mean overlap error of 6.8% and a mean volume difference of 2.7%, whereas the average symmetric surface distance and the root mean square symmetric surface distance can reach 1.3 mm and 2.7 mm, respectively. PMID:25769030

  15. Staggered grid lagrangian method with local structured adaptive mesh refinement for modeling shock hydrodynamics

    SciTech Connect

    Anderson, R W; Pember, R B; Elliot, N S

    2000-09-26

    A new method for the solution of the unsteady Euler equations has been developed. The method combines staggered grid Lagrangian techniques with structured local adaptive mesh refinement (AMR). This method is a precursor to a more general adaptive arbitrary Lagrangian Eulerian (ALE-AMR) algorithm under development, which will facilitate 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. Many of the core issues involved in the development of the ALE-AMR method hinge upon the integration of AMR with a Lagrange step, which is the focus of the work described here. The novel components of the method are mainly driven by the need to reconcile traditional AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. These new algorithmic components are first developed in one dimension and are then generalized to two dimensions. Solutions of several model problems involving shock hydrodynamics are presented and discussed.

  16. Adaptive-feedback control algorithm.

    PubMed

    Huang, Debin

    2006-06-01

    This paper is motivated by giving the detailed proofs and some interesting remarks on the results the author obtained in a series of papers [Phys. Rev. Lett. 93, 214101 (2004); Phys. Rev. E 71, 037203 (2005); 69, 067201 (2004)], where an adaptive-feedback algorithm was proposed to effectively stabilize and synchronize chaotic systems. This note proves in detail the strictness of this algorithm from the viewpoint of mathematics, and gives some interesting remarks for its potential applications to chaos control & synchronization. In addition, a significant comment on synchronization-based parameter estimation is given, which shows some techniques proposed in literature less strict and ineffective in some cases.

  17. Curved Mesh Correction And Adaptation Tool to Improve COMPASS Electromagnetic Analyses

    SciTech Connect

    Luo, X.; Shephard, M.; Lee, L.Q.; Ng, C.; Ge, L.; /SLAC

    2011-11-14

    SLAC performs large-scale simulations for the next-generation accelerator design using higher-order finite elements. This method requires using valid curved meshes and adaptive mesh refinement in complex 3D curved domains to achieve its fast rate of convergence. ITAPS has developed a procedure to address those mesh requirements to enable petascale electromagnetic accelerator simulations by SLAC. The results demonstrate that those correct valid curvilinear meshes can not only make the simulation more reliable but also improve computational efficiency up to 30%. This paper presents a procedure to track moving adaptive mesh refinement in curved domains. The procedure is capable of generating suitable curvilinear meshes to enable large-scale accelerator simulations. The procedure can generate valid curved meshes with substantially fewer elements to improve the computational efficiency and reliability of the COMPASS electromagnetic analyses. Future work will focus on the scalable parallelization of all steps for petascale simulations.

  18. Adaptive Mesh Refinement in Reactive Transport Modeling of Subsurface Environments

    NASA Astrophysics Data System (ADS)

    Molins, S.; Day, M.; Trebotich, D.; Graves, D. T.

    2015-12-01

    Adaptive mesh refinement (AMR) is a numerical technique for locally adjusting the resolution of computational grids. AMR makes it possible to superimpose levels of finer grids on the global computational grid in an adaptive manner allowing for more accurate calculations locally. AMR codes rely on the fundamental concept that the solution can be computed in different regions of the domain with different spatial resolutions. AMR codes have been applied to a wide range of problem including (but not limited to): fully compressible hydrodynamics, astrophysical flows, cosmological applications, combustion, blood flow, heat transfer in nuclear reactors, and land ice and atmospheric models for climate. In subsurface applications, in particular, reactive transport modeling, AMR may be particularly useful in accurately capturing concentration gradients (hence, reaction rates) that develop in localized areas of the simulation domain. Accurate evaluation of reaction rates is critical in many subsurface applications. In this contribution, we will discuss recent applications that bring to bear AMR capabilities on reactive transport problems from the pore scale to the flood plain scale.

  19. Parallel adaptive mesh-refining scheme on a three-dimensional unstructured tetrahedral mesh and its applications

    NASA Astrophysics Data System (ADS)

    Lian, Y.-Y.; Hsu, K.-H.; Shao, Y.-L.; Lee, Y.-M.; Jeng, Y.-W.; Wu, J.-S.

    2006-12-01

    The development of a parallel three-dimensional (3-D) adaptive mesh refinement (PAMR) scheme for an unstructured tetrahedral mesh using dynamic domain decomposition on a memory-distributed machine is presented in detail. A memory-saving cell-based data structure is designed such that the resulting mesh information can be readily utilized in both node- or cell-based numerical methods. The general procedures include isotropic refinement from one parent cell into eight child cells and then followed by anisotropic refinement which effectively removes hanging nodes. A simple but effective mesh-quality control mechanism is employed to preserve the mesh quality. The resulting parallel performance of this PAMR is found to scale approximately as N for N⩽32. Two test cases, including a particle method (parallel DSMC solver for rarefied gas dynamics) and an equation-based method (parallel Poisson-Boltzmann equation solver for electrostatic field), are used to demonstrate the generality of the PAMR module. It is argued that this PAMR scheme can be applied in any numerical method if the unstructured tetrahedral mesh is adopted.

  20. A new adaptive mesh refinement data structure with an application to detonation

    NASA Astrophysics Data System (ADS)

    Ji, Hua; Lien, Fue-Sang; Yee, Eugene

    2010-11-01

    A new Cell-based Structured Adaptive Mesh Refinement (CSAMR) data structure is developed. In our CSAMR data structure, Cartesian-like indices are used to identify each cell. With these stored indices, the information on the parent, children and neighbors of a given cell can be accessed simply and efficiently. Owing to the usage of these indices, the computer memory required for storage of the proposed AMR data structure is only {5}/{8} word per cell, in contrast to the conventional oct-tree [P. MacNeice, K.M. Olson, C. Mobary, R. deFainchtein, C. Packer, PARAMESH: a parallel adaptive mesh refinement community toolkit, Comput. Phys. Commun. 330 (2000) 126] and the fully threaded tree (FTT) [A.M. Khokhlov, Fully threaded tree algorithms for adaptive mesh fluid dynamics simulations, J. Comput. Phys. 143 (1998) 519] data structures which require, respectively, 19 and 2{3}/{8} words per cell for storage of the connectivity information. Because the connectivity information (e.g., parent, children and neighbors) of a cell in our proposed AMR data structure can be accessed using only the cell indices, a tree structure which was required in previous approaches for the organization of the AMR data is no longer needed for this new data structure. Instead, a much simpler hash table structure is used to maintain the AMR data, with the entry keys in the hash table obtained directly from the explicitly stored cell indices. The proposed AMR data structure simplifies the implementation and parallelization of an AMR code. Two three-dimensional test cases are used to illustrate and evaluate the computational performance of the new CSAMR data structure.

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

    NASA Technical Reports Server (NTRS)

    Lemke, Max; Witsch, Kristian; Quinlan, Daniel

    1993-01-01

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

  2. Finite-difference lattice Boltzmann method with a block-structured adaptive-mesh-refinement technique.

    PubMed

    Fakhari, Abbas; Lee, Taehun

    2014-03-01

    An adaptive-mesh-refinement (AMR) algorithm for the finite-difference lattice Boltzmann method (FDLBM) is presented in this study. The idea behind the proposed AMR is to remove the need for a tree-type data structure. Instead, pointer attributes are used to determine the neighbors of a certain block via appropriate adjustment of its children identifications. As a result, the memory and time required for tree traversal are completely eliminated, leaving us with an efficient algorithm that is easier to implement and use on parallel machines. To allow different mesh sizes at separate parts of the computational domain, the Eulerian formulation of the streaming process is invoked. As a result, there is no need for rescaling the distribution functions or using a temporal interpolation at the fine-coarse grid boundaries. The accuracy and efficiency of the proposed FDLBM AMR are extensively assessed by investigating a variety of vorticity-dominated flow fields, including Taylor-Green vortex flow, lid-driven cavity flow, thin shear layer flow, and the flow past a square cylinder.

  3. Finite-difference lattice Boltzmann method with a block-structured adaptive-mesh-refinement technique

    NASA Astrophysics Data System (ADS)

    Fakhari, Abbas; Lee, Taehun

    2014-03-01

    An adaptive-mesh-refinement (AMR) algorithm for the finite-difference lattice Boltzmann method (FDLBM) is presented in this study. The idea behind the proposed AMR is to remove the need for a tree-type data structure. Instead, pointer attributes are used to determine the neighbors of a certain block via appropriate adjustment of its children identifications. As a result, the memory and time required for tree traversal are completely eliminated, leaving us with an efficient algorithm that is easier to implement and use on parallel machines. To allow different mesh sizes at separate parts of the computational domain, the Eulerian formulation of the streaming process is invoked. As a result, there is no need for rescaling the distribution functions or using a temporal interpolation at the fine-coarse grid boundaries. The accuracy and efficiency of the proposed FDLBM AMR are extensively assessed by investigating a variety of vorticity-dominated flow fields, including Taylor-Green vortex flow, lid-driven cavity flow, thin shear layer flow, and the flow past a square cylinder.

  4. Numerical study of three-dimensional liquid jet breakup with adaptive unstructured meshes

    NASA Astrophysics Data System (ADS)

    Xie, Zhihua; Pavlidis, Dimitrios; Salinas, Pablo; Pain, Christopher; Matar, Omar

    2016-11-01

    Liquid jet breakup is an important fundamental multiphase flow, often found in many industrial engineering applications. The breakup process is very complex, involving jets, liquid films, ligaments, and small droplets, featuring tremendous complexity in interfacial topology and a large range of spatial scales. The objective of this study is to investigate the fluid dynamics of three-dimensional liquid jet breakup problems, such as liquid jet primary breakup and gas-sheared liquid jet breakup. An adaptive unstructured mesh modelling framework is employed here, which can modify and adapt unstructured meshes to optimally represent the underlying physics of multiphase problems and reduce computational effort without sacrificing accuracy. The numerical framework consists of a mixed control volume and finite element formulation, a 'volume of fluid' type method for the interface capturing based on a compressive control volume advection method and second-order finite element methods, and a force-balanced algorithm for the surface tension implementation. Numerical examples of some benchmark tests and the dynamics of liquid jet breakup with and without ambient gas are presented to demonstrate the capability of this method.

  5. A high order special relativistic hydrodynamic and magnetohydrodynamic code with space-time adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Zanotti, Olindo; Dumbser, Michael

    2015-03-01

    We present a high order one-step ADER-WENO finite volume scheme with space-time adaptive mesh refinement (AMR) for the solution of the special relativistic hydrodynamic and magnetohydrodynamic equations. By adopting a local discontinuous Galerkin predictor method, a high order one-step time discretization is obtained, with no need for Runge-Kutta sub-steps. This turns out to be particularly advantageous in combination with space-time adaptive mesh refinement, which has been implemented following a "cell-by-cell" approach. As in existing second order AMR methods, also the present higher order AMR algorithm features time-accurate local time stepping (LTS), where grids on different spatial refinement levels are allowed to use different time steps. We also compare two different Riemann solvers for the computation of the numerical fluxes at the cell interfaces. The new scheme has been validated over a sample of numerical test problems in one, two and three spatial dimensions, exploring its ability in resolving the propagation of relativistic hydrodynamical and magnetohydrodynamical waves in different physical regimes. The astrophysical relevance of the new code for the study of the Richtmyer-Meshkov instability is briefly discussed in view of future applications.

  6. Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations

    DTIC Science & Technology

    1983-03-01

    grids. We use either the Coarse Mesh Approximation fethod ( Ciment , [1971]) or interpolation from a coarser grid to get the boundary values. In Berger...Problems, Math. Conp. 31 (1977), 333-390. M. Ciment , Stable Difference Schemes with Uneven Mesh Spacings, Math. Comp. 25 (1971), 219-227. H. Cramr

  7. Expectation maximization SPECT reconstruction with a content-adaptive singularity-based mesh-domain image model

    NASA Astrophysics Data System (ADS)

    Lu, Yao; Ye, Hongwei; Xu, Yuesheng; Hu, Xiaofei; Vogelsang, Levon; Shen, Lixin; Feiglin, David; Lipson, Edward; Krol, Andrzej

    2008-03-01

    To improve the speed and quality of ordered-subsets expectation-maximization (OSEM) SPECT reconstruction, we have implemented a content-adaptive, singularity-based, mesh-domain, image model (CASMIM) with an accurate algorithm for estimation of the mesh-domain system matrix. A preliminary image, used to initialize CASMIM reconstruction, was obtained using pixel-domain OSEM. The mesh-domain representation of the image was produced by a 2D wavelet transform followed by Delaunay triangulation to obtain joint estimation of nodal locations and their activity values. A system matrix with attenuation compensation was investigated. Digital chest phantom SPECT was simulated and reconstructed. The quality of images reconstructed with OSEM-CASMIM is comparable to that from pixel-domain OSEM, but images are obtained five times faster by the CASMIM method.

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

    NASA Technical Reports Server (NTRS)

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

    1999-01-01

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

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

    NASA Technical Reports Server (NTRS)

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

    1999-01-01

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

  10. Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions

    NASA Astrophysics Data System (ADS)

    Rosenberg, D.; Pouquet, A.; Mininni, P. D.

    2007-08-01

    We examine the effect of accuracy of high-order spectral element methods, with or without adaptive mesh refinement (AMR), in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called Orszag-Tang (OT) vortex made up of a magnetic X-point centred on a stagnation point of the velocity. A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code is applied to simulate this problem. The MHD solver is explicit, and uses the Elsässer formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described elsewhere in the fluid context (Rosenberg et al 2006 J. Comput. Phys. 215 59-80) the code allows both statically refined and dynamically refined grids. Tests of the algorithm using analytic solutions are described, and comparisons of the OT solutions with pseudo-spectral computations are performed. We demonstrate for moderate Reynolds numbers that the algorithms using both static and refined grids reproduce the pseudo-spectral solutions quite well. We show that low-order truncation—even with a comparable number of global degrees of freedom—fails to correctly model some strong (sup-norm) quantities in this problem, even though it satisfies adequately the weak (integrated) balance diagnostics.

  11. Adaptive Numerical Algorithms in Space Weather Modeling

    NASA Technical Reports Server (NTRS)

    Toth, Gabor; vanderHolst, Bart; Sokolov, Igor V.; DeZeeuw, Darren; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Nakib, Dalal; Powell, Kenneth G.; Stout, Quentin F.; Glocer, Alex; Ma, Ying-Juan; Opher, Merav

    2010-01-01

    Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical

  12. Adaptive numerical algorithms in space weather modeling

    NASA Astrophysics Data System (ADS)

    Tóth, Gábor; van der Holst, Bart; Sokolov, Igor V.; De Zeeuw, Darren L.; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Najib, Dalal; Powell, Kenneth G.; Stout, Quentin F.; Glocer, Alex; Ma, Ying-Juan; Opher, Merav

    2012-02-01

    Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different relevant physics in different domains. A multi-physics system can be modeled by a software framework comprising several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamic (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit

  13. Adaptive Meshing of Ship Air-Wake Flowfields

    DTIC Science & Technology

    2014-03-03

    this code are currently generated using Pointwise .[2] This code also uses a second order spatial finite-volume scheme with first order explicit...simulated with the two codes and is shown below. The surface mesh from the 3D mesh generated by Pointwise serves as the geometry for the OctFlow code. A...Geometries", AIAA- 2000-1006,2000. 2. " Pointwise ." Pointwise , Inc., http://www.pointwise.com. 3. O’Connell, M., and Karman, S., "Mesh Rupturing: A

  14. RAM: a Relativistic Adaptive Mesh Refinement Hydrodynamics Code

    SciTech Connect

    Zhang, Wei-Qun; MacFadyen, Andrew I.; /Princeton, Inst. Advanced Study

    2005-06-06

    The authors have developed a new computer code, RAM, to solve the conservative equations of special relativistic hydrodynamics (SRHD) using adaptive mesh refinement (AMR) on parallel computers. They have implemented a characteristic-wise, finite difference, weighted essentially non-oscillatory (WENO) scheme using the full characteristic decomposition of the SRHD equations to achieve fifth-order accuracy in space. For time integration they use the method of lines with a third-order total variation diminishing (TVD) Runge-Kutta scheme. They have also implemented fourth and fifth order Runge-Kutta time integration schemes for comparison. The implementation of AMR and parallelization is based on the FLASH code. RAM is modular and includes the capability to easily swap hydrodynamics solvers, reconstruction methods and physics modules. In addition to WENO they have implemented a finite volume module with the piecewise parabolic method (PPM) for reconstruction and the modified Marquina approximate Riemann solver to work with TVD Runge-Kutta time integration. They examine the difficulty of accurately simulating shear flows in numerical relativistic hydrodynamics codes. They show that under-resolved simulations of simple test problems with transverse velocity components produce incorrect results and demonstrate the ability of RAM to correctly solve these problems. RAM has been tested in one, two and three dimensions and in Cartesian, cylindrical and spherical coordinates. they have demonstrated fifth-order accuracy for WENO in one and two dimensions and performed detailed comparison with other schemes for which they show significantly lower convergence rates. Extensive testing is presented demonstrating the ability of RAM to address challenging open questions in relativistic astrophysics.

  15. Simulation of tsunamis generated by landslides using adaptive mesh refinement on GPU

    NASA Astrophysics Data System (ADS)

    de la Asunción, M.; Castro, M. J.

    2017-09-01

    Adaptive mesh refinement (AMR) is a widely used technique to accelerate computationally intensive simulations, which consists of dynamically increasing the spatial resolution of the areas of interest of the domain as the simulation advances. During the last years there have appeared many publications that tackle the implementation of AMR-based applications in GPUs in order to take advantage of their massively parallel architecture. In this paper we present the first AMR-based application implemented on GPU for the simulation of tsunamis generated by landslides by using a two-layer shallow water system. We also propose a new strategy for the interpolation and projection of the values of the fine cells in the AMR algorithm based on the fluctuations of the state values instead of the usual approach of considering the current state values. Numerical experiments on artificial and realistic problems show the validity and efficiency of the solver.

  16. Damping of spurious numerical reflections off of coarse-fine adaptive mesh refinement grid boundaries

    NASA Astrophysics Data System (ADS)

    Chilton, Sven; Colella, Phillip

    2010-11-01

    Adaptive mesh refinement (AMR) is an efficient technique for solving systems of partial differential equations numerically. The underlying algorithm determines where and when a base spatial and temporal grid must be resolved further in order to achieve the desired precision and accuracy in the numerical solution. However, propagating wave solutions prove problematic for AMR. In systems with low degrees of dissipation (e.g. the Maxwell-Vlasov system) a wave traveling from a finely resolved region into a coarsely resolved region encounters a numerical impedance mismatch, resulting in spurious reflections off of the coarse-fine grid boundary. These reflected waves then become trapped inside the fine region. Here, we present a scheme for damping these spurious reflections. We demonstrate its application to the scalar wave equation and an implementation for Maxwell's Equations. We also discuss a possible extension to the Maxwell-Vlasov system.

  17. MPI parallelization of full PIC simulation code with Adaptive Mesh Refinement

    NASA Astrophysics Data System (ADS)

    Matsui, Tatsuki; Nunami, Masanori; Usui, Hideyuki; Moritaka, Toseo

    2010-11-01

    A new parallelization technique developed for PIC method with adaptive mesh refinement (AMR) is introduced. In AMR technique, the complicated cell arrangements are organized and managed as interconnected pointers with multiple resolution levels, forming a fully threaded tree structure as a whole. In order to retain this tree structure distributed over multiple processes, remote memory access, an extended feature of MPI2 standards, is employed. Another important feature of the present simulation technique is the domain decomposition according to the modified Morton ordering. This algorithm can group up the equal number of particle calculation loops, which allows for the better load balance. Using this advanced simulation code, preliminary results for basic physical problems are exhibited for the validity check, together with the benchmarks to test the performance and the scalability.

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

    NASA Technical Reports Server (NTRS)

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

    1994-01-01

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

  19. Dynamic Mesh Adaptation for Front Evolution Using Discontinuous Galerkin Based Weighted Condition Number Mesh Relaxation

    SciTech Connect

    Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert

    2016-06-21

    A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.

  20. Software abstractions and computational issues in parallel structure adaptive mesh methods for electronic structure calculations

    SciTech Connect

    Kohn, S.; Weare, J.; Ong, E.; Baden, S.

    1997-05-01

    We have applied structured adaptive mesh refinement techniques to the solution of the LDA equations for electronic structure calculations. Local spatial refinement concentrates memory resources and numerical effort where it is most needed, near the atomic centers and in regions of rapidly varying charge density. The structured grid representation enables us to employ efficient iterative solver techniques such as conjugate gradient with FAC multigrid preconditioning. We have parallelized our solver using an object- oriented adaptive mesh refinement framework.

  1. Adaptive meshing technique applied to an orthopaedic finite element contact problem.

    PubMed

    Roarty, Colleen M; Grosland, Nicole M

    2004-01-01

    Finite element methods have been applied extensively and with much success in the analysis of orthopaedic implants. Recently a growing interest has developed, in the orthopaedic biomechanics community, in how numerical models can be constructed for the optimal solution of problems in contact mechanics. New developments in this area are of paramount importance in the design of improved implants for orthopaedic surgery. Finite element and other computational techniques are widely applied in the analysis and design of hip and knee implants, with additional joints (ankle, shoulder, wrist) attracting increased attention. The objective of this investigation was to develop a simplified adaptive meshing scheme to facilitate the finite element analysis of a dual-curvature total wrist implant. Using currently available software, the analyst has great flexibility in mesh generation, but must prescribe element sizes and refinement schemes throughout the domain of interest. Unfortunately, it is often difficult to predict in advance a mesh spacing that will give acceptable results. Adaptive finite-element mesh capabilities operate to continuously refine the mesh to improve accuracy where it is required, with minimal intervention by the analyst. Such mesh adaptation generally means that in certain areas of the analysis domain, the size of the elements is decreased (or increased) and/or the order of the elements may be increased (or decreased). In concept, mesh adaptation is very appealing. Although there have been several previous applications of adaptive meshing for in-house FE codes, we have coupled an adaptive mesh formulation with the pre-existing commercial programs PATRAN (MacNeal-Schwendler Corp., USA) and ABAQUS (Hibbit Karlson and Sorensen, Pawtucket, RI). In doing so, we have retained several attributes of the commercial software, which are very attractive for orthopaedic implant applications.

  2. Fast animation of lightning using an adaptive mesh.

    PubMed

    Kim, Theodore; Lin, Ming C

    2007-01-01

    We present a fast method for simulating, animating, and rendering lightning using adaptive grids. The "dielectric breakdown model" is an elegant algorithm for electrical pattern formation that we extend to enable animation of lightning. The simulation can be slow, particularly in 3D, because it involves solving a large Poisson problem. Losasso et al. recently proposed an octree data structure for simulating water and smoke, and we show that this discretization can be applied to the problem of lightning simulation as well. However, implementing the incomplete Cholesky conjugate gradient (ICCG) solver for this problem can be daunting, so we provide an extensive discussion of implementation issues. ICCG solvers can usually be accelerated using "Eisenstat's trick," but the trick cannot be directly applied to the adaptive case. Fortunately, we show that an "almost incomplete Cholesky" factorization can be computed so that Eisenstat's trick can still be used. We then present a fast rendering method based on convolution that is competitive with Monte Carlo ray tracing but orders of magnitude faster, and we also show how to further improve the visual results using jittering.

  3. IIR algorithms for adaptive line enhancement

    SciTech Connect

    David, R.A.; Stearns, S.D.; Elliott, G.R.; Etter, D.M.

    1983-01-01

    We introduce a simple IIR structure for the adaptive line enhancer. Two algorithms based on gradient-search techniques are presented for adapting the structure. Results from experiments which utilized real data as well as computer simulations are provided.

  4. SU-D-207-04: GPU-Based 4D Cone-Beam CT Reconstruction Using Adaptive Meshing Method

    SciTech Connect

    Zhong, Z; Gu, X; Iyengar, P; Mao, W; Wang, J; Guo, X

    2015-06-15

    Purpose: Due to the limited number of projections at each phase, the image quality of a four-dimensional cone-beam CT (4D-CBCT) is often degraded, which decreases the accuracy of subsequent motion modeling. One of the promising methods is the simultaneous motion estimation and image reconstruction (SMEIR) approach. The objective of this work is to enhance the computational speed of the SMEIR algorithm using adaptive feature-based tetrahedral meshing and GPU-based parallelization. Methods: The first step is to generate the tetrahedral mesh based on the features of a reference phase 4D-CBCT, so that the deformation can be well captured and accurately diffused from the mesh vertices to voxels of the image volume. After the mesh generation, the updated motion model and other phases of 4D-CBCT can be obtained by matching the 4D-CBCT projection images at each phase with the corresponding forward projections of the deformed reference phase of 4D-CBCT. The entire process of this 4D-CBCT reconstruction method is implemented on GPU, resulting in significantly increasing the computational efficiency due to its tremendous parallel computing ability. Results: A 4D XCAT digital phantom was used to test the proposed mesh-based image reconstruction algorithm. The image Result shows both bone structures and inside of the lung are well-preserved and the tumor position can be well captured. Compared to the previous voxel-based CPU implementation of SMEIR, the proposed method is about 157 times faster for reconstructing a 10 -phase 4D-CBCT with dimension 256×256×150. Conclusion: The GPU-based parallel 4D CBCT reconstruction method uses the feature-based mesh for estimating motion model and demonstrates equivalent image Result with previous voxel-based SMEIR approach, with significantly improved computational speed.

  5. Star formation with adaptive mesh refinement and magnetohydrodynamics

    NASA Astrophysics Data System (ADS)

    Collins, David C.

    2009-01-01

    In this thesis, we develop an adaptive mesh refinement (AMR) code including magnetic fields, and use it to perform high resolution simulations of magnetized molecular clouds. The purpose of these simulations is to study present day star formation in the presence of turbulence and magnetic fields. We first present MHDEnzo, the extension of the cosmology and astrophysics code Enzo to include the effects magnetic fields. We use a higher order Godunov Riemann solver for the computation of interface fluxes; constrained transport to compute the electric field from those interface fluxes, which advances the induction equation in a divergence free manner; divergence free reconstruction technique to interpolate the magnetic fields to fine grids; operator splitting to include gravity and cosmological expansion. We present a series of test problems to demonstrate the quality of solution achieved. Additionally, we present several other solvers that were developed along the way. Finally we present the results from several AMR simulations that study isothermal turbulence in the presence of magnetic fields and self gravity. Ten simulations with initial Mach number 8.9 were studied varying several parameters; virial parameter a from 0.52 to 3.1; whether they were continuously stirred or allowed to decay; and the number of refinement levels (4 or 6). Measurements of the density probability density function (PDF) were made, showing both the expected log normal distribution and an additional power law. Measurements of the line of sight magnetic field vs. column density are done, giving excellent agreement with recent observations. The line width vs. size relationship is measured and compared with good agreement to observations, reproducing both turbulent and collapse signatures The core mass distribution is measured and agrees well with observations of Serpens and Perseus core samples, but the power-law distribution in Ophiuchus is not reproduced by our simulations. Finally we

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

    NASA Astrophysics Data System (ADS)

    Slattery, Stuart R.

    2016-02-01

    In this paper 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 smoothness 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. 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.

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

    SciTech Connect

    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 smoothness 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.

  8. 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

  9. Parallel adaptive mesh refinement method based on WENO finite difference scheme for the simulation of multi-dimensional detonation

    NASA Astrophysics Data System (ADS)

    Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang

    2015-10-01

    For numerical simulation of detonation, computational cost using uniform meshes is large due to the vast separation in both time and space scales. Adaptive mesh refinement (AMR) is advantageous for problems with vastly different scales. This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation. A well-designed AMR method based on finite difference weighted essentially non-oscillatory (WENO) scheme, named as AMR&WENO is proposed. A new cell-based data structure is used to organize the adaptive meshes. The new data structure makes it possible for cells to communicate with each other quickly and easily. In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure. Based on the message passing interface (MPI) platform, we have developed a workload balancing parallel AMR&WENO code using the Hilbert space-filling curve algorithm. Our numerical experiments with detonation simulations indicate that the AMR&WENO is accurate and has a high resolution. Moreover, we evaluate and compare the performance of the uniform mesh WENO scheme and the parallel AMR&WENO method. The comparison results provide us further insight into the high performance of the parallel AMR&WENO method.

  10. Parallel adaptive simplical re-meshing for deforming domain CFD computations

    NASA Astrophysics Data System (ADS)

    Menon, Sandeep; Mooney, Kyle G.; Stapf, K. G.; Schmidt, David P.

    2015-10-01

    Deforming domains occur in many fields of computational fluid dynamics (CFD), such as interface tracking, simulation of pumps and engines, and fluid/structure interaction. The deformation of the domain presents a challenge to the integrity of the computational mesh; substantial motion of the domain boundaries requires vertex motion and changes in mesh connectivity. For cases of simple boundary motion or structured meshes, predetermined changes to the mesh structure can be sufficient. However, without a priori knowledge of how the domain will change, a more robust solution is required. The present work offers a parallelized solution for simplical meshes that is well-suited to extremely complex geometry. The mesh continuously evolves without user intervention or the use of target meshes. Varying length scales imposed by evolving boundary curvatures and narrow gaps are resolved with a fast length-scale algorithm. The set of algorithms are incorporated into an object-oriented code structure that permits broad application to a range of CFD problems. The robustness and versatility of the algorithm is demonstrated in several examples, representing motion of internal and external boundaries, where the boundary motion may or may not be known a priori.

  11. Multigroup radiation hydrodynamics with flux-limited diffusion and adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    González, M.; Vaytet, N.; Commerçon, B.; Masson, J.

    2015-06-01

    Context. Radiative transfer plays a crucial role in the star formation process. Because of the high computational cost, radiation-hydrodynamics simulations performed up to now have mainly been carried out in the grey approximation. In recent years, multifrequency radiation-hydrodynamics models have started to be developed in an attempt to better account for the large variations in opacities as a function of frequency. Aims: We wish to develop an efficient multigroup algorithm for the adaptive mesh refinement code RAMSES which is suited to heavy proto-stellar collapse calculations. Methods: Because of the prohibitive timestep constraints of an explicit radiative transfer method, we constructed a time-implicit solver based on a stabilized bi-conjugate gradient algorithm, and implemented it in RAMSES under the flux-limited diffusion approximation. Results: We present a series of tests that demonstrate the high performance of our scheme in dealing with frequency-dependent radiation-hydrodynamic flows. We also present a preliminary simulation of a 3D proto-stellar collapse using 20 frequency groups. Differences between grey and multigroup results are briefly discussed, and the large amount of information this new method brings us is also illustrated. Conclusions: We have implemented a multigroup flux-limited diffusion algorithm in the RAMSES code. The method performed well against standard radiation-hydrodynamics tests, and was also shown to be ripe for exploitation in the computational star formation context.

  12. Standard and goal-oriented adaptive mesh refinement applied to radiation transport on 2D unstructured triangular meshes

    SciTech Connect

    Wang Yaqi; Ragusa, Jean C.

    2011-02-01

    Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest are functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.

  13. 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.

  14. Adaptive Mesh Refinement and Adaptive Time Integration for Electrical Wave Propagation on the Purkinje System.

    PubMed

    Ying, Wenjun; Henriquez, Craig S

    2015-01-01

    A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.

  15. Adaptive Mesh Refinement and Adaptive Time Integration for Electrical Wave Propagation on the Purkinje System

    PubMed Central

    Ying, Wenjun; Henriquez, Craig S.

    2015-01-01

    A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented. PMID:26581455

  16. 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

  17. 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

  18. 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.

  19. Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations

    NASA Astrophysics Data System (ADS)

    Kopera, Michal A.; Giraldo, Francis X.

    2014-10-01

    The resolutions of interests in atmospheric simulations require prohibitively large computational resources. Adaptive mesh refinement (AMR) tries to mitigate this problem by putting high resolution in crucial areas of the domain. We investigate the performance of a tree-based AMR algorithm for the high order discontinuous Galerkin method on quadrilateral grids with non-conforming elements. We perform a detailed analysis of the cost of AMR by comparing this to uniform reference simulations of two standard atmospheric test cases: density current and rising thermal bubble. The analysis shows up to 15 times speed-up of the AMR simulations with the cost of mesh adaptation below 1% of the total runtime. We pay particular attention to the implicit-explicit (IMEX) time integration methods and show that the ARK2 method is more robust with respect to dynamically adapting meshes than BDF2. Preliminary analysis of preconditioning reveals that it can be an important factor in the AMR overhead. The compiler optimizations provide significant runtime reduction and positively affect the effectiveness of AMR allowing for speed-ups greater than it would follow from the simple performance model.

  20. Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains

    NASA Astrophysics Data System (ADS)

    Kast, Steven M.; Fidkowski, Krzysztof J.

    2013-11-01

    We present an output-based mesh adaptation strategy for Navier-Stokes simulations on deforming domains. The equations are solved with an arbitrary Lagrangian-Eulerian (ALE) approach, using a discontinuous Galerkin finite-element discretization in both space and time. Discrete unsteady adjoint solutions, derived for both the state and the geometric conservation law, provide output error estimates and drive adaptation of the space-time mesh. Spatial adaptation consists of dynamic order increment or decrement on a fixed tessellation of the domain, while a combination of coarsening and refinement is used to provide an efficient time step distribution. Results from compressible Navier-Stokes simulations in both two and three dimensions demonstrate the accuracy and efficiency of the proposed approach. In particular, the method is shown to outperform other common adaptation strategies, which, while sometimes adequate for static problems, struggle in the presence of mesh motion.

  1. Energy dependent mesh adaptivity of discontinuous isogeometric discrete ordinate methods with dual weighted residual error estimators

    NASA Astrophysics Data System (ADS)

    Owens, A. R.; Kópházi, J.; Welch, J. A.; Eaton, M. D.

    2017-04-01

    In this paper a hanging-node, discontinuous Galerkin, isogeometric discretisation of the multigroup, discrete ordinates (SN) equations is presented in which each energy group has its own mesh. The equations are discretised using Non-Uniform Rational B-Splines (NURBS), which allows the coarsest mesh to exactly represent the geometry for a wide range of engineering problems of interest; this would not be the case using straight-sided finite elements. Information is transferred between meshes via the construction of a supermesh. This is a non-trivial task for two arbitrary meshes, but is significantly simplified here by deriving every mesh from a common coarsest initial mesh. In order to take full advantage of this flexible discretisation, goal-based error estimators are derived for the multigroup, discrete ordinates equations with both fixed (extraneous) and fission sources, and these estimators are used to drive an adaptive mesh refinement (AMR) procedure. The method is applied to a variety of test cases for both fixed and fission source problems. The error estimators are found to be extremely accurate for linear NURBS discretisations, with degraded performance for quadratic discretisations owing to a reduction in relative accuracy of the ;exact; adjoint solution required to calculate the estimators. Nevertheless, the method seems to produce optimal meshes in the AMR process for both linear and quadratic discretisations, and is ≈×100 more accurate than uniform refinement for the same amount of computational effort for a 67 group deep penetration shielding problem.

  2. AMR++: A design for parallel object-oriented adaptive mesh refinement

    SciTech Connect

    Quinlan, D.

    1997-11-01

    Adaptive mesh refinement computations are complicated by their dynamic nature. In the serial environment they require substantial infrastructures to support the regridding processes, intergrid operations, and local bookkeeping of positions of grids relative to one another. In the parallel environment the dynamic behavior is more problematic because it requires dynamic distribution support and load balancing. Parallel AMR is further complicated by the substantial task parallelism, in addition to the obvious data parallelism, this task parallelism requires additional infrastructure to support efficiently. The degree of parallelism is typically dependent upon the algorithms in use and the equations being solved. Different algorithms have significant compromises between computation and communication. Substantial research work is often required to define efficient methods and suitable infrastructure. The purpose of this paper is to introduce AMR++ as an object-oriented library which forms a part of the OVERTURE framework, a much larger object-oriented numerical framework developed and supported at Los Alamos National Laboratory and distributed on the Web for the last several years.

  3. Modeling NIF Experimental Designs with Adaptive Mesh Refinement and Lagrangian Hydrodynamics

    SciTech Connect

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

    2005-08-31

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

  4. 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.

  5. CRASH: A Block-adaptive-mesh Code for Radiative Shock Hydrodynamics—Implementation and Verification

    NASA Astrophysics Data System (ADS)

    van der Holst, B.; Tóth, G.; Sokolov, I. V.; Powell, K. G.; Holloway, J. P.; Myra, E. S.; Stout, Q.; Adams, M. L.; Morel, J. E.; Karni, S.; Fryxell, B.; Drake, R. P.

    2011-06-01

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

  6. CRASH: A Block-Adaptive-Mesh Code for Radiative Shock Hydrodynamics

    NASA Astrophysics Data System (ADS)

    van der Holst, B.; Toth, G.; Sokolov, I. V.; Powell, K. G.; Holloway, J. P.; Myra, E. S.; Stout, Q.; Adams, M. L.; Morel, J. E.; Drake, R. P.

    2011-01-01

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

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

    SciTech Connect

    Van der Holst, B.; Toth, G.; Sokolov, I. V.; Myra, E. S.; Fryxell, B.; Drake, R. P.; Powell, K. G.; Holloway, J. P.; Stout, Q.; Adams, M. L.; Morel, J. E.; Karni, S.

    2011-06-01

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

  8. Improved LMS algorithm for adaptive beamforming

    NASA Technical Reports Server (NTRS)

    Godara, Lal C.

    1990-01-01

    Two adaptive algorithms which make use of all the available samples to estimate the required gradient are proposed and studied. The first algorithm is referred to as the recursive LMS (least mean squares) and is applicable to a general array. The second algorithm is referred to as the improved LMS algorithm and exploits the Toeplitz structure of the ACM (array correlation matrix); it can be used only for an equispaced linear array.

  9. 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.

  10. Block-structured adaptive meshes and reduced grids for atmospheric general circulation models.

    PubMed

    Jablonowski, Christiane; Oehmke, Robert C; Stout, Quentin F

    2009-11-28

    Adaptive mesh refinement techniques offer a flexible framework for future variable-resolution climate and weather models since they can focus their computational mesh on certain geographical areas or atmospheric events. Adaptive meshes can also be used to coarsen a latitude-longitude grid in polar regions. This allows for the so-called reduced grid setups. A spherical, block-structured adaptive grid technique is applied to the Lin-Rood finite-volume dynamical core for weather and climate research. This hydrostatic dynamics package is based on a conservative and monotonic finite-volume discretization in flux form with vertically floating Lagrangian layers. The adaptive dynamical core is built upon a flexible latitude-longitude computational grid and tested in two- and three-dimensional model configurations. The discussion is focused on static mesh adaptations and reduced grids. The two-dimensional shallow water setup serves as an ideal testbed and allows the use of shallow water test cases like the advection of a cosine bell, moving vortices, a steady-state flow, the Rossby-Haurwitz wave or cross-polar flows. It is shown that reduced grid configurations are viable candidates for pure advection applications but should be used moderately in nonlinear simulations. In addition, static grid adaptations can be successfully used to resolve three-dimensional baroclinic waves in the storm-track region.

  11. Thickness-based adaptive mesh refinement methods for multi-phase flow simulations with thin regions

    SciTech Connect

    Chen, Xiaodong; Yang, Vigor

    2014-07-15

    In numerical simulations of multi-scale, multi-phase flows, grid refinement is required to resolve regions with small scales. A notable example is liquid-jet atomization and subsequent droplet dynamics. It is essential to characterize the detailed flow physics with variable length scales with high fidelity, in order to elucidate the underlying mechanisms. In this paper, two thickness-based mesh refinement schemes are developed based on distance- and topology-oriented criteria for thin regions with confining wall/plane of symmetry and in any situation, respectively. Both techniques are implemented in a general framework with a volume-of-fluid formulation and an adaptive-mesh-refinement capability. The distance-oriented technique compares against a critical value, the ratio of an interfacial cell size to the distance between the mass center of the cell and a reference plane. The topology-oriented technique is developed from digital topology theories to handle more general conditions. The requirement for interfacial mesh refinement can be detected swiftly, without the need of thickness information, equation solving, variable averaging or mesh repairing. The mesh refinement level increases smoothly on demand in thin regions. The schemes have been verified and validated against several benchmark cases to demonstrate their effectiveness and robustness. These include the dynamics of colliding droplets, droplet motions in a microchannel, and atomization of liquid impinging jets. Overall, the thickness-based refinement technique provides highly adaptive meshes for problems with thin regions in an efficient and fully automatic manner.

  12. Adaptive unstructured meshing for thermal stress analysis of built-up structures

    NASA Technical Reports Server (NTRS)

    Dechaumphai, Pramote

    1992-01-01

    An adaptive unstructured meshing technique for mechanical and thermal stress analysis of built-up structures has been developed. A triangular membrane finite element and a new plate bending element are evaluated on a panel with a circular cutout and a frame stiffened panel. The adaptive unstructured meshing technique, without a priori knowledge of the solution to the problem, generates clustered elements only where needed. An improved solution accuracy is obtained at a reduced problem size and analysis computational time as compared to the results produced by the standard finite element procedure.

  13. 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.

  14. 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.

  15. QPSO-based adaptive DNA computing algorithm.

    PubMed

    Karakose, Mehmet; Cigdem, Ugur

    2013-01-01

    DNA (deoxyribonucleic acid) computing that is a new computation model based on DNA molecules for information storage has been increasingly used for optimization and data analysis in recent years. However, DNA computing algorithm has some limitations in terms of convergence speed, adaptability, and effectiveness. In this paper, a new approach for improvement of DNA computing is proposed. This new approach aims to perform DNA computing algorithm with adaptive parameters towards the desired goal using quantum-behaved particle swarm optimization (QPSO). Some contributions provided by the proposed QPSO based on adaptive DNA computing algorithm are as follows: (1) parameters of population size, crossover rate, maximum number of operations, enzyme and virus mutation rate, and fitness function of DNA computing algorithm are simultaneously tuned for adaptive process, (2) adaptive algorithm is performed using QPSO algorithm for goal-driven progress, faster operation, and flexibility in data, and (3) numerical realization of DNA computing algorithm with proposed approach is implemented in system identification. Two experiments with different systems were carried out to evaluate the performance of the proposed approach with comparative results. Experimental results obtained with Matlab and FPGA demonstrate ability to provide effective optimization, considerable convergence speed, and high accuracy according to DNA computing algorithm.

  16. Three-dimensional Wavelet-based Adaptive Mesh Refinement for Global Atmospheric Chemical Transport Modeling

    NASA Astrophysics Data System (ADS)

    Rastigejev, Y.; Semakin, A. N.

    2013-12-01

    Accurate numerical simulations of global scale three-dimensional atmospheric chemical transport models (CTMs) are essential for studies of many important atmospheric chemistry problems such as adverse effect of air pollutants on human health, ecosystems and the Earth's climate. These simulations usually require large CPU time due to numerical difficulties associated with a wide range of spatial and temporal scales, nonlinearity and large number of reacting species. In our previous work we have shown that in order to achieve adequate convergence rate and accuracy, the mesh spacing in numerical simulation of global synoptic-scale pollution plume transport must be decreased to a few kilometers. This resolution is difficult to achieve for global CTMs on uniform or quasi-uniform grids. To address the described above difficulty we developed a three-dimensional Wavelet-based Adaptive Mesh Refinement (WAMR) algorithm. The method employs a highly non-uniform adaptive grid with fine resolution over the areas of interest without requiring small grid-spacing throughout the entire domain. The method uses multi-grid iterative solver that naturally takes advantage of a multilevel structure of the adaptive grid. In order to represent the multilevel adaptive grid efficiently, a dynamic data structure based on indirect memory addressing has been developed. The data structure allows rapid access to individual points, fast inter-grid operations and re-gridding. The WAMR method has been implemented on parallel computer architectures. The parallel algorithm is based on run-time partitioning and load-balancing scheme for the adaptive grid. The partitioning scheme maintains locality to reduce communications between computing nodes. The parallel scheme was found to be cost-effective. Specifically we obtained an order of magnitude increase in computational speed for numerical simulations performed on a twelve-core single processor workstation. We have applied the WAMR method for numerical

  17. Parallel Computation of Three-Dimensional Flows using Overlapping Grids with Adaptive Mesh Refinement

    SciTech Connect

    Henshaw, W; Schwendeman, D

    2007-11-15

    This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel. The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advection-diffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the solutions are shown to be well resolved on the finest grid. The parallel performance of the approach is examined in detail for the shock diffraction problem.

  18. Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Henshaw, William D.; Schwendeman, Donald W.

    2008-08-01

    This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel. The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advection-diffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the accuracy of the numerical solutions is assessed quantitatively through an estimation of the errors from a grid convergence study. The parallel performance of the

  19. Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries

    NASA Technical Reports Server (NTRS)

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

    2002-01-01

    This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.

  20. Modeling, mesh generation, and adaptive numerical methods for partial differential equations

    SciTech Connect

    Babuska, I.; Henshaw, W.D.; Oliger, J.E.; Flaherty, J.E.; Hopcroft, J.E.; Tezduyar, T.

    1995-12-31

    Mesh generation is one of the most time consuming aspects of computational solutions of problems involving partial differential equations. It is, furthermore, no longer acceptable to compute solutions without proper verification that specified accuracy criteria are being satisfied. Mesh generation must be related to the solution through computable estimates of discretization errors. Thus, an iterative process of alternate mesh and solution generation evolves in an adaptive manner with the end result that the solution is computed to prescribed specifications in an optimal, or at least efficient, manner. While mesh generation and adaptive strategies are becoming available, major computational challenges remain. One, in particular, involves moving boundaries and interfaces, such as free-surface flows and fluid-structure interactions. A 3-week program was held from July 5 to July 23, 1993 with 173 participants and 66 keynote, invited, and contributed presentations. This volume represents written versions of 21 of these lectures. These proceedings are organized roughly in order of their presentation at the workshop. Thus, the initial papers are concerned with geometry and mesh generation and discuss the representation of physical objects and surfaces on a computer and techniques to use this data to generate, principally, unstructured meshes of tetrahedral or hexahedral elements. The remainder of the papers cover adaptive strategies, error estimation, and applications. Several submissions deal with high-order p- and hp-refinement methods where mesh refinement/coarsening (h-refinement) is combined with local variation of method order (p-refinement). Combinations of mathematically verified and physically motivated approaches to error estimation are represented. Applications center on fluid mechanics. Selected papers are indexed separately for inclusion in the Energy Science and Technology Database.

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

    PubMed

    Wang, Tianyang; Chu, Fulei; Han, Qinkai

    2017-03-01

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

  2. Implementation of a mesh adaptive scheme based on an element-level error indicator

    NASA Technical Reports Server (NTRS)

    Keating, Scott; Felippa, Carlos A.; Militello, Carmelo

    1993-01-01

    We investigate the formulation and application of element-level error indicators based on parametrized variational principles. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited to drive adaptive mesh refinement on parallel computers where access to neighboring elements resident on different processors may incur significant computational overhead. Furthermore, such indicators are not affected by physical jumps at junctures or interfaces. An element-level indicator has been derived from the higher-order element energy and applied to r and h mesh adaptation of meshes in plates and shell structures. We report on our initial experiments with a cylindrical shell that intersects with fist plates forming a simplified 'wing-body intersection' benchmark problem.

  3. 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

  4. Rain compensation algorithm using adaptive linear prediction

    NASA Technical Reports Server (NTRS)

    Satorius, Edgar

    1992-01-01

    Rain compensation algorithm using adaptive linear prediction is presented in viewgraph form. Topics covered include AMT scenario, summary of AMT-RCA, empirical basis for reducing attenuation extrapolation errors, and candidate adaptive 1-pole prediction filter for application to AMT-RCA (at the mobile terminal (MT)).

  5. 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.

  6. 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.

  7. A fast, robust, and simple implicit method for adaptive time-stepping on adaptive mesh-refinement grids

    NASA Astrophysics Data System (ADS)

    Commerçon, B.; Debout, V.; Teyssier, R.

    2014-03-01

    Context. Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. Aims: We present a new method for implicit adaptive time-stepping on adaptive mesh-refinement grids. We implement it in the radiation-hydrodynamics solver we designed for the RAMSES code for astrophysical purposes and, more particularly, for protostellar collapse. Methods: We briefly recall the radiation-hydrodynamics equations and the adaptive time-stepping methodology used for hydrodynamical solvers. We then introduce the different types of boundary conditions (Dirichlet, Neumann, and Robin) that are used at the interface between levels and present our implementation of the new method in the RAMSES code. The method is tested against classical diffusion and radiation-hydrodynamics tests, after which we present an application for protostellar collapse. Results: We show that using Dirichlet boundary conditions at level interfaces is a good compromise between robustness and accuracy and that it can be used in structure formation calculations. The gain in computational time over our former unique time step method ranges from factors of 5 to 50 depending on the level of adaptive time-stepping and on the problem. We successfully compare the old and new methods for protostellar collapse calculations that involve highly non linear physics. Conclusions: We have developed a simple but robust method for adaptive time-stepping of implicit scheme on adaptive mesh-refinement grids. It can be applied to a wide variety of physical problems that involve diffusion processes.

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

    NASA Astrophysics Data System (ADS)

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

    2016-06-01

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

  9. GALAXY CLUSTER RADIO RELICS IN ADAPTIVE MESH REFINEMENT COSMOLOGICAL SIMULATIONS: RELIC PROPERTIES AND SCALING RELATIONSHIPS

    SciTech Connect

    Skillman, Samuel W.; Hallman, Eric J.; Burns, Jack O.; Smith, Britton D.; O'Shea, Brian W.; Turk, Matthew J.

    2011-07-10

    Cosmological shocks are a critical part of large-scale structure formation, and are responsible for heating the intracluster medium in galaxy clusters. In addition, they are capable of accelerating non-thermal electrons and protons. In this work, we focus on the acceleration of electrons at shock fronts, which is thought to be responsible for radio relics-extended radio features in the vicinity of merging galaxy clusters. By combining high-resolution adaptive mesh refinement/N-body cosmological simulations with an accurate shock-finding algorithm and a model for electron acceleration, we calculate the expected synchrotron emission resulting from cosmological structure formation. We produce synthetic radio maps of a large sample of galaxy clusters and present luminosity functions and scaling relationships. With upcoming long-wavelength radio telescopes, we expect to see an abundance of radio emission associated with merger shocks in the intracluster medium. By producing observationally motivated statistics, we provide predictions that can be compared with observations to further improve our understanding of magnetic fields and electron shock acceleration.

  10. Adaptive Mesh Refinement for a High-Symmetry Singular Euler Flow

    NASA Astrophysics Data System (ADS)

    Germaschewski, K.; Bhattacharjee, A.; Grauer, R.

    2002-11-01

    Starting from a highly symmetric initial condition motivated by the work of Kida [J. Phys. Soc Jpn. 54, 2132 (1995)] and Boratav and Pelz [Phys. Fluids 6, 2757 (1994)], we use the technique of block-structured adaptive mesh refinement (AMR) to numerically investigate the development of a self-similar singular solution to the incompressible Euler equations. The scheme, previously used by Grauer et al [Phys. Rev. Lett. 84, 4850 (1998)], is particularly well suited to follow the development of singular structures as it allows for effective resolutions far beyond those accessible using fixed grid algorithms. A self-similar collapse is observed in the simulation, where the maximum vorticity blows up as 1/(t_crit-t). Ng and Bhattacharjee [Phys Rev E 54, 1530 (1996)] have presented a sufficient condition for a finite-time singularity in this highly symmetric flow involving the fourth-order spatial derivative of the pressure at and near the origin. We test this sufficient condition and investigate the evolution of the spatial range over which this condition holds in our numerical results. We also demonstrate numerically that this singularity is unstable because in a full simulation that does not build in the symmetries of the initial condition, small perturbations introduced by AMR lead to nonsymmetric evolution of the vortices.

  11. Relativistic Flows Using Spatial And Temporal Adaptive Structured Mesh Refinement. I. Hydrodynamics

    SciTech Connect

    Wang, Peng; Abel, Tom; Zhang, Weiqun; /KIPAC, Menlo Park

    2007-04-02

    Astrophysical relativistic flow problems require high resolution three-dimensional numerical simulations. In this paper, we describe a new parallel three-dimensional code for simulations of special relativistic hydrodynamics (SRHD) using both spatially and temporally structured adaptive mesh refinement (AMR). We used method of lines to discrete SRHD equations spatially and used a total variation diminishing (TVD) Runge-Kutta scheme for time integration. For spatial reconstruction, we have implemented piecewise linear method (PLM), piecewise parabolic method (PPM), third order convex essentially non-oscillatory (CENO) and third and fifth order weighted essentially non-oscillatory (WENO) schemes. Flux is computed using either direct flux reconstruction or approximate Riemann solvers including HLL, modified Marquina flux, local Lax-Friedrichs flux formulas and HLLC. The AMR part of the code is built on top of the cosmological Eulerian AMR code enzo, which uses the Berger-Colella AMR algorithm and is parallel with dynamical load balancing using the widely available Message Passing Interface library. We discuss the coupling of the AMR framework with the relativistic solvers and show its performance on eleven test problems.

  12. 3D Boltzmann Simulation of the Io's Plasma Environment with Adaptive Mesh and Particle Refinement

    NASA Astrophysics Data System (ADS)

    Lipatov, A. S.; Combi, M. R.

    2002-12-01

    The global dynamics of the ionized and neutral components in the environment of Io plays an important role in the interaction of Jupiter's corotating magnetospheric plasma with Io [Combi et al., 2002; 1998; Kabin et al., 2001]. The stationary simulation of this problem was done in the MHD [Combi et al., 1998; Linker et al, 1998; Kabin et al., 2001] and the electrodynamic [Saur et al., 1999] approaches. In this report, we develop a method of kinetic ion-neutral simulation, which is based on a multiscale adaptive mesh, particle and algorithm refinement. This method employs the fluid description for electrons whereas for ions the drift-kinetic and particle approaches are used. This method takes into account charge-exchange and photoionization processes. The first results of such simulation of the dynamics of ions in the Io's environment are discussed in this report. ~ M R Combi et al., J. Geophys. Res., 103, 9071, 1998. M R Combi, T I Gombosi, K Kabin, Atmospheres in the Solar System: Comparative\\ Aeronomy. Geophys. Monograph Series, 130, 151, 2002. K Kabin et al., Planetary and Space Sci., 49, 337, 2001. J A Linker et al., J. Geophys. Res., 103(E9), 19867, 1998. J Saur et al., J. Geophys. Res., 104, 25105, 1999.

  13. Incremental approach for radial basis functions mesh deformation with greedy algorithm

    NASA Astrophysics Data System (ADS)

    Selim, Mohamed M.; Koomullil, Roy P.; Shehata, Ahmed S.

    2017-07-01

    Mesh Deformation is an important element of any fluid-structure interaction simulation. In this article, a new methodology is presented for the deformation of volume meshes using incremental radial basis function (RBF) based interpolation. A greedy algorithm is used to select a small subset of the surface nodes iteratively. Two incremental approaches are introduced to solve the RBF system of equations: 1) block matrix inversion based approach and 2) modified LU decomposition approach. The use of incremental approach decreased the computational complexity of solving the system of equations within each greedy algorithm's iteration from O (n3) to O (n2). Results are presented from an accuracy study using specified deformations on a 2D surface. Mesh deformations for bending and twisting of a 3D rectangular supercritical wing have been demonstrated. Outcomes showed the incremental approaches reduce the CPU time up to 67% as compared to a traditional RBF matrix solver. Finally, the proposed mesh deformation approach was integrated within a fluid-structure interaction solver for investigating a flow induced cantilever beam vibration.

  14. Smart algorithms and adaptive methods in computational fluid dynamics

    NASA Astrophysics Data System (ADS)

    Tinsley Oden, J.

    1989-05-01

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

  15. The Graft Tool: An All-Hexahedral Transition Algorithm for Creating a Multi-Directional Swept Volume Mesh

    SciTech Connect

    BENZLEY,STEVEN E.; JANKOVICH,STEVEN R.; MITCHELL,SCOTT A.; SHEPHERD,JASON F.

    1999-09-27

    Sweeping algorithms have become very mature and can create a semi-structured mesh on a large set of solids. However, these algorithms require that all linking surfaces be mappable or submappable. This restriction excludes solids with imprints or protrusions on the linking surfaces. The grafting algorithm allows these solids to be swept. It then locally modifies the position and connectivity of the nodes on the linking surfaces to align with the graft surfaces. Once a high-quality surface mesh is formed on the graft surface, it is swept along the branch creating a 2 3/4-D mesh.

  16. Assessment and improvement of mapping algorithms for non-matching meshes and geometries in computational FSI

    NASA Astrophysics Data System (ADS)

    Wang, Tianyang; Wüchner, Roland; Sicklinger, Stefan; Bletzinger, Kai-Uwe

    2016-05-01

    This paper investigates data mapping between non-matching meshes and geometries in fluid-structure interaction. Mapping algorithms for surface meshes including nearest element interpolation, the standard mortar method and the dual mortar method are studied and comparatively assessed. The inconsistency problem of mortar methods at curved edges of fluid-structure-interfaces is solved by a newly developed enforcing consistency approach, which is robust enough to handle even the case that fluid boundary facets are totally not in contact with structure boundary elements due to high fluid refinement. Besides, tests with representative geometries show that the mortar methods are suitable for conservative mapping but it is better to use the nearest element interpolation in a direct way, and moreover, the dual mortar method can give slight oscillations. This work also develops a co-rotating mapping algorithm for 1D beam elements. Its novelty lies in the ability of handling large displacements and rotations.

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

    NASA Astrophysics Data System (ADS)

    Luo, Hongbin; Li, Lemin; Yu, Hongfang

    2006-12-01

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

  18. 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

  19. Gram-Schmidt Adaptive Algorithms.

    DTIC Science & Technology

    1980-03-01

    Calahan et al. 1976; Liles and Demmel 1978; Blakely 1977; Berra and Singhania 1976; Sameh and Kuck 1975]. Sameh and Kuck [1975, 1977a, 1977b, 1978] have...Griffiss Air Force Base, New York, November 1976; A. H. Sameh and D. J. Kuck, Linear System Solvers for Parallel Computers, Department of Computer...Sciences, Report No. UIUCDCS-R-75-701, University of Illinois at Urbana-Champaign, February 1975. A. H. Sameh , "Numerical Parallel Algorithms--A Survey

  20. Adaptive Meshing of Ship Air-Wake Flowfields

    DTIC Science & Technology

    2014-10-21

    resolve gradients of the adaptation function. The third method is a meshless method that uses a physics-based force model to move nodes around to...method that uses a physics-based force model to move nodes around to resolve the geometry and flowfield. The initial phase of the research conducted...three codes all solve the unsteady Euler equations, but use different discretization strategies. The target application is an aircraft in a landing

  1. 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.

  2. 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.

  3. An implicit algorithm for the conservative transonic full potential equation using an arbitrary mesh

    NASA Technical Reports Server (NTRS)

    Holst, T. L.

    1978-01-01

    A new, implicit approximate factorization (AF) algorithm designed to solve the conservative full-potential equation for the transonic flow past arbitrary airfoils has been developed. The new algorithm uses an upwind bias of the density coefficient to provide stability in supersonic regions. This allows the simple two- and three-banded matrix form of the AF scheme to be retained over the entire flow field, even in regions of supersonic flow. A numerical transformation is used to establish an arbitrary body-fitted finite-difference mesh. Airfoil pressure distributions have been computed and are in good agreement with independent results.

  4. Solving kinetic equations with adaptive mesh in phase space for rarefied gas dynamics and plasma physics (Invited)

    SciTech Connect

    Kolobov, Vladimir; Arslanbekov, Robert; Frolova, Anna

    2014-12-09

    The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.

  5. Adaptive mesh refinement strategies in isogeometric analysis— A computational comparison

    NASA Astrophysics Data System (ADS)

    Hennig, Paul; Kästner, Markus; Morgenstern, Philipp; Peterseim, Daniel

    2017-04-01

    We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods in comparison are Truncated Hierarchical B-splines with two different refinement strategies, T-splines with the refinement strategy introduced by Scott et al. in 2012, and T-splines with an alternative refinement strategy introduced by some of the authors. In four examples, including singular and non-singular problems of linear elasticity and the Poisson problem, the H1-errors of the discrete solutions, the number of degrees of freedom as well as sparsity patterns and condition numbers of the discretized problem are compared.

  6. 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.

  7. 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.

  8. 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.

  9. Adaptive link selection algorithms for distributed estimation

    NASA Astrophysics Data System (ADS)

    Xu, Songcen; de Lamare, Rodrigo C.; Poor, H. Vincent

    2015-12-01

    This paper presents adaptive link selection algorithms for distributed estimation and considers their application to wireless sensor networks and smart grids. In particular, exhaustive search-based least mean squares (LMS) / recursive least squares (RLS) link selection algorithms and sparsity-inspired LMS / RLS link selection algorithms that can exploit the topology of networks with poor-quality links are considered. The proposed link selection algorithms are then analyzed in terms of their stability, steady-state, and tracking performance and computational complexity. In comparison with the existing centralized or distributed estimation strategies, the key features of the proposed algorithms are as follows: (1) more accurate estimates and faster convergence speed can be obtained and (2) the network is equipped with the ability of link selection that can circumvent link failures and improve the estimation performance. The performance of the proposed algorithms for distributed estimation is illustrated via simulations in applications of wireless sensor networks and smart grids.

  10. 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

  11. Using adaptive sampling and triangular meshes for the processing and inversion of potential field data

    NASA Astrophysics Data System (ADS)

    Foks, Nathan Leon

    The interpretation of geophysical data plays an important role in the analysis of potential field data in resource exploration industries. Two categories of interpretation techniques are discussed in this thesis; boundary detection and geophysical inversion. Fault or boundary detection is a method to interpret the locations of subsurface boundaries from measured data, while inversion is a computationally intensive method that provides 3D information about subsurface structure. My research focuses on these two aspects of interpretation techniques. First, I develop a method to aid in the interpretation of faults and boundaries from magnetic data. These processes are traditionally carried out using raster grid and image processing techniques. Instead, I use unstructured meshes of triangular facets that can extract inferred boundaries using mesh edges. Next, to address the computational issues of geophysical inversion, I develop an approach to reduce the number of data in a data set. The approach selects the data points according to a user specified proxy for its signal content. The approach is performed in the data domain and requires no modification to existing inversion codes. This technique adds to the existing suite of compressive inversion algorithms. Finally, I develop an algorithm to invert gravity data for an interfacing surface using an unstructured mesh of triangular facets. A pertinent property of unstructured meshes is their flexibility at representing oblique, or arbitrarily oriented structures. This flexibility makes unstructured meshes an ideal candidate for geometry based interface inversions. The approaches I have developed provide a suite of algorithms geared towards large-scale interpretation of potential field data, by using an unstructured representation of both the data and model parameters.

  12. Adaptive cuckoo search algorithm for unconstrained optimization.

    PubMed

    Ong, Pauline

    2014-01-01

    Modification of the intensification and diversification approaches in the recently developed cuckoo search algorithm (CSA) is performed. The alteration involves the implementation of adaptive step size adjustment strategy, and thus enabling faster convergence to the global optimal solutions. The feasibility of the proposed algorithm is validated against benchmark optimization functions, where the obtained results demonstrate a marked improvement over the standard CSA, in all the cases.

  13. Using high-order methods on adaptively refined block-structured meshes - discretizations, interpolations, and filters.

    SciTech Connect

    Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.

    2006-01-01

    Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.

  14. Optimal Hops-Based Adaptive Clustering Algorithm

    NASA Astrophysics Data System (ADS)

    Xuan, Xin; Chen, Jian; Zhen, Shanshan; Kuo, Yonghong

    This paper proposes an optimal hops-based adaptive clustering algorithm (OHACA). The algorithm sets an energy selection threshold before the cluster forms so that the nodes with less energy are more likely to go to sleep immediately. In setup phase, OHACA introduces an adaptive mechanism to adjust cluster head and load balance. And the optimal distance theory is applied to discover the practical optimal routing path to minimize the total energy for transmission. Simulation results show that OHACA prolongs the life of network, improves utilizing rate and transmits more data because of energy balance.

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

    NASA Astrophysics Data System (ADS)

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

    2016-10-01

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

  16. Adaptive mesh compression and transmission in Internet-based interactive walkthrough virtual environments

    NASA Astrophysics Data System (ADS)

    Yang, Sheng; Kuo, C.-C. Jay

    2002-07-01

    An Internet-based interactive walkthrough virtual environment is presented in this work to facilitate interactive streaming and browsing of 3D graphic models across the Internet. The models are compressed by the view-dependent progressive mesh compression algorithm to enable the decorrelation of partitions and finer granularity. Following the fundamental framework of mesh representation, an interactive protocol based on the real time streaming protocol (RTSP) is developed to enhance the interaction between the server and the client. Finally, the data of the virtual world is re-organized and transmitted according to the viewer's requests. Experimental results demonstrate that the proposed algorithm reduces the required transmission bandwidth, and provides an acceptable visual quality even at low bit rates.

  17. Arbitrary Lagrangian-Eulerian Method with Local Structured Adaptive Mesh Refinement for Modeling Shock Hydrodynamics

    SciTech Connect

    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 traditional 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.

  18. 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.

  19. 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.

  20. GAMMA-RAY BURST DYNAMICS AND AFTERGLOW RADIATION FROM ADAPTIVE MESH REFINEMENT, SPECIAL RELATIVISTIC HYDRODYNAMIC SIMULATIONS

    SciTech Connect

    De Colle, Fabio; Ramirez-Ruiz, Enrico; Granot, Jonathan; Lopez-Camara, Diego

    2012-02-20

    We report on the development of Mezcal-SRHD, a new adaptive mesh refinement, special relativistic hydrodynamics (SRHD) code, developed with the aim of studying the highly relativistic flows in gamma-ray burst sources. The SRHD equations are solved using finite-volume conservative solvers, with second-order interpolation in space and time. The correct implementation of the algorithms is verified by one-dimensional (1D) and multi-dimensional tests. The code is then applied to study the propagation of 1D spherical impulsive blast waves expanding in a stratified medium with {rho}{proportional_to}r{sup -k}, bridging between the relativistic and Newtonian phases (which are described by the Blandford-McKee and Sedov-Taylor self-similar solutions, respectively), as well as to a two-dimensional (2D) cylindrically symmetric impulsive jet propagating in a constant density medium. It is shown that the deceleration to nonrelativistic speeds in one dimension occurs on scales significantly larger than the Sedov length. This transition is further delayed with respect to the Sedov length as the degree of stratification of the ambient medium is increased. This result, together with the scaling of position, Lorentz factor, and the shock velocity as a function of time and shock radius, is explained here using a simple analytical model based on energy conservation. The method used for calculating the afterglow radiation by post-processing the results of the simulations is described in detail. The light curves computed using the results of 1D numerical simulations during the relativistic stage correctly reproduce those calculated assuming the self-similar Blandford-McKee solution for the evolution of the flow. The jet dynamics from our 2D simulations and the resulting afterglow light curves, including the jet break, are in good agreement with those presented in previous works. Finally, we show how the details of the dynamics critically depend on properly resolving the structure of the

  1. Gamma-Ray Burst Dynamics and Afterglow Radiation from Adaptive Mesh Refinement, Special Relativistic Hydrodynamic Simulations

    NASA Astrophysics Data System (ADS)

    De Colle, Fabio; Granot, Jonathan; López-Cámara, Diego; Ramirez-Ruiz, Enrico

    2012-02-01

    We report on the development of Mezcal-SRHD, a new adaptive mesh refinement, special relativistic hydrodynamics (SRHD) code, developed with the aim of studying the highly relativistic flows in gamma-ray burst sources. The SRHD equations are solved using finite-volume conservative solvers, with second-order interpolation in space and time. The correct implementation of the algorithms is verified by one-dimensional (1D) and multi-dimensional tests. The code is then applied to study the propagation of 1D spherical impulsive blast waves expanding in a stratified medium with ρvpropr -k , bridging between the relativistic and Newtonian phases (which are described by the Blandford-McKee and Sedov-Taylor self-similar solutions, respectively), as well as to a two-dimensional (2D) cylindrically symmetric impulsive jet propagating in a constant density medium. It is shown that the deceleration to nonrelativistic speeds in one dimension occurs on scales significantly larger than the Sedov length. This transition is further delayed with respect to the Sedov length as the degree of stratification of the ambient medium is increased. This result, together with the scaling of position, Lorentz factor, and the shock velocity as a function of time and shock radius, is explained here using a simple analytical model based on energy conservation. The method used for calculating the afterglow radiation by post-processing the results of the simulations is described in detail. The light curves computed using the results of 1D numerical simulations during the relativistic stage correctly reproduce those calculated assuming the self-similar Blandford-McKee solution for the evolution of the flow. The jet dynamics from our 2D simulations and the resulting afterglow light curves, including the jet break, are in good agreement with those presented in previous works. Finally, we show how the details of the dynamics critically depend on properly resolving the structure of the relativistic flow.

  2. Adaptive mesh refinement for time-domain electromagnetics using vector finite elements :a feasibility study.

    SciTech Connect

    Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis

    2005-12-01

    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.

  3. 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

  4. Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes. Parts 1 and 2

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Kwak, Dochan (Technical Monitor)

    1995-01-01

    The Advisory Group for Aerospace Research and Development (AGARD) has requested my participation in the lecture series entitled Parallel Computing in Computational Fluid Dynamics to be held at the von Karman Institute in Brussels, Belgium on May 15-19, 1995. In addition, a request has been made from the US Coordinator for AGARD at the Pentagon for NASA Ames to hold a repetition of the lecture series on October 16-20, 1995. I have been asked to be a local coordinator for the Ames event. All AGARD lecture series events have attendance limited to NATO allied countries. A brief of the lecture series is provided in the attached enclosure. Specifically, I have been asked to give two lectures of approximately 75 minutes each on the subject of parallel solution techniques for the fluid flow equations on unstructured meshes. The title of my lectures is "Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes" (Parts I-II). The contents of these lectures will be largely review in nature and will draw upon previously published work in this area. Topics of my lectures will include: (1) Mesh partitioning algorithms. Recursive techniques based on coordinate bisection, Cuthill-McKee level structures, and spectral bisection. (2) Newton's method for large scale CFD problems. Size and complexity estimates for Newton's method, modifications for insuring global convergence. (3) Techniques for constructing the Jacobian matrix. Analytic and numerical techniques for Jacobian matrix-vector products, constructing the transposed matrix, extensions to optimization and homotopy theories. (4) Iterative solution algorithms. Practical experience with GIVIRES and BICG-STAB matrix solvers. (5) Parallel matrix preconditioning. Incomplete Lower-Upper (ILU) factorization, domain-decomposed ILU, approximate Schur complement strategies.

  5. Adaptive Mesh Computations with the PLUTO Code for Astrophysical Fluid Dynamics

    NASA Astrophysics Data System (ADS)

    Mignone, A.; Zanni, C.

    2012-07-01

    We present an overview of the current version of the PLUTO code for numerical simulations of astrophysical fluid flows over block-structured adaptive grids. The code preserves its modular framework for the solution of the classical or relativistic magnetohydrodynamics (MHD) equations while exploiting the distributed infrastructure of the Chombo library for multidimensional adaptive mesh refinement (AMR) parallel computations. Equations are evolved in time using an explicit second-order, dimensionally unsplit time stepping scheme based on a cell-centered discretization of the flow variables. Efficiency and robustness are shown through multidimensional benchmarks and applications to problems of astrophysical relevance.

  6. Fluidity: a fully-unstructured adaptive mesh computational framework for geodynamics

    NASA Astrophysics Data System (ADS)

    Kramer, S. C.; Davies, D.; Wilson, C. R.

    2010-12-01

    Fluidity is a finite element, finite volume fluid dynamics model developed by the Applied Modelling and Computation Group at Imperial College London. Several features of the model make it attractive for use in geodynamics. A core finite element library enables the rapid implementation and investigation of new numerical schemes. For example, the function spaces used for each variable can be changed allowing properties of the discretisation, such as stability, conservation and balance, to be easily varied and investigated. Furthermore, unstructured, simplex meshes allow the underlying resolution to vary rapidly across the computational domain. Combined with dynamic mesh adaptivity, where the mesh is periodically optimised to the current conditions, this allows significant savings in computational cost over traditional chessboard-like structured mesh simulations [1]. In this study we extend Fluidity (using the Portable, Extensible Toolkit for Scientific Computation [PETSc, 2]) to Stokes flow problems relevant to geodynamics. However, due to the assumptions inherent in all models, it is necessary to properly verify and validate the code before applying it to any large-scale problems. In recent years this has been made easier by the publication of a series of ‘community benchmarks’ for geodynamic modelling. We discuss the use of several of these to help validate Fluidity [e.g. 3, 4]. The experimental results of Vatteville et al. [5] are then used to validate Fluidity against laboratory measurements. This test case is also used to highlight the computational advantages of using adaptive, unstructured meshes - significantly reducing the number of nodes and total CPU time required to match a fixed mesh simulation. References: 1. C. C. Pain et al. Comput. Meth. Appl. M, 190:3771-3796, 2001. doi:10.1016/S0045-7825(00)00294-2. 2. B. Satish et al. http://www.mcs.anl.gov/petsc/petsc-2/, 2001. 3. Blankenbach et al. Geophys. J. Int., 98:23-28, 1989. 4. Busse et al. Geophys

  7. A Block-Structured Adaptive Mesh Refinement Technique with a Finite-Difference-Based Lattice Boltzmann Method

    NASA Astrophysics Data System (ADS)

    Fakhari, Abbas; Lee, Taehun

    2013-11-01

    A novel adaptive mesh refinement (AMR) algorithm for the numerical solution of fluid flow problems is presented in this study. The proposed AMR algorithm can be used to solve partial differential equations including, but not limited to, the Navier-Stokes equations using an AMR technique. Here, the lattice Boltzmann method (LBM) is employed as a substitute of the nearly incompressible Navier-Stokes equations. Besides its simplicity, the proposed AMR algorithm is straightforward and yet efficient. The idea is to remove the need for a tree-type data structure by using the pointer attributes in a unique way, along with an appropriate adjustment of the child block's IDs, to determine the neighbors of a certain block. Thanks to the unique way of invoking pointers, there is no need to construct a quad-tree (in 2D) or oct-tree (in 3D) data structure for maintaining the connectivity data between different blocks. As a result, the memory and time required for tree traversal are completely eliminated, leaving us with a clean and efficient algorithm that is easier to implement and use on parallel machines. Several benchmark studies are carried out to assess the accuracy and efficiency of the proposed AMR-LBM, including lid-driven cavity flow, vortex shedding past a square cylinder, and Kelvin-Helmholtz instability for single-phase and multiphase fluids.

  8. Enhanced pool sharing: a constraint-based routing algorithm for shared mesh restoration networks [Invited

    NASA Astrophysics Data System (ADS)

    Naser, Hassan; Mouftah, Hussein

    2004-05-01

    We investigate the availability performance of networks with shared mesh restoration and demonstrate that these networks cannot provide highly available protection services. A major factor in the poor performance of shared mesh restoration is that the resources at backup links are shared among demands. If multiple service-affecting failures occur in the network a multitude of these demands will rush to utilize the spare resources on backup links. These resources are not adequate to serve all of these demands simultaneously. We propose a heuristic routing algorithm that attempts to improve the availability performance of shared mesh restoration. We measure the likelihood that a backup link will not be available to restore a newly arrived demand if or when more than one failure occurs in the network. We adjust the backup bandwidth on that link if the measured likelihood exceeds a preset threshold. As a typical representative, we show that the downtime improves by 7%, 11%, and 18% when the total backup bandwidth in the network is increased by 5%, 10%, and 20%, respectively. These values are obtained through a series of fitting experiments.

  9. Impact of space-time mesh adaptation on solute transport modeling in porous media

    NASA Astrophysics Data System (ADS)

    Esfandiar, Bahman; Porta, Giovanni; Perotto, Simona; Guadagnini, Alberto

    2015-02-01

    We implement a space-time grid adaptation procedure to efficiently improve the accuracy of numerical simulations of solute transport in porous media in the context of model parameter estimation. We focus on the Advection Dispersion Equation (ADE) for the interpretation of nonreactive transport experiments in laboratory-scale heterogeneous porous media. When compared to a numerical approximation based on a fixed space-time discretization, our approach is grounded on a joint automatic selection of the spatial grid and the time step to capture the main (space-time) system dynamics. Spatial mesh adaptation is driven by an anisotropic recovery-based error estimator which enables us to properly select the size, shape, and orientation of the mesh elements. Adaptation of the time step is performed through an ad hoc local reconstruction of the temporal derivative of the solution via a recovery-based approach. The impact of the proposed adaptation strategy on the ability to provide reliable estimates of the key parameters of an ADE model is assessed on the basis of experimental solute breakthrough data measured following tracer injection in a nonuniform porous system. Model calibration is performed in a Maximum Likelihood (ML) framework upon relying on the representation of the ADE solution through a generalized Polynomial Chaos Expansion (gPCE). Our results show that the proposed anisotropic space-time grid adaptation leads to ML parameter estimates and to model results of markedly improved quality when compared to classical inversion approaches based on a uniform space-time discretization.

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

    NASA Technical Reports Server (NTRS)

    Nielsen, Eric J.

    2006-01-01

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

  11. 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.

  12. A Mesh Adaptive and Mass Conservative Three Dimensional Numerical Model For Ocean Hydrodynamics and Transport Simulations

    NASA Astrophysics Data System (ADS)

    Savant, G.; Trahan, C. J.

    2016-02-01

    Next generation finite element method (FEM)hydrodynamic and transport code are expected to be at the fore front of Ocean modeling, of particular importance are the FEM codes that conserve hydrodynamic and transport mass (locally and globally). This talk will introduce the new U.S. Army Corps of Engineers enterprise implicit time stepping and multi-dimensional FEM model, this model is characterized by adaptive meshing to resolve the fine detail required to capture baroclinic effects on hydrodynamics as well as on transported quantities such as salt/heat/tracers etc. The FEM developmental theory that guarantees local and global mass conservation, and results from simulations will be presented, also presented will be the aspects of the Eulerian-Lagrangian meshing that removes certain limitations of sigma and z-gridding in hydrodynamic models.

  13. Adaptive Algorithms for HF Antenna Arrays.

    DTIC Science & Technology

    1987-07-01

    SUBJECT TERMS (Contnue on reverse dfnoceaq and identiy by bkICk numnber) FIELD GROUP SUB-GROUP HP Adaptive Arrays HrF Comunications Systems 4 HP...Although their heavy computational load renders them impractical *1 for many applications, the advancements in cheap, fast digital hardware have...or digital form. For many applications, the LMS algorithm represents a good trade off between speed of convergence* and implementational The speed of

  14. Adaptive Mesh Euler Equation Computation of Vortex Breakdown in Delta Wing Flow.

    NASA Astrophysics Data System (ADS)

    Modiano, David Laurence

    A solution method for the three-dimensional Euler equations is formulated and implemented. The solver uses an unstructured mesh of tetrahedral cells and performs adaptive refinement by mesh-point embedding to increase mesh resolution in regions of interesting flow features. The fourth-difference artificial dissipation is increased to a higher order of accuracy using the method of Holmes and Connell. A new method of temporal integration is developed to accelerate the explicit computation of unsteady flows. The solver is applied to the solution of the flow around a sharp edged delta wing, with emphasis on the behavior of the leading edge vortex above the leeside of the wing at high angle of attack, under which conditions the vortex suffers from vortex breakdown. Large deviations in entropy, which indicate vortical regions of the flow, specify the region in which adaptation is performed. Adaptive flow calculations are performed at ten different angles of attack, at seven of which vortex breakdown occurs. The aerodynamic normal force coefficients show excellent agreement with wind tunnel data measured by Jarrah, which demonstrates the importance of adaptation in obtaining an accurate solution. The pitching moment coefficient and the location of vortex breakdown are compared with experimental data measured by Hummel and Srinivasan, with which fairly good agreement is seen in cases in which the location of breakdown is over the wing. A series of unsteady calculations involving a pitching delta wing were performed. The use of the acceleration technique is validated. A hysteresis in the normal force is observed, as in experiments, and a lag in the breakdown position is demonstrated. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.).

  15. Uniform remeshing with an adaptive domain: a new scheme for view-dependent level-of-detail rendering of meshes.

    PubMed

    Zhu, Yuanchen

    2005-01-01

    We present a new algorithm for view-dependent level-of-detail rendering of meshes. Not only can it effectively resolve complex geometry features similar to edge collapse-based schemes, but it also produces meshes that modern graphics hardware can render efficiently. This is accomplished through a novel hybrid approach: For each frame, we view-dependently refine the progressive mesh (PM) representation of the original mesh and use the output as the base domain of uniform regular refinements. The algorithm exploits frame-to-frame coherence and only updates portions of the output mesh corresponding to modified domain triangles. The PM representation is built using a custom volume preservation-based error function. A simple k-d tree enhanced jump-and-walk scheme is used to quickly map from the dynamic base domain to the original mesh during regular refinements. In practice, the PM refinement provides a view-optimized base domain for later regular refinements. The regular refinements ensure almost-everywhere regularity of output meshes, allowing optimization for vertex cache coherence and caching of geometry data in high-performance graphics memory. Combined, they also have the effect of allowing our algorithm to operate on uniform clusters of triangles instead of individual ones, reducing CPU workload.

  16. Spherical mesh adaptive direct search for separating quasi-uncorrelated sources by range-based independent component analysis.

    PubMed

    Selvan, S Easter; Borckmans, Pierre B; Chattopadhyay, A; Absil, P-A

    2013-09-01

    It is seemingly paradoxical to the classical definition of the independent component analysis (ICA), that in reality, the true sources are often not strictly uncorrelated. With this in mind, this letter concerns a framework to extract quasi-uncorrelated sources with finite supports by optimizing a range-based contrast function under unit-norm constraints (to handle the inherent scaling indeterminacy of ICA) but without orthogonality constraints. Albeit the appealing contrast properties of the range-based function (e.g., the absence of mixing local optima), the function is not differentiable everywhere. Unfortunately, there is a dearth of literature on derivative-free optimizers that effectively handle such a nonsmooth yet promising contrast function. This is the compelling reason for the design of a nonsmooth optimization algorithm on a manifold of matrices having unit-norm columns with the following objectives: to ascertain convergence to a Clarke stationary point of the contrast function and adhere to the necessary unit-norm constraints more naturally. The proposed nonsmooth optimization algorithm crucially relies on the design and analysis of an extension of the mesh adaptive direct search (MADS) method to handle locally Lipschitz objective functions defined on the sphere. The applicability of the algorithm in the ICA domain is demonstrated with simulations involving natural, face, aerial, and texture images.

  17. Adaptive path planning: Algorithm and analysis

    SciTech Connect

    Chen, Pang C.

    1993-03-01

    Path planning has to be fast to support real-time robot programming. Unfortunately, current planning techniques are still too slow to be effective, as they often require several minutes, if not hours of computation. To alleviate this problem, we present a learning algorithm that uses past experience to enhance future performance. The algorithm relies on an existing path planner to provide solutions to difficult tasks. From these solutions, an evolving sparse network of useful subgoals is learned to support faster planning. The algorithm is suitable for both stationary and incrementally-changing environments. To analyze our algorithm, we use a previously developed stochastic model that quantifies experience utility. Using this model, we characterize the situations in which the adaptive planner is useful, and provide quantitative bounds to predict its behavior. The results are demonstrated with problems in manipulator planning. Our algorithm and analysis are sufficiently general that they may also be applied to task planning or other planning domains in which experience is useful.

  18. Modelling of Sea Ice Formation and Mushy-Layer Convection with Adaptive Mesh Refinement

    NASA Astrophysics Data System (ADS)

    Parkinson, J.; Martin, D. F.; Wells, A.; Katz, R. F.

    2016-12-01

    Solidification of sea water leads to patterns of varying sea ice porosity and flow. Features develop on multiple scales, including narrow brine channels which mediate salt fluxes into the ocean. Consequently, adaptive mesh refinement techniques provide a valuable tool for efficiently simulating multiscale flow during initial sea ice growth. These processes are relevant across an increasing area of the world's ocean, as a result of the rapid retreat of the summer sea ice extent and more resilient winter extent. Sea ice formation is a dynamical process, during which convective cells form within a porous layer composed of ice crystals and an interstitial brine. Downwelling at the edge of such cells leads to the development of narrow, entirely liquid channels, through which cold saline brine is efficiently rejected into the underlying ocean. Thus it provides an important buoyancy forcing, which contributes to ocean mixing, the formation of deep water masses and the maintenance of the Arctic halocline. Previous attempts to numerically simulate such processes have struggled to resolve the narrow brine channels, which occupy just a few percent of the domain and evolve in time, at acceptable computational cost. To overcome this limitation we use the Chombo software framework to implement a computational mesh which adapts to provide additional resolution near brine channels. We present initial results that model the early growth of a reactive porous sea ice layer, using simulations with adaptive mesh refinement. Where possible, we make comparisons with previous numerical, experimental and observational studies. This method is also suitable for investigating the more general problem of solidification of a binary alloy, with applications in fields such as magma dynamics and metal casting.

  19. Simulations of recoiling black holes: adaptive mesh refinement and radiative transfer

    NASA Astrophysics Data System (ADS)

    Meliani, Zakaria; Mizuno, Yosuke; Olivares, Hector; Porth, Oliver; Rezzolla, Luciano; Younsi, Ziri

    2017-01-01

    Context. In many astrophysical phenomena, and especially in those that involve the high-energy regimes that always accompany the astronomical phenomenology of black holes and neutron stars, physical conditions that are achieved are extreme in terms of speeds, temperatures, and gravitational fields. In such relativistic regimes, numerical calculations are the only tool to accurately model the dynamics of the flows and the transport of radiation in the accreting matter. Aims: We here continue our effort of modelling the behaviour of matter when it orbits or is accreted onto a generic black hole by developing a new numerical code that employs advanced techniques geared towards solving the equations of general-relativistic hydrodynamics. Methods: More specifically, the new code employs a number of high-resolution shock-capturing Riemann solvers and reconstruction algorithms, exploiting the enhanced accuracy and the reduced computational cost of adaptive mesh-refinement (AMR) techniques. In addition, the code makes use of sophisticated ray-tracing libraries that, coupled with general-relativistic radiation-transfer calculations, allow us to accurately compute the electromagnetic emissions from such accretion flows. Results: We validate the new code by presenting an extensive series of stationary accretion flows either in spherical or axial symmetry that are performed either in two or three spatial dimensions. In addition, we consider the highly nonlinear scenario of a recoiling black hole produced in the merger of a supermassive black-hole binary interacting with the surrounding circumbinary disc. In this way, we can present for the first time ray-traced images of the shocked fluid and the light curve resulting from consistent general-relativistic radiation-transport calculations from this process. Conclusions: The work presented here lays the ground for the development of a generic computational infrastructure employing AMR techniques to accurately and self

  20. Adaptive mesh refinement versus subgrid friction interpolation in simulations of Antarctic ice dynamics

    DOE PAGES

    Cornford, S. L.; Martin, D. F.; Lee, V.; ...

    2016-05-13

    At least in conventional hydrostatic ice-sheet models, the numerical error associated with grounding line dynamics can be reduced by modifications to the discretization scheme. These involve altering the integration formulae for the basal traction and/or driving stress close to the grounding line and exhibit lower – if still first-order – error in the MISMIP3d experiments. MISMIP3d may not represent the variety of real ice streams, in that it lacks strong lateral stresses, and imposes a large basal traction at the grounding line. We study resolution sensitivity in the context of extreme forcing simulations of the entire Antarctic ice sheet, using the BISICLES adaptive mesh ice-sheet model with two schemes: the original treatment, and a scheme, which modifies the discretization of the basal traction. The second scheme does indeed improve accuracy – by around a factor of two – for a given mesh spacing, butmore » $$\\lesssim 1$$ km resolution is still necessary. For example, in coarser resolution simulations Thwaites Glacier retreats so slowly that other ice streams divert its trunk. In contrast, with $$\\lesssim 1$$ km meshes, the same glacier retreats far more quickly and triggers the final phase of West Antarctic collapse a century before any such diversion can take place.« less

  1. Compact integration factor methods for complex domains and adaptive mesh refinement.

    PubMed

    Liu, Xinfeng; Nie, Qing

    2010-08-10

    Implicit integration factor (IIF) method, a class of efficient semi-implicit temporal scheme, was introduced recently for stiff reaction-diffusion equations. To reduce cost of IIF, compact implicit integration factor (cIIF) method was later developed for efficient storage and calculation of exponential matrices associated with the diffusion operators in two and three spatial dimensions for Cartesian coordinates with regular meshes. Unlike IIF, cIIF cannot be directly extended to other curvilinear coordinates, such as polar and spherical coordinate, due to the compact representation for the diffusion terms in cIIF. In this paper, we present a method to generalize cIIF for other curvilinear coordinates through examples of polar and spherical coordinates. The new cIIF method in polar and spherical coordinates has similar computational efficiency and stability properties as the cIIF in Cartesian coordinate. In addition, we present a method for integrating cIIF with adaptive mesh refinement (AMR) to take advantage of the excellent stability condition for cIIF. Because the second order cIIF is unconditionally stable, it allows large time steps for AMR, unlike a typical explicit temporal scheme whose time step is severely restricted by the smallest mesh size in the entire spatial domain. Finally, we apply those methods to simulating a cell signaling system described by a system of stiff reaction-diffusion equations in both two and three spatial dimensions using AMR, curvilinear and Cartesian coordinates. Excellent performance of the new methods is observed.

  2. PARAMESH: A Parallel, Adaptive Mesh Refinement Toolkit and Performance of the ASCI/FLASH code

    NASA Astrophysics Data System (ADS)

    Olson, K. M.; MacNeice, P.; Fryxell, B.; Ricker, P.; Timmes, F. X.; Zingale, M.

    1999-12-01

    We describe a package of routines known as PARAMESH which enables a user to easily convert an existing serial, uniform grid code to a parallel code with adaptive-mesh refinement. The package does this through the use of a block-structured form of AMR in combination with a tree data structure for distributing blocks to processors. We also describe some of the applications which have been developed using PARAMESH with special emaphasis on the ASCI/FLASH code. Performance results are also discussed for a variety of parallel architectures.

  3. Adaptive Trajectory Prediction Algorithm for Climbing Flights

    NASA Technical Reports Server (NTRS)

    Schultz, Charles Alexander; Thipphavong, David P.; Erzberger, Heinz

    2012-01-01

    Aircraft climb trajectories are difficult to predict, and large errors in these predictions reduce the potential operational benefits of some advanced features for NextGen. The algorithm described in this paper improves climb trajectory prediction accuracy by adjusting trajectory predictions based on observed track data. It utilizes rate-of-climb and airspeed measurements derived from position data to dynamically adjust the aircraft weight modeled for trajectory predictions. In simulations with weight uncertainty, the algorithm is able to adapt to within 3 percent of the actual gross weight within two minutes of the initial adaptation. The root-mean-square of altitude errors for five-minute predictions was reduced by 73 percent. Conflict detection performance also improved, with a 15 percent reduction in missed alerts and a 10 percent reduction in false alerts. In a simulation with climb speed capture intent and weight uncertainty, the algorithm improved climb trajectory prediction accuracy by up to 30 percent and conflict detection performance, reducing missed and false alerts by up to 10 percent.

  4. Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

    NASA Technical Reports Server (NTRS)

    Slack, David C.; Whitaker, D. L.; Walters, Robert W.

    1994-01-01

    Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

  5. Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

    NASA Astrophysics Data System (ADS)

    Slack, David C.; Whitaker, D. L.; Walters, Robert W.

    1994-06-01

    Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

  6. Three-dimensional modeling of a thermal dendrite using the phase field method with automatic anisotropic and unstructured adaptive finite element meshing

    NASA Astrophysics Data System (ADS)

    Sarkis, C.; Silva, L.; Gandin, Ch-A.; Plapp, M.

    2016-03-01

    Dendritic growth is computed with automatic adaptation of an anisotropic and unstructured finite element mesh. The energy conservation equation is formulated for solid and liquid phases considering an interface balance that includes the Gibbs-Thomson effect. An equation for a diffuse interface is also developed by considering a phase field function with constant negative value in the liquid and constant positive value in the solid. Unknowns are the phase field function and a dimensionless temperature, as proposed by [1]. Linear finite element interpolation is used for both variables, and discretization stabilization techniques ensure convergence towards a correct non-oscillating solution. In order to perform quantitative computations of dendritic growth on a large domain, two additional numerical ingredients are necessary: automatic anisotropic unstructured adaptive meshing [2,[3] and parallel implementations [4], both made available with the numerical platform used (CimLib) based on C++ developments. Mesh adaptation is found to greatly reduce the number of degrees of freedom. Results of phase field simulations for dendritic solidification of a pure material in two and three dimensions are shown and compared with reference work [1]. Discussion on algorithm details and the CPU time will be outlined.

  7. Distributed Synchronization Technique for OFDMA-Based Wireless Mesh Networks Using a Bio-Inspired Algorithm

    PubMed Central

    Kim, Mi Jeong; Maeng, Sung Joon; Cho, Yong Soo

    2015-01-01

    In this paper, a distributed synchronization technique based on a bio-inspired algorithm is proposed for an orthogonal frequency division multiple access (OFDMA)-based wireless mesh network (WMN) with a time difference of arrival. The proposed time- and frequency-synchronization technique uses only the signals received from the neighbor nodes, by considering the effect of the propagation delay between the nodes. It achieves a fast synchronization with a relatively low computational complexity because it is operated in a distributed manner, not requiring any feedback channel for the compensation of the propagation delays. In addition, a self-organization scheme that can be effectively used to construct 1-hop neighbor nodes is proposed for an OFDMA-based WMN with a large number of nodes. The performance of the proposed technique is evaluated with regard to the convergence property and synchronization success probability using a computer simulation. PMID:26225974

  8. Distributed Synchronization Technique for OFDMA-Based Wireless Mesh Networks Using a Bio-Inspired Algorithm.

    PubMed

    Kim, Mi Jeong; Maeng, Sung Joon; Cho, Yong Soo

    2015-07-28

    In this paper, a distributed synchronization technique based on a bio-inspired algorithm is proposed for an orthogonal frequency division multiple access (OFDMA)-based wireless mesh network (WMN) with a time difference of arrival. The proposed time- and frequency-synchronization technique uses only the signals received from the neighbor nodes, by considering the effect of the propagation delay between the nodes. It achieves a fast synchronization with a relatively low computational complexity because it is operated in a distributed manner, not requiring any feedback channel for the compensation of the propagation delays. In addition, a self-organization scheme that can be effectively used to construct 1-hop neighbor nodes is proposed for an OFDMA-based WMN with a large number of nodes. The performance of the proposed technique is evaluated with regard to the convergence property and synchronization success probability using a computer simulation.

  9. 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.

  10. Digital adaptation algorithms of adaptive optics corrected images

    NASA Astrophysics Data System (ADS)

    Polskikh, Sergey D.; Sviridov, Konstantin N.

    2000-07-01

    The technology is considered of space object image obtainment with high angular resolution, based on the adaptive tuning of image spatial spectra (digital adaptation), corrected by adaptive optics. As the basis of the technology, the algorithm is taken of the integral equation of the I-st kind of convolution type with unknown core and imprecisely given right part. It's shown the procedure of the inverse operator construction for this equation solution is connected with minimization of nonlinear regularizing multiextremel functionals and could be realized on the base of global optimization methods. The structure of multiextremel functionals is analyzed, and the main global extremum search methods are researched. It is shown, that as the basis of the optimal construction of the channel for the obtainment of images with high resolution, the principle must be taken of the sequential reduction of the global extremum search space dimensionality, and what's more, the predetector processing of the wavefront by the adaptive optics is the first stage of this reduction. The results are given of numerical modelling including the examples of the distorted and restorated images of model objects under different signal-to-noise ratios.

  11. A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries

    SciTech Connect

    Nivarti, Girish V. Salehi, M. Mahdi; Bushe, W. Kendal

    2015-01-15

    Highlights: •An algorithm for partitioning computational meshes is proposed. •The Morton order space-filling curve is modified to achieve improved locality. •A spatial locality metric is defined to compare results with existing approaches. •Results indicate improved performance of the algorithm in complex geometries. -- Abstract: A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton order curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.

  12. Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation

    PubMed Central

    Dione, Ibrahima; Briffard, Thomas; Doyon, Nicolas

    2016-01-01

    In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer. PMID:27548674

  13. Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation.

    PubMed

    Dione, Ibrahima; Deteix, Jean; Briffard, Thomas; Chamberland, Eric; Doyon, Nicolas

    2016-01-01

    In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer.

  14. Parallel grid library with adaptive mesh refinement for development of highly scalable simulations

    NASA Astrophysics Data System (ADS)

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

    2012-04-01

    As the single CPU core performance is saturating while the number of cores in the fastest supercomputers increases exponentially, the parallel performance of simulations on distributed memory machines is crucial. At the same time, utilizing efficiently the large number of available cores presents a challenge, especially in simulations with run-time adaptive mesh refinement. We have developed a generic grid library (dccrg) aimed at finite volume simulations that is easy to use and scales well up to tens of thousands of cores. The grid has several attractive features: It 1) allows an arbitrary C++ class or structure to be used as cell data; 2) provides a simple interface for adaptive mesh refinement during a simulation; 3) encapsulates the details of MPI communication when updating the data of neighboring cells between processes; and 4) provides a simple interface to run-time load balancing, e.g. domain decomposition, through the Zoltan library. Dccrg is freely available for anyone to use, study and modify under the GNU Lesser General Public License v3. We will present the implementation of dccrg, simple and advanced usage examples and scalability results on various supercomputers and problems.

  15. 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.

  16. Fast reconfiguration algorithm of computer generated holograms for adaptive view direction change in holographic three-dimensional display.

    PubMed

    Cho, Jaebum; Hahn, Joonku; Kim, Hwi

    2012-12-17

    Reconfiguration is a computational algorithm of adaptively updating computer generated holograms (CGHs) for the positional change of an observer's viewing window with low computational load by efficiently using pre-calculated elementary CGHs. A fast reconfiguration algorithm of CGHs for three-dimensional mesh objects is proposed. Remarkable improvement is achieved in the computation speed of CGHs, which is at least 20-times faster than repetitive re-computation of CGHs. The image quality of reconfigured CGHs is analyzed.

  17. Multi-dimensional upwind fluctuation splitting scheme with mesh adaption for hypersonic viscous flow

    NASA Astrophysics Data System (ADS)

    Wood, William Alfred, III

    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. A viscous Mach 17.6 (perfect gas) cylinder case demonstrates solution monotonicity and heat transfer capability with the fluctuation splitting scheme. While fluctuation splitting is recommended over DMFDSFV, the difference in performance between the schemes is not so great as to obsolete DMFDSFV. The second half of the dissertation develops a local, compact, anisotropic unstructured mesh adaption scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. This alignment behavior stands in contrast to the curvature clustering nature of the local, anisotropic unstructured adaption strategy based upon a posteriori error estimation that is used for comparison. The characteristic alignment is most pronounced for linear advection, with reduced improvement seen for the more complex non-linear advection and advection-diffusion cases. The adaption strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization. The system test case for the adaption strategy is a sting mounted capsule at Mach-10 wind tunnel conditions, considered in both two-dimensional and axisymmetric configurations. For this complex flowfield the adaption results are disappointing since feature alignment does not emerge from the local operations. Aggressive adaption is shown to result in a loss of robustness for the solver, particularly in the bow shock/stagnation point interaction region. Reducing the adaption strength maintains solution robustness but fails to produce significant improvement in the surface heat transfer predictions.

  18. Synaptic dynamics: linear model and adaptation algorithm.

    PubMed

    Yousefi, Ali; Dibazar, Alireza A; Berger, Theodore W

    2014-08-01

    In this research, temporal processing in brain neural circuitries is addressed by a dynamic model of synaptic connections in which the synapse model accounts for both pre- and post-synaptic processes determining its temporal dynamics and strength. Neurons, which are excited by the post-synaptic potentials of hundred of the synapses, build the computational engine capable of processing dynamic neural stimuli. Temporal dynamics in neural models with dynamic synapses will be analyzed, and learning algorithms for synaptic adaptation of neural networks with hundreds of synaptic connections are proposed. The paper starts by introducing a linear approximate model for the temporal dynamics of synaptic transmission. The proposed linear model substantially simplifies the analysis and training of spiking neural networks. Furthermore, it is capable of replicating the synaptic response of the non-linear facilitation-depression model with an accuracy better than 92.5%. In the second part of the paper, a supervised spike-in-spike-out learning rule for synaptic adaptation in dynamic synapse neural networks (DSNN) is proposed. The proposed learning rule is a biologically plausible process, and it is capable of simultaneously adjusting both pre- and post-synaptic components of individual synapses. The last section of the paper starts with presenting the rigorous analysis of the learning algorithm in a system identification task with hundreds of synaptic connections which confirms the learning algorithm's accuracy, repeatability and scalability. The DSNN is utilized to predict the spiking activity of cortical neurons and pattern recognition tasks. The DSNN model is demonstrated to be a generative model capable of producing different cortical neuron spiking patterns and CA1 Pyramidal neurons recordings. A single-layer DSNN classifier on a benchmark pattern recognition task outperforms a 2-Layer Neural Network and GMM classifiers while having fewer numbers of free parameters and

  19. MLEM algorithm adaptation for improved SPECT scintimammography

    NASA Astrophysics Data System (ADS)

    Krol, Andrzej; Feiglin, David H.; Lee, Wei; Kunniyur, Vikram R.; Gangal, Kedar R.; Coman, Ioana L.; Lipson, Edward D.; Karczewski, Deborah A.; Thomas, F. Deaver

    2005-04-01

    Standard MLEM and OSEM algorithms used in SPECT Tc-99m sestamibi scintimammography produce hot-spot artifacts (HSA) at the image support peripheries. We investigated a suitable adaptation of MLEM and OSEM algorithms needed to reduce HSA. Patients with suspicious breast lesions were administered 10 mCi of Tc-99m sestamibi and SPECT scans were acquired for patients in prone position with uncompressed breasts. In addition, to simulate breast lesions, some patients were imaged with a number of breast skin markers each containing 1 mCi of Tc-99m. In order to reduce HSA in reconstruction, we removed from the backprojection step the rays that traverse the periphery of the support region on the way to a detector bin, when their path length through this region was shorter than some critical length. Such very short paths result in a very low projection counts contributed to the detector bin, and consequently to overestimation of the activity in the peripheral voxels in the backprojection step-thus creating HSA. We analyzed the breast-lesion contrast and suppression of HSA in the images reconstructed using standard and modified MLEM and OSEM algorithms vs. critical path length (CPL). For CPL >= 0.01 pixel size, we observed improved breast-lesion contrast and lower noise in the reconstructed images, and a very significant reduction of HSA in the maximum intensity projection (MIP) images.

  20. Adaptive Hybrid Algorithm for Flow and Transport in Porous Media

    NASA Astrophysics Data System (ADS)

    Yousefzadeh, M.; Battiato, I.

    2016-12-01

    Flow and transport phenomena in the subsurface happen over various scales. Depending on the physics of the problem one has to incorporate all relevant scales. Often the behavior of the system is governed by the phenomena at the pore-scale. Therefore accurate and efficient modeling of any large domain requires simulating parts of it at the pore-scale (i.e., wherein continuum models become invalid) and the rest at the continuum scale. Hybrid models use pore-scale and continuum-scale representations. Desirable features of hybrid models are: 1) their ability to track where and when to use pore-scale models, i.e. their adaptability to time- and space-dependent phenomena, 2) their flexibility in implementing coupling conditions, and 3) computational speed-up when the sub-domain wherein pore-scale simulations are required is much smaller than the total computational domain. Moreover, coupling conditions should be physics-based in order reduce the overall number of assumptions. Another challenge in accurate modeling of the flow and transport in porous media is the complex geometry at the fine-scale (i.e. pore-scale), which calls for a compuationally expensive mesh generation algorithm. A Cartesian algorithm (IBM) for simulating flow and transport in porous media has been developed and utilized. We propose a general, robust and non-intrusive hybrid model based on IBM to model flow and reactive transport in porous media. To evaluate the flexibility of the hybrid algorithm numerical implementation has been carried out for several passive and reactive transport and flow scenarios.

  1. A novel survivable traffic grooming algorithm with inter-layer sharing in IP/MPLS-over-WDM mesh networks

    NASA Astrophysics Data System (ADS)

    Gong, Dayue; Zhang, Xiaoning; Yu, Hongfang; Ling, Ximo; Liao, Dan; Luo, Hongbin

    2009-11-01

    We propose a Mixed Sharing Auxiliary Graph (MSAG) for dynamic traffic grooming in heterogeneous WDM mesh networks. Based on MSAG model, a novel heuristic named BLSW-ILMS (Backup LSP Shared Working Lightpath with Inter-layer Mixed Sharing) is proposed. Simulation results show that the proposed algorithm can efficiently decrease the blocking probability.

  2. An Adaptive Path Planning Algorithm for Cooperating Unmanned Air Vehicles

    SciTech Connect

    Cunningham, C.T.; Roberts, R.S.

    2000-09-12

    An adaptive path planning algorithm is presented for cooperating Unmanned Air Vehicles (UAVs) that are used to deploy and operate land-based sensor networks. The algorithm employs a global cost function to generate paths for the UAVs, and adapts the paths to exceptions that might occur. Examples are provided of the paths and adaptation.

  3. Adaptive path planning algorithm for cooperating unmanned air vehicles

    SciTech Connect

    Cunningham, C T; Roberts, R S

    2001-02-08

    An adaptive path planning algorithm is presented for cooperating Unmanned Air Vehicles (UAVs) that are used to deploy and operate land-based sensor networks. The algorithm employs a global cost function to generate paths for the UAVs, and adapts the paths to exceptions that might occur. Examples are provided of the paths and adaptation.

  4. Modeling, mesh generation and adaptive numerical methods for partial differential equations: IMA summer program. Final report, April 1, 1993--March 31, 1994

    SciTech Connect

    Friedman, A.; Miller, W. Jr.

    1993-12-31

    The program was divided into segments: (Week 1) geometric modeling and mesh generation (Weeks 2 and 3) error estimation and adaptive strategies. Participants in the program came from a wide variety of disciplines dealing with remarkably analogous problems in this area. Ideas were exchanged and interdisciplinary collaboration was initiated in informal contexts as well as in the talks and question periods. In the talks, a number of algorithms were described along with specific applications to problems of great current interest in various scientific and engineering disciplines. In this emerging field, participants developed criteria for evaluation of algorithms and established guidelines for selection of algorithms appropriate to any specific problem. Special features of a problem may include curved surfaces, complicated boundaries, evolving interfaces (such as occur in coating flows), and/or criticality of error estimation.

  5. Generalized Framework and Algorithms for Illustrative Visualization of Time-Varying Data on Unstructured Meshes

    SciTech Connect

    Alexander S. Rattner; Donna Post Guillen; Alark Joshi

    2012-12-01

    Photo- and physically-realistic techniques are often insufficient for visualization of simulation results, especially for 3D and time-varying datasets. Substantial research efforts have been dedicated to the development of non-photorealistic and illustration-inspired visualization techniques for compact and intuitive presentation of such complex datasets. While these efforts have yielded valuable visualization results, a great deal of work has been reproduced in studies as individual research groups often develop purpose-built platforms. Additionally, interoperability between illustrative visualization software is limited due to specialized processing and rendering architectures employed in different studies. In this investigation, a generalized framework for illustrative visualization is proposed, and implemented in marmotViz, a ParaView plugin, enabling its use on variety of computing platforms with various data file formats and mesh geometries. Detailed descriptions of the region-of-interest identification and feature-tracking algorithms incorporated into this tool are provided. Additionally, implementations of multiple illustrative effect algorithms are presented to demonstrate the use and flexibility of this framework. By providing a framework and useful underlying functionality, the marmotViz tool can act as a springboard for future research in the field of illustrative visualization.

  6. Minimum Interference Channel Assignment Algorithm for Multicast in a Wireless Mesh Network

    PubMed Central

    Choi, Sangil; Park, Jong Hyuk

    2016-01-01

    Wireless mesh networks (WMNs) have been considered as one of the key technologies for the configuration of wireless machines since they emerged. In a WMN, wireless routers provide multi-hop wireless connectivity between hosts in the network and also allow them to access the Internet via gateway devices. Wireless routers are typically equipped with multiple radios operating on different channels to increase network throughput. Multicast is a form of communication that delivers data from a source to a set of destinations simultaneously. It is used in a number of applications, such as distributed games, distance education, and video conferencing. In this study, we address a channel assignment problem for multicast in multi-radio multi-channel WMNs. In a multi-radio multi-channel WMN, two nearby nodes will interfere with each other and cause a throughput decrease when they transmit on the same channel. Thus, an important goal for multicast channel assignment is to reduce the interference among networked devices. We have developed a minimum interference channel assignment (MICA) algorithm for multicast that accurately models the interference relationship between pairs of multicast tree nodes using the concept of the interference factor and assigns channels to tree nodes to minimize interference within the multicast tree. Simulation results show that MICA achieves higher throughput and lower end-to-end packet delay compared with an existing channel assignment algorithm named multi-channel multicast (MCM). In addition, MICA achieves much lower throughput variation among the destination nodes than MCM. PMID:27918438

  7. Framework and algorithms for illustrative visualizations of time-varying flows on unstructured meshes

    SciTech Connect

    Rattner, Alexander S.; Guillen, Donna Post; Joshi, Alark; Garimella, Srinivas

    2016-03-17

    Photo- and physically realistic techniques are often insufficient for visualization of fluid flow simulations, especially for 3D and time-varying studies. Substantial research effort has been dedicated to the development of non-photorealistic and illustration-inspired visualization techniques for compact and intuitive presentation of such complex datasets. However, a great deal of work has been reproduced in this field, as many research groups have developed specialized visualization software. Additionally, interoperability between illustrative visualization software is limited due to diverse processing and rendering architectures employed in different studies. In this investigation, a framework for illustrative visualization is proposed, and implemented in MarmotViz, a ParaView plug-in, enabling its use on a variety of computing platforms with various data file formats and mesh geometries. Region-of-interest identification and feature-tracking algorithms incorporated into this tool are described. Implementations of multiple illustrative effect algorithms are also presented to demonstrate the use and flexibility of this framework. Here, by providing an integrated framework for illustrative visualization of CFD data, MarmotViz can serve as a valuable asset for the interpretation of simulations of ever-growing scale.

  8. Minimum Interference Channel Assignment Algorithm for Multicast in a Wireless Mesh Network.

    PubMed

    Choi, Sangil; Park, Jong Hyuk

    2016-12-02

    Wireless mesh networks (WMNs) have been considered as one of the key technologies for the configuration of wireless machines since they emerged. In a WMN, wireless routers provide multi-hop wireless connectivity between hosts in the network and also allow them to access the Internet via gateway devices. Wireless routers are typically equipped with multiple radios operating on different channels to increase network throughput. Multicast is a form of communication that delivers data from a source to a set of destinations simultaneously. It is used in a number of applications, such as distributed games, distance education, and video conferencing. In this study, we address a channel assignment problem for multicast in multi-radio multi-channel WMNs. In a multi-radio multi-channel WMN, two nearby nodes will interfere with each other and cause a throughput decrease when they transmit on the same channel. Thus, an important goal for multicast channel assignment is to reduce the interference among networked devices. We have developed a minimum interference channel assignment (MICA) algorithm for multicast that accurately models the interference relationship between pairs of multicast tree nodes using the concept of the interference factor and assigns channels to tree nodes to minimize interference within the multicast tree. Simulation results show that MICA achieves higher throughput and lower end-to-end packet delay compared with an existing channel assignment algorithm named multi-channel multicast (MCM). In addition, MICA achieves much lower throughput variation among the destination nodes than MCM.

  9. Framework and algorithms for illustrative visualizations of time-varying flows on unstructured meshes

    DOE PAGES

    Rattner, Alexander S.; Guillen, Donna Post; Joshi, Alark; ...

    2016-03-17

    Photo- and physically realistic techniques are often insufficient for visualization of fluid flow simulations, especially for 3D and time-varying studies. Substantial research effort has been dedicated to the development of non-photorealistic and illustration-inspired visualization techniques for compact and intuitive presentation of such complex datasets. However, a great deal of work has been reproduced in this field, as many research groups have developed specialized visualization software. Additionally, interoperability between illustrative visualization software is limited due to diverse processing and rendering architectures employed in different studies. In this investigation, a framework for illustrative visualization is proposed, and implemented in MarmotViz, a ParaViewmore » plug-in, enabling its use on a variety of computing platforms with various data file formats and mesh geometries. Region-of-interest identification and feature-tracking algorithms incorporated into this tool are described. Implementations of multiple illustrative effect algorithms are also presented to demonstrate the use and flexibility of this framework. Here, by providing an integrated framework for illustrative visualization of CFD data, MarmotViz can serve as a valuable asset for the interpretation of simulations of ever-growing scale.« less

  10. Scalable and Adaptive Streaming of 3D Mesh to Heterogeneous Devices

    NASA Astrophysics Data System (ADS)

    Abderrahim, Zeineb; Bouhlel, Mohamed Salim

    2016-12-01

    This article comprises a presentation of a web platform for the diffusion and visualization of 3D compressed data on the web. Indeed, the major goal of this work resides in the proposal of the transfer adaptation of the three-dimensional data to resources (network bandwidth, the type of visualization terminals, display resolution, user's preferences...). Also, it is an attempt to provide an effective consultation adapted to the user's request (preferences, levels of the requested detail, etc.). Such a platform can adapt the levels of detail to the change in the bandwidth and the rendering time when loading the mesh at the client level. In addition, the levels of detail are adapted to the distance between the object and the camera. These features are able to minimize the latency time and to make the real time interaction possible. The experiences as well as the comparison with the existing solutions show auspicious results in terms of latency, scalability and the quality of the experience offered to the users.

  11. Adaptive mesh refinement versus subgrid friction interpolation in simulations of Antarctic ice dynamics

    SciTech Connect

    Cornford, S. L.; Martin, D. F.; Lee, V.; Payne, A. J.; Ng, E. G.

    2016-05-13

    At least in conventional hydrostatic ice-sheet models, the numerical error associated with grounding line dynamics can be reduced by modifications to the discretization scheme. These involve altering the integration formulae for the basal traction and/or driving stress close to the grounding line and exhibit lower – if still first-order – error in the MISMIP3d experiments. MISMIP3d may not represent the variety of real ice streams, in that it lacks strong lateral stresses, and imposes a large basal traction at the grounding line. We study resolution sensitivity in the context of extreme forcing simulations of the entire Antarctic ice sheet, using the BISICLES adaptive mesh ice-sheet model with two schemes: the original treatment, and a scheme, which modifies the discretization of the basal traction. The second scheme does indeed improve accuracy – by around a factor of two – for a given mesh spacing, but $\\lesssim 1$ km resolution is still necessary. For example, in coarser resolution simulations Thwaites Glacier retreats so slowly that other ice streams divert its trunk. In contrast, with $\\lesssim 1$ km meshes, the same glacier retreats far more quickly and triggers the final phase of West Antarctic collapse a century before any such diversion can take place.

  12. 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.

  13. A versatile embedded boundary adaptive mesh method for compressible flow in complex geometry

    NASA Astrophysics Data System (ADS)

    Al-Marouf, M.; Samtaney, R.

    2017-05-01

    We present an embedded ghost fluid method for numerical solutions of the compressible Navier Stokes (CNS) equations in arbitrary complex domains. A PDE multidimensional extrapolation approach is used to reconstruct the solution in the ghost fluid regions and imposing boundary conditions on the fluid-solid interface, coupled with a multi-dimensional algebraic interpolation for freshly cleared cells. The CNS equations are numerically solved by the second order multidimensional upwind method. Block-structured adaptive mesh refinement, implemented with the Chombo framework, is utilized to reduce the computational cost while keeping high resolution mesh around the embedded boundary and regions of high gradient solutions. The versatility of the method is demonstrated via several numerical examples, in both static and moving geometry, ranging from low Mach number nearly incompressible flows to supersonic flows. Our simulation results are extensively verified against other numerical results and validated against available experimental results where applicable. The significance and advantages of our implementation, which revolve around balancing between the solution accuracy and implementation difficulties, are briefly discussed as well.

  14. WHITE DWARF MERGERS ON ADAPTIVE MESHES. I. METHODOLOGY AND CODE VERIFICATION

    SciTech Connect

    Katz, Max P.; Zingale, Michael; Calder, Alan C.; Swesty, F. Douglas; Almgren, Ann S.; Zhang, Weiqun

    2016-03-10

    The Type Ia supernova (SN Ia) progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf (WD) merger scenario, which has the potential to naturally explain many of the observed characteristics of SNe Ia. To date there have been relatively few self-consistent simulations of merging WD systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.

  15. White Dwarf Mergers on Adaptive Meshes. I. Methodology and Code Verification

    NASA Astrophysics Data System (ADS)

    Katz, Max P.; Zingale, Michael; Calder, Alan C.; Swesty, F. Douglas; Almgren, Ann S.; Zhang, Weiqun

    2016-03-01

    The Type Ia supernova (SN Ia) progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf (WD) merger scenario, which has the potential to naturally explain many of the observed characteristics of SNe Ia. To date there have been relatively few self-consistent simulations of merging WD systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.

  16. 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.

  17. A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers

    NASA Astrophysics Data System (ADS)

    Saintillan, David; Darve, Eric; Shaqfeh, Eric S. G.

    2005-03-01

    Large-scale simulations of non-Brownian rigid fibers sedimenting under gravity at zero Reynolds number have been performed using a fast algorithm. The mathematical formulation follows the previous simulations by Butler and Shaqfeh ["Dynamic simulations of the inhomogeneous sedimentation of rigid fibres," J. Fluid Mech. 468, 205 (2002)]. The motion of the fibers is described using slender-body theory, and the line distribution of point forces along their lengths is approximated by a Legendre polynomial in which only the total force, torque, and particle stresslet are retained. Periodic boundary conditions are used to simulate an infinite suspension, and both far-field hydrodynamic interactions and short-range lubrication forces are considered in all simulations. The calculation of the hydrodynamic interactions, which is typically the bottleneck for large systems with periodic boundary conditions, is accelerated using a smooth particle-mesh Ewald (SPME) algorithm previously used in molecular dynamics simulations. In SPME the slowly decaying Green's function is split into two fast-converging sums: the first involves the distribution of point forces and accounts for the singular short-range part of the interactions, while the second is expressed in terms of the Fourier transform of the force distribution and accounts for the smooth and long-range part. Because of its smoothness, the second sum can be computed efficiently on an underlying grid using the fast Fourier transform algorithm, resulting in a significant speed-up of the calculations. Systems of up to 512 fibers were simulated on a single-processor workstation, providing a different insight into the formation, structure, and dynamics of the inhomogeneities that occur in sedimenting fiber suspensions.

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

    DOE PAGES

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

    2017-07-08

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

  19. An Optimal Pull-Push Scheduling Algorithm Based on Network Coding for Mesh Peer-to-Peer Live Streaming

    NASA Astrophysics Data System (ADS)

    Cui, Laizhong; Jiang, Yong; Wu, Jianping; Xia, Shutao

    Most large-scale Peer-to-Peer (P2P) live streaming systems are constructed as a mesh structure, which can provide robustness in the dynamic P2P environment. The pull scheduling algorithm is widely used in this mesh structure, which degrades the performance of the entire system. Recently, network coding was introduced in mesh P2P streaming systems to improve the performance, which makes the push strategy feasible. One of the most famous scheduling algorithms based on network coding is R2, with a random push strategy. Although R2 has achieved some success, the push scheduling strategy still lacks a theoretical model and optimal solution. In this paper, we propose a novel optimal pull-push scheduling algorithm based on network coding, which consists of two stages: the initial pull stage and the push stage. The main contributions of this paper are: 1) we put forward a theoretical analysis model that considers the scarcity and timeliness of segments; 2) we formulate the push scheduling problem to be a global optimization problem and decompose it into local optimization problems on individual peers; 3) we introduce some rules to transform the local optimization problem into a classical min-cost optimization problem for solving it; 4) We combine the pull strategy with the push strategy and systematically realize our scheduling algorithm. Simulation results demonstrate that decode delay, decode ratio and redundant fraction of the P2P streaming system with our algorithm can be significantly improved, without losing throughput and increasing overhead.

  20. On the Computation of Integral Curves in Adaptive Mesh Refinement Vector Fields

    SciTech Connect

    Deines, Eduard; Weber, Gunther H.; Garth, Christoph; Van Straalen, Brian; Borovikov, Sergey; Martin, Daniel F.; Joy, Kenneth I.

    2011-06-27

    Integral curves, such as streamlines, streaklines, pathlines, and timelines, are an essential tool in the analysis of vector field structures, offering straightforward and intuitive interpretation of visualization results. While such curves have a long-standing tradition in vector field visualization, their application to Adaptive Mesh Refinement (AMR) simulation results poses unique problems. AMR is a highly effective discretization method for a variety of physical simulation problems and has recently been applied to the study of vector fields in flow and magnetohydrodynamic applications. The cell-centered nature of AMR data and discontinuities in the vector field representation arising from AMR level boundaries complicate the application of numerical integration methods to compute integral curves. In this paper, we propose a novel approach to alleviate these problems and show its application to streamline visualization in an AMR model of the magnetic field of the solar system as well as to a simulation of two incompressible viscous vortex rings merging.

  1. 3D Adaptive Mesh Refinement Simulations of Pellet Injection in Tokamaks

    SciTech Connect

    R. Samtaney; S.C. Jardin; P. Colella; D.F. Martin

    2003-10-20

    We present results of Adaptive Mesh Refinement (AMR) simulations of the pellet injection process, a proven method of refueling tokamaks. AMR is a computationally efficient way to provide the resolution required to simulate realistic pellet sizes relative to device dimensions. The mathematical model comprises of single-fluid MHD equations with source terms in the continuity equation along with a pellet ablation rate model. The numerical method developed is an explicit unsplit upwinding treatment of the 8-wave formulation, coupled with a MAC projection method to enforce the solenoidal property of the magnetic field. The Chombo framework is used for AMR. The role of the E x B drift in mass redistribution during inside and outside pellet injections is emphasized.

  2. Dynamic Implicit 3D Adaptive Mesh Refinement for Non-Equilibrium Radiation Diffusion

    SciTech Connect

    Philip, Bobby; Wang, Zhen; Berrill, Mark A; Rodriguez Rodriguez, Manuel; Pernice, Michael

    2014-01-01

    The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multiphysics systems: implicit time integration for efficient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent linear solver convergence.

  3. A GPU implementation of adaptive mesh refinement to simulate tsunamis generated by landslides

    NASA Astrophysics Data System (ADS)

    de la Asunción, Marc; Castro, Manuel J.

    2016-04-01

    In this work we propose a CUDA implementation for the simulation of landslide-generated tsunamis using a two-layer Savage-Hutter type model and adaptive mesh refinement (AMR). The AMR method consists of dynamically increasing the spatial resolution of the regions of interest of the domain while keeping the rest of the domain at low resolution, thus obtaining better runtimes and similar results compared to increasing the spatial resolution of the entire domain. Our AMR implementation uses a patch-based approach, it supports up to three levels, power-of-two ratios of refinement, different refinement criteria and also several user parameters to control the refinement and clustering behaviour. A strategy based on the variation of the cell values during the simulation is used to interpolate and propagate the values of the fine cells. Several numerical experiments using artificial and realistic scenarios are presented.

  4. Detached Eddy Simulation of the UH-60 Rotor Wake Using Adaptive Mesh Refinement

    NASA Technical Reports Server (NTRS)

    Chaderjian, Neal M.; Ahmad, Jasim U.

    2012-01-01

    Time-dependent Navier-Stokes flow simulations have been carried out for a UH-60 rotor with simplified hub in forward flight and hover flight conditions. Flexible rotor blades and flight trim conditions are modeled and established by loosely coupling the OVERFLOW Computational Fluid Dynamics (CFD) code with the CAMRAD II helicopter comprehensive code. High order spatial differences, Adaptive Mesh Refinement (AMR), and Detached Eddy Simulation (DES) are used to obtain highly resolved vortex wakes, where the largest turbulent structures are captured. Special attention is directed towards ensuring the dual time accuracy is within the asymptotic range, and verifying the loose coupling convergence process using AMR. The AMR/DES simulation produced vortical worms for forward flight and hover conditions, similar to previous results obtained for the TRAM rotor in hover. AMR proved to be an efficient means to capture a rotor wake without a priori knowledge of the wake shape.

  5. Galaxy Mergers with Adaptive Mesh Refinement: Star Formation and Hot Gas Outflow

    SciTech Connect

    Kim, Ji-hoon; Wise, John H.; Abel, Tom; /KIPAC, Menlo Park /Stanford U., Phys. Dept.

    2011-06-22

    In hierarchical structure formation, merging of galaxies is frequent and known to dramatically affect their properties. To comprehend these interactions high-resolution simulations are indispensable because of the nonlinear coupling between pc and Mpc scales. To this end, we present the first adaptive mesh refinement (AMR) simulation of two merging, low mass, initially gas-rich galaxies (1.8 x 10{sup 10} M{sub {circle_dot}} each), including star formation and feedback. With galaxies resolved by {approx} 2 x 10{sup 7} total computational elements, we achieve unprecedented resolution of the multiphase interstellar medium, finding a widespread starburst in the merging galaxies via shock-induced star formation. The high dynamic range of AMR also allows us to follow the interplay between the galaxies and their embedding medium depicting how galactic outflows and a hot metal-rich halo form. These results demonstrate that AMR provides a powerful tool in understanding interacting galaxies.

  6. Adaptive RED algorithm based on minority game

    NASA Astrophysics Data System (ADS)

    Wei, Jiaolong; Lei, Ling; Qian, Jingjing

    2007-11-01

    With more and more applications appearing and the technology developing in the Internet, only relying on terminal system can not satisfy the complicated demand of QoS network. Router mechanisms must be participated into protecting responsive flows from the non-responsive. Routers mainly use active queue management mechanism (AQM) to avoid congestion. In the point of interaction between the routers, the paper applies minority game to describe the interaction of the users and observes the affection on the length of average queue. The parameters α, β of ARED being hard to confirm, adaptive RED based on minority game can depict the interactions of main body and amend the parameter α, β of ARED to the best. Adaptive RED based on minority game optimizes ARED and realizes the smoothness of average queue length. At the same time, this paper extends the network simulator plat - NS by adding new elements. Simulation has been implemented and the results show that new algorithm can reach the anticipative objects.

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

    NASA Astrophysics Data System (ADS)

    Hu, Zixi; Yao, Zhewei; Li, Jinglai

    2017-03-01

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

  8. A Parallel Ocean Model With Adaptive Mesh Refinement Capability For Global Ocean Prediction

    SciTech Connect

    Herrnstein, Aaron R.

    2005-12-01

    An ocean model with adaptive mesh refinement (AMR) capability is presented for simulating ocean circulation on decade time scales. The model closely resembles the LLNL ocean general circulation model with some components incorporated from other well known ocean models when appropriate. Spatial components are discretized using finite differences on a staggered grid where tracer and pressure variables are defined at cell centers and velocities at cell vertices (B-grid). Horizontal motion is modeled explicitly with leapfrog and Euler forward-backward time integration, and vertical motion is modeled semi-implicitly. New AMR strategies are presented for horizontal refinement on a B-grid, leapfrog time integration, and time integration of coupled systems with unequal time steps. These AMR capabilities are added to the LLNL software package SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) and validated with standard benchmark tests. The ocean model is built on top of the amended SAMRAI library. The resulting model has the capability to dynamically increase resolution in localized areas of the domain. Limited basin tests are conducted using various refinement criteria and produce convergence trends in the model solution as refinement is increased. Carbon sequestration simulations are performed on decade time scales in domains the size of the North Atlantic and the global ocean. A suggestion is given for refinement criteria in such simulations. AMR predicts maximum pH changes and increases in CO2 concentration near the injection sites that are virtually unattainable with a uniform high resolution due to extremely long run times. Fine scale details near the injection sites are achieved by AMR with shorter run times than the finest uniform resolution tested despite the need for enhanced parallel performance. The North Atlantic simulations show a reduction in passive tracer errors when AMR is applied instead of a uniform coarse resolution. No

  9. Multiphase flow modelling of explosive volcanic eruptions using adaptive unstructured meshes

    NASA Astrophysics Data System (ADS)

    Jacobs, Christian T.; Collins, Gareth S.; Piggott, Matthew D.; Kramer, Stephan C.

    2014-05-01

    Explosive volcanic eruptions generate highly energetic plumes of hot gas and ash particles that produce diagnostic deposits and pose an extreme environmental hazard. The formation, dispersion and collapse of these volcanic plumes are complex multiscale processes that are extremely challenging to simulate numerically. Accurate description of particle and droplet aggregation, movement and settling requires a model capable of capturing the dynamics on a range of scales (from cm to km) and a model that can correctly describe the important multiphase interactions that take place. However, even the most advanced models of eruption dynamics to date are restricted by the fixed mesh-based approaches that they employ. The research presented herein describes the development of a compressible multiphase flow model within Fluidity, a combined finite element / control volume computational fluid dynamics (CFD) code, for the study of explosive volcanic eruptions. Fluidity adopts a state-of-the-art adaptive unstructured mesh-based approach to discretise the domain and focus numerical resolution only in areas important to the dynamics, while decreasing resolution where it is not needed as a simulation progresses. This allows the accurate but economical representation of the flow dynamics throughout time, and potentially allows large multi-scale problems to become tractable in complex 3D domains. The multiphase flow model is verified with the method of manufactured solutions, and validated by simulating published gas-solid shock tube experiments and comparing the numerical results against pressure gauge data. The application of the model considers an idealised 7 km by 7 km domain in which the violent eruption of hot gas and volcanic ash high into the atmosphere is simulated. Although the simulations do not correspond to a particular eruption case study, the key flow features observed in a typical explosive eruption event are successfully captured. These include a shock wave resulting

  10. Stabilized Conservative Level Set Method with Adaptive Wavelet-based Mesh Refinement

    NASA Astrophysics Data System (ADS)

    Shervani-Tabar, Navid; Vasilyev, Oleg V.

    2016-11-01

    This paper addresses one of the main challenges of the conservative level set method, namely the ill-conditioned behavior of the normal vector away from the interface. An alternative formulation for reconstruction of the interface is proposed. Unlike the commonly used methods which rely on the unit normal vector, Stabilized Conservative Level Set (SCLS) uses a modified renormalization vector with diminishing magnitude away from the interface. With the new formulation, in the vicinity of the interface the reinitialization procedure utilizes compressive flux and diffusive terms only in the normal direction to the interface, thus, preserving the conservative level set properties, while away from the interfaces the directional diffusion mechanism automatically switches to homogeneous diffusion. The proposed formulation is robust and general. It is especially well suited for use with adaptive mesh refinement (AMR) approaches due to need for a finer resolution in the vicinity of the interface in comparison with the rest of the domain. All of the results were obtained using the Adaptive Wavelet Collocation Method, a general AMR-type method, which utilizes wavelet decomposition to adapt on steep gradients in the solution while retaining a predetermined order of accuracy.

  11. THE PLUTO CODE FOR ADAPTIVE MESH COMPUTATIONS IN ASTROPHYSICAL FLUID DYNAMICS

    SciTech Connect

    Mignone, A.; Tzeferacos, P.; Zanni, C.; Bodo, G.; Van Straalen, B.; Colella, P.

    2012-01-01

    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, 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.

  12. The PLUTO Code for Adaptive Mesh Computations in Astrophysical Fluid Dynamics

    NASA Astrophysics Data System (ADS)

    Mignone, A.; Zanni, C.; Tzeferacos, P.; van Straalen, B.; Colella, P.; Bodo, G.

    2012-01-01

    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, 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.

  13. Adaptive Mesh Refinement With Spectral Accuracy for Magnetohydrodynamics in Two Space Dimensions

    NASA Astrophysics Data System (ADS)

    Rosenberg, D.; Pouquet, A.; Mininni, P.

    2006-12-01

    We examine the effect of accuracy of high-order adaptive mesh refinement (AMR) in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called Orszag-Tang vortex made up of a magnetic X-point centered on a stagnation point of the velocity. A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code is applied to simulate this problem. The MHD solver is explicit, and uses the Elsasser formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described elsewhere [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] in the fluid context, allowing both statically refined and dynamically refined grids. Comparisons with pseudo-spectral computations are performed. Refinement and coarsening criteria are examined, and several tests are described. We show that low-order truncation--even with a comparable number of global degrees of freedom--fails to correctly model some strong (inf-norm) quantities in this problem, even though it satisfies adequately the weak (integrated) balance diagnostics.

  14. Development of a scalable gas-dynamics solver with adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Korkut, Burak

    There are various computational physics areas in which Direct Simulation Monte Carlo (DSMC) and Particle in Cell (PIC) methods are being employed. The accuracy of results from such simulations depend on the fidelity of the physical models being used. The computationally demanding nature of these problems make them ideal candidates to make use of modern supercomputers. The software developed to run such simulations also needs special attention so that the maintainability and extendability is considered with the recent numerical methods and programming paradigms. Suited for gas-dynamics problems, a software called SUGAR (Scalable Unstructured Gas dynamics with Adaptive mesh Refinement) has recently been developed and written in C++ and MPI. Physical and numerical models were added to this framework to simulate ion thruster plumes. SUGAR is used to model the charge-exchange (CEX) reactions occurring between the neutral and ion species as well as the induced electric field effect due to ions. Multiple adaptive mesh refinement (AMR) meshes were used in order to capture different physical length scales present in the flow. A multiple-thruster configuration was run to extend the studies to cases for which there is no axial or radial symmetry present that could only be modeled with a three-dimensional simulation capability. The combined plume structure showed interactions between individual thrusters where AMR capability captured this in an automated way. The back flow for ions was found to occur when CEX and momentum-exchange (MEX) collisions are present and strongly enhanced when the induced electric field is considered. The ion energy distributions in the back flow region were obtained and it was found that the inclusion of the electric field modeling is the most important factor in determining its shape. The plume back flow structure was also examined for a triple-thruster, 3-D geometry case and it was found that the ion velocity in the back flow region appears to be

  15. Fast precalculated triangular mesh algorithm for 3D binary computer-generated holograms.

    PubMed

    Yang, Fan; Kaczorowski, Andrzej; Wilkinson, Tim D

    2014-12-10

    A new method for constructing computer-generated holograms using a precalculated triangular mesh is presented. The speed of calculation can be increased dramatically by exploiting both the precalculated base triangle and GPU parallel computing. Unlike algorithms using point-based sources, this method can reconstruct a more vivid 3D object instead of a "hollow image." In addition, there is no need to do a fast Fourier transform for each 3D element every time. A ferroelectric liquid crystal spatial light modulator is used to display the binary hologram within our experiment and the hologram of a base right triangle is produced by utilizing just a one-step Fourier transform in the 2D case, which can be expanded to the 3D case by multiplying by a suitable Fresnel phase plane. All 3D holograms generated in this paper are based on Fresnel propagation; thus, the Fresnel plane is treated as a vital element in producing the hologram. A GeForce GTX 770 graphics card with 2 GB memory is used to achieve parallel computing.

  16. Adaptive segment protection algorithm of multicast on WDM networks against single link failure

    NASA Astrophysics Data System (ADS)

    Lu, Cai; Nie, Xiaoyan; Wang, Sheng; Li, Lemin

    2005-11-01

    This paper investigates the problem of protecting multicast sessions in mesh WDM (wavelength-division multiplexing) networks against single link failures, e.g., a fiber cut in optical networks. Firstly, we study the two characters of multicast sessions in mesh WDM networks with sparse light splitters configuration. Traditionally, a multicast tree does not contain any circles. The first character is that the multicast tree has better performances if it contains some circles. What is more, a multicast tree has several branches. If we add a path between the leaves nodes on different branches, the segment between them on multicast tree is protected. Based the two characters, the survivable multicast sessions routing problem is formulated into an Integer Linear Programming (ILP). Then a heuristic algorithm, named adaptive shared segment protection (ASSP) algorithm, is proposed for multicast session. ASSP algorithm does not identify the segment for multicast tree previously. The segments are determined during the process of algorithm according to the multicast tree and the sparse networks resource. Comparisons are made between ASSP and other two reported schemes link disjoint trees (LDT) and shared disjoint paths (SDP) in terms of blocking probability and resource cost on USNET topology. Simulations show that ASSP algorithm has better performances than other existing schemes.

  17. Consistent properties reconstruction on adaptive Cartesian meshes for complex fluids computations

    SciTech Connect

    Xia, Guoping . E-mail: xiag@purdue.edu; Li, Ding; Merkle, Charles L.

    2007-07-01

    An efficient reconstruction procedure for evaluating the constitutive properties of a complex fluid from general or specialized thermodynamic databases is presented. Properties and their pertinent derivatives are evaluated by means of an adaptive Cartesian mesh in the thermodynamic plane that provides user-specified accuracy over any selected domain. The Cartesian grid produces a binary tree data structure whose search efficiency is competitive with that for an equally spaced table or with simple equations of state such as a perfect gas. Reconstruction is accomplished on a triangular subdivision of the 2D Cartesian mesh that ensures function continuity across cell boundaries in equally and unequally spaced portions of the table to C {sup 0}, C {sup 1} or C {sup 2} levels. The C {sup 0} and C {sup 1} reconstructions fit the equation of state and enthalpy relations separately, while the C {sup 2} reconstruction fits the Helmholtz or Gibbs function enabling EOS/enthalpy consistency also. All three reconstruction levels appear effective for CFD solutions obtained to date. The efficiency of the method is demonstrated through storage and data retrieval examples for air, water and carbon dioxide. The time required for property evaluations is approximately two orders of magnitude faster with the reconstruction procedure than with the complete thermodynamic equations resulting in estimated 3D CFD savings of from 30 to 60. Storage requirements are modest for today's computers, with the C {sup 1} method requiring slightly less storage than those for the C {sup 0} and C {sup 2} reconstructions when the same accuracy is specified. Sample fluid dynamic calculations based upon the procedure show that the C {sup 1} and C {sup 2} methods are approximately a factor of two slower than the C {sup 0} method but that the reconstruction procedure enables arbitrary fluid CFD calculations that are as efficient as those for a perfect gas or an incompressible fluid for all three accuracy

  18. Space-time mesh adaptation for solute transport in randomly heterogeneous porous media.

    PubMed

    Dell'Oca, Aronne; Porta, Giovanni Michele; Guadagnini, Alberto; Riva, Monica

    2017-07-05

    We assess the impact of an anisotropic space and time grid adaptation technique on our ability to solve numerically solute transport in heterogeneous porous media. Heterogeneity is characterized in terms of the spatial distribution of hydraulic conductivity, whose natural logarithm, Y, is treated as a second-order stationary random process. We consider nonreactive transport of dissolved chemicals to be governed by an Advection Dispersion Equation at the continuum scale. The flow field, which provides the advective component of transport, is obtained through the numerical solution of Darcy's law. A suitable recovery-based error estimator is analyzed to guide the adaptive discretization. We investigate two diverse strategies guiding the (space-time) anisotropic mesh adaptation. These are respectively grounded on the definition of the guiding error estimator through the spatial gradients of: (i) the concentration field only; (ii) both concentration and velocity components. We test the approach for two-dimensional computational scenarios with moderate and high levels of heterogeneity, the latter being expressed in terms of the variance of Y. As quantities of interest, we key our analysis towards the time evolution of section-averaged and point-wise solute breakthrough curves, second centered spatial moment of concentration, and scalar dissipation rate. As a reference against which we test our results, we consider corresponding solutions associated with uniform space-time grids whose level of refinement is established through a detailed convergence study. We find a satisfactory comparison between results for the adaptive methodologies and such reference solutions, our adaptive technique being associated with a markedly reduced computational cost. Comparison of the two adaptive strategies tested suggests that: (i) defining the error estimator relying solely on concentration fields yields some advantages in grasping the key features of solute transport taking place within

  19. A finite-element mesh generator based on growing neural networks.

    PubMed

    Triantafyllidis, D G; Labridis, D P

    2002-01-01

    A mesh generator for the production of high-quality finite-element meshes is being proposed. The mesh generator uses an artificial neural network, which grows during the training process in order to adapt itself to a prespecified probability distribution. The initial mesh is a constrained Delaunay triangulation of the domain to be triangulated. Two new algorithms to accelerate the location of the best matching unit are introduced. The mesh generator has been found able to produce meshes of high quality in a number of classic cases examined and is highly suited for problems where the mesh density vector can be calculated in advance.

  20. Adaptive Harris corner detection algorithm based on iterative threshold

    NASA Astrophysics Data System (ADS)

    Wang, Zhicheng; Li, Rong; Shao, Zhihao; Ma, Mengxin; Liang, Jianhui; Liu, Weizhao; Wang, Jie; Liu, Yongli

    2017-05-01

    An adaptive Harris corner detection algorithm based on the iterative threshold is proposed for the problem that the corner detection algorithm must be given a proper threshold when the corner detection algorithm is extracted. In order to avoid the phenomenon of clustering and restrain the pseudo corner, this algorithm realizes the adaptive threshold selection by iteration instead of the threshold value of the Harris corner detection algorithm. Simulation results show that the proposed method achieves good results in terms of threshold setting and feature extraction.

  1. 6th International Meshing Roundtable '97

    SciTech Connect

    White, D.

    1997-09-01

    The goal of the 6th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the pas~ the Roundtable has enjoyed significant participation born each of these groups from a wide variety of countries. The Roundtable will consist of technical presentations from contributed papers and abstracts, two invited speakers, and two invited panels of experts discussing topics related to the development and use of automatic mesh generation tools. In addition, this year we will feature a "Bring Your Best Mesh" competition and poster session to encourage discussion and participation from a wide variety of mesh generation tool users. The schedule and evening social events are designed to provide numerous opportunities for informal dialog. A proceedings will be published by Sandia National Laboratories and distributed at the Roundtable. In addition, papers of exceptionally high quaIity will be submitted to a special issue of the International Journal of Computational Geometry and Applications. Papers and one page abstracts were sought that present original results on the meshing process. Potential topics include but are got limited to: Unstructured triangular and tetrahedral mesh generation Unstructured quadrilateral and hexahedral mesh generation Automated blocking and structured mesh generation Mixed element meshing Surface mesh generation Geometry decomposition and clean-up techniques Geometry modification techniques related to meshing Adaptive mesh refinement and mesh quality control Mesh visualization Special purpose meshing algorithms for particular applications Theoretical or novel ideas with practical potential Technical presentations from industrial researchers.

  2. An Adaptive Unified Differential Evolution Algorithm for Global Optimization

    SciTech Connect

    Qiang, Ji; Mitchell, Chad

    2014-11-03

    In this paper, we propose a new adaptive unified differential evolution algorithm for single-objective global optimization. Instead of the multiple mutation strate- gies proposed in conventional differential evolution algorithms, this algorithm employs a single equation unifying multiple strategies into one expression. It has the virtue of mathematical simplicity and also provides users the flexibility for broader exploration of the space of mutation operators. By making all control parameters in the proposed algorithm self-adaptively evolve during the process of optimization, it frees the application users from the burden of choosing appro- priate control parameters and also improves the performance of the algorithm. In numerical tests using thirteen basic unimodal and multimodal functions, the proposed adaptive unified algorithm shows promising performance in compari- son to several conventional differential evolution algorithms.

  3. Methods for high-resolution anisotropic finite element modeling of the human head: automatic MR white matter anisotropy-adaptive mesh generation.

    PubMed

    Lee, Won Hee; Kim, Tae-Seong

    2012-01-01

    This study proposes an advanced finite element (FE) head modeling technique through which high-resolution FE meshes adaptive to the degree of tissue anisotropy can be generated. Our adaptive meshing scheme (called wMesh) uses MRI structural information and fractional anisotropy maps derived from diffusion tensors in the FE mesh generation process, optimally reflecting electrical properties of the human brain. We examined the characteristics of the wMeshes through various qualitative and quantitative comparisons to the conventional FE regular-sized meshes that are non-adaptive to the degree of white matter anisotropy. We investigated numerical differences in the FE forward solutions that include the electrical potential and current density generated by current sources in the brain. The quantitative difference was calculated by two statistical measures of relative difference measure (RDM) and magnification factor (MAG). The results show that the wMeshes are adaptive to the anisotropic density of the WM anisotropy, and they better reflect the density and directionality of tissue conductivity anisotropy. Our comparison results between various anisotropic regular mesh and wMesh models show that there are substantial differences in the EEG forward solutions in the brain (up to RDM=0.48 and MAG=0.63 in the electrical potential, and RDM=0.65 and MAG=0.52 in the current density). Our analysis results indicate that the wMeshes produce different forward solutions that are different from the conventional regular meshes. We present some results that the wMesh head modeling approach enhances the sensitivity and accuracy of the FE solutions at the interfaces or in the regions where the anisotropic conductivities change sharply or their directional changes are complex. The fully automatic wMesh generation technique should be useful for modeling an individual-specific and high-resolution anisotropic FE head model incorporating realistic anisotropic conductivity distributions

  4. An adaptive algorithm for simulation of stochastic reaction-diffusion processes

    SciTech Connect

    Ferm, Lars Hellander, Andreas Loetstedt, Per

    2010-01-20

    We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.

  5. Lyapunov exponents and adaptive mesh refinement for high-speed flows using a discontinuous Galerkin scheme

    NASA Astrophysics Data System (ADS)

    Moura, R. C.; Silva, A. F. C.; Bigarella, E. D. V.; Fazenda, A. L.; Ortega, M. A.

    2016-08-01

    This paper proposes two important improvements to shock-capturing strategies using a discontinuous Galerkin scheme, namely, accurate shock identification via finite-time Lyapunov exponent (FTLE) operators and efficient shock treatment through a point-implicit discretization of a PDE-based artificial viscosity technique. The advocated approach is based on the FTLE operator, originally developed in the context of dynamical systems theory to identify certain types of coherent structures in a flow. We propose the application of FTLEs in the detection of shock waves and demonstrate the operator's ability to identify strong and weak shocks equally well. The detection algorithm is coupled with a mesh refinement procedure and applied to transonic and supersonic flows. While the proposed strategy can be used potentially with any numerical method, a high-order discontinuous Galerkin solver is used in this study. In this context, two artificial viscosity approaches are employed to regularize the solution near shocks: an element-wise constant viscosity technique and a PDE-based smooth viscosity model. As the latter approach is more sophisticated and preferable for complex problems, a point-implicit discretization in time is proposed to reduce the extra stiffness introduced by the PDE-based technique, making it more competitive in terms of computational cost.

  6. Output-Based Adaptive Meshing Applied to Space Launch System Booster Separation Analysis

    NASA Technical Reports Server (NTRS)

    Dalle, Derek J.; Rogers, Stuart E.

    2015-01-01

    This paper presents details of Computational Fluid Dynamic (CFD) simulations of the Space Launch System during solid-rocket booster separation using the Cart3D inviscid code with comparisons to Overflow viscous CFD results and a wind tunnel test performed at NASA Langley Research Center's Unitary PlanWind Tunnel. The Space Launch System (SLS) launch vehicle includes two solid-rocket boosters that burn out before the primary core stage and thus must be discarded during the ascent trajectory. The main challenges for creating an aerodynamic database for this separation event are the large number of basis variables (including orientation of the core, relative position and orientation of the boosters, and rocket thrust levels) and the complex flow caused by the booster separation motors. The solid-rocket boosters are modified from their form when used with the Space Shuttle Launch Vehicle, which has a rich flight history. However, the differences between the SLS core and the Space Shuttle External Tank result in the boosters separating with much narrower clearances, and so reducing aerodynamic uncertainty is necessary to clear the integrated system for flight. This paper discusses an approach that has been developed to analyze about 6000 wind tunnel simulations and 5000 flight vehicle simulations using Cart3D in adaptive-meshing mode. In addition, a discussion is presented of Overflow viscous CFD runs used for uncertainty quantification. Finally, the article presents lessons learned and improvements that will be implemented in future separation databases.

  7. 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.

  8. Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion

    NASA Astrophysics Data System (ADS)

    Philip, B.; Wang, Z.; Berrill, M. A.; Birke, M.; Pernice, M.

    2014-04-01

    The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

  9. Numerical simulation of current sheet formation in a quasiseparatrix layer using adaptive mesh refinement

    SciTech Connect

    Effenberger, Frederic; Thust, Kay; Grauer, Rainer; Dreher, Juergen; Arnold, Lukas

    2011-03-15

    The formation of a thin current sheet in a magnetic quasiseparatrix layer (QSL) is investigated by means of numerical simulation using a simplified ideal, low-{beta}, MHD model. The initial configuration and driving boundary conditions are relevant to phenomena observed in the solar corona and were studied earlier by Aulanier et al. [Astron. Astrophys. 444, 961 (2005)]. In extension to that work, we use the technique of adaptive mesh refinement (AMR) to significantly enhance the local spatial resolution of the current sheet during its formation, which enables us to follow the evolution into a later stage. Our simulations are in good agreement with the results of Aulanier et al. up to the calculated time in that work. In a later phase, we observe a basically unarrested collapse of the sheet to length scales that are more than one order of magnitude smaller than those reported earlier. The current density attains correspondingly larger maximum values within the sheet. During this thinning process, which is finally limited by lack of resolution even in the AMR studies, the current sheet moves upward, following a global expansion of the magnetic structure during the quasistatic evolution. The sheet is locally one-dimensional and the plasma flow in its vicinity, when transformed into a comoving frame, qualitatively resembles a stagnation point flow. In conclusion, our simulations support the idea that extremely high current densities are generated in the vicinities of QSLs as a response to external perturbations, with no sign of saturation.

  10. Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion

    SciTech Connect

    B. Philip; Z. Wang; M.A. Berrill; M. Birke; M. Pernice

    2014-04-01

    The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton–Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

  11. Advances in Rotor Performance and Turbulent Wake Simulation Using DES and Adaptive Mesh Refinement

    NASA Technical Reports Server (NTRS)

    Chaderjian, Neal M.

    2012-01-01

    Time-dependent Navier-Stokes simulations have been carried out for a rigid V22 rotor in hover, and a flexible UH-60A rotor in forward flight. Emphasis is placed on understanding and characterizing the effects of high-order spatial differencing, grid resolution, and Spalart-Allmaras (SA) detached eddy simulation (DES) in predicting the rotor figure of merit (FM) and resolving the turbulent rotor wake. The FM was accurately predicted within experimental error using SA-DES. Moreover, a new adaptive mesh refinement (AMR) procedure revealed a complex and more realistic turbulent rotor wake, including the formation of turbulent structures resembling vortical worms. Time-dependent flow visualization played a crucial role in understanding the physical mechanisms involved in these complex viscous flows. The predicted vortex core growth with wake age was in good agreement with experiment. High-resolution wakes for the UH-60A in forward flight exhibited complex turbulent interactions and turbulent worms, similar to the V22. The normal force and pitching moment coefficients were in good agreement with flight-test data.

  12. EMMA: an adaptive mesh refinement cosmological simulation code with radiative transfer

    NASA Astrophysics Data System (ADS)

    Aubert, Dominique; Deparis, Nicolas; Ocvirk, Pierre

    2015-11-01

    EMMA is a cosmological simulation code aimed at investigating the reionization epoch. It handles simultaneously collisionless and gas dynamics, as well as radiative transfer physics using a moment-based description with the M1 approximation. Field quantities are stored and computed on an adaptive three-dimensional mesh and the spatial resolution can be dynamically modified based on physically motivated criteria. Physical processes can be coupled at all spatial and temporal scales. We also introduce a new and optional approximation to handle radiation: the light is transported at the resolution of the non-refined grid and only once the dynamics has been fully updated, whereas thermo-chemical processes are still tracked on the refined elements. Such an approximation reduces the overheads induced by the treatment of radiation physics. A suite of standard tests are presented and passed by EMMA, providing a validation for its future use in studies of the reionization epoch. The code is parallel and is able to use graphics processing units (GPUs) to accelerate hydrodynamics and radiative transfer calculations. Depending on the optimizations and the compilers used to generate the CPU reference, global GPU acceleration factors between ×3.9 and ×16.9 can be obtained. Vectorization and transfer operations currently prevent better GPU performance and we expect that future optimizations and hardware evolution will lead to greater accelerations.

  13. MASS AND MAGNETIC DISTRIBUTIONS IN SELF-GRAVITATING SUPER-ALFVENIC TURBULENCE WITH ADAPTIVE MESH REFINEMENT

    SciTech Connect

    Collins, David C.; Norman, Michael L.; Padoan, Paolo; Xu Hao

    2011-04-10

    In this work, we present the mass and magnetic distributions found in a recent adaptive mesh refinement magnetohydrodynamic simulation of supersonic, super-Alfvenic, self-gravitating turbulence. Power-law tails are found in both mass density and magnetic field probability density functions, with P({rho}) {proportional_to} {rho}{sup -1.6} and P(B) {proportional_to} B{sup -2.7}. A power-law relationship is also found between magnetic field strength and density, with B {proportional_to} {rho}{sup 0.5}, throughout the collapsing gas. The mass distribution of gravitationally bound cores is shown to be in excellent agreement with recent observation of prestellar cores. The mass-to-flux distribution of cores is also found to be in excellent agreement with recent Zeeman splitting measurements. We also compare the relationship between velocity dispersion and density to the same cores, and find an increasing relationship between the two, with {sigma} {proportional_to} n{sup 0.25}, also in agreement with the observations. We then estimate the potential effects of ambipolar diffusion in our cores and find that due to the weakness of the magnetic field in our simulation, the inclusion of ambipolar diffusion in our simulation will not cause significant alterations of the flow dynamics.

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

    NASA Astrophysics Data System (ADS)

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

    2017-05-01

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

  15. Hexahedral Mesh Untangling

    SciTech Connect

    KNUPP,PATRICK

    2000-12-13

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

  16. Higher-order conservative interpolation between control-volume meshes: Application to advection and multiphase flow problems with dynamic mesh adaptivity

    NASA Astrophysics Data System (ADS)

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

    2016-09-01

    A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.

  17. Characterization of the non-uniqueness of used nuclear fuel burnup signatures through a Mesh-Adaptive Direct Search

    NASA Astrophysics Data System (ADS)

    Skutnik, Steven E.; Davis, David R.

    2016-05-01

    The use of passive gamma and neutron signatures from fission indicators is a common means of estimating used fuel burnup, enrichment, and cooling time. However, while characteristic fission product signatures such as 134Cs, 137Cs, 154Eu, and others are generally reliable estimators for used fuel burnup within the context where the assembly initial enrichment and the discharge time are known, in the absence of initial enrichment and/or cooling time information (such as when applying NDA measurements in a safeguards/verification context), these fission product indicators no longer yield a unique solution for assembly enrichment, burnup, and cooling time after discharge. Through the use of a new Mesh-Adaptive Direct Search (MADS) algorithm, it is possible to directly probe the shape of this "degeneracy space" characteristic of individual nuclides (and combinations thereof), both as a function of constrained parameters (such as the assembly irradiation history) and unconstrained parameters (e.g., the cooling time before measurement and the measurement precision for particular indicator nuclides). In doing so, this affords the identification of potential means of narrowing the uncertainty space of potential assembly enrichment, burnup, and cooling time combinations, thereby bounding estimates of assembly plutonium content. In particular, combinations of gamma-emitting nuclides with distinct half-lives (e.g., 134Cs with 137Cs and 154Eu) in conjunction with gross neutron counting (via 244Cm) are able to reasonably constrain the degeneracy space of possible solutions to a space small enough to perform useful discrimination and verification of fuel assemblies based on their irradiation history.

  18. An adaptive Cauchy differential evolution algorithm for global numerical optimization.

    PubMed

    Choi, Tae Jong; Ahn, Chang Wook; An, Jinung

    2013-01-01

    Adaptation of control parameters, such as scaling factor (F), crossover rate (CR), and population size (NP), appropriately is one of the major problems of Differential Evolution (DE) literature. Well-designed adaptive or self-adaptive parameter control method can highly improve the performance of DE. Although there are many suggestions for adapting the control parameters, it is still a challenging task to properly adapt the control parameters for problem. In this paper, we present an adaptive parameter control DE algorithm. In the proposed algorithm, each individual has its own control parameters. The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals' parameter values by using the Cauchy distribution. Through this, the control parameters of each individual are assigned either near the average parameter value or far from that of the average parameter value which might be better parameter value for next generation. The experimental results show that the proposed algorithm is more robust than the standard DE algorithm and several state-of-the-art adaptive DE algorithms in solving various unimodal and multimodal problems.

  19. An Adaptive Cauchy Differential Evolution Algorithm for Global Numerical Optimization

    PubMed Central

    Choi, Tae Jong; Ahn, Chang Wook; An, Jinung

    2013-01-01

    Adaptation of control parameters, such as scaling factor (F), crossover rate (CR), and population size (NP), appropriately is one of the major problems of Differential Evolution (DE) literature. Well-designed adaptive or self-adaptive parameter control method can highly improve the performance of DE. Although there are many suggestions for adapting the control parameters, it is still a challenging task to properly adapt the control parameters for problem. In this paper, we present an adaptive parameter control DE algorithm. In the proposed algorithm, each individual has its own control parameters. The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals' parameter values by using the Cauchy distribution. Through this, the control parameters of each individual are assigned either near the average parameter value or far from that of the average parameter value which might be better parameter value for next generation. The experimental results show that the proposed algorithm is more robust than the standard DE algorithm and several state-of-the-art adaptive DE algorithms in solving various unimodal and multimodal problems. PMID:23935445

  20. A novel routing algorithm of multi-priority label switch path in MPLS over WDM mesh networks

    NASA Astrophysics Data System (ADS)

    Su, Yang; Xu, Zhanqi; Liu, Zengji

    2005-11-01

    An extended layered graph of MPLS over WDM mesh networks is proposed in this paper, in which the label switch path (LSP) with various wavelengths and the limitation of optical transceivers at a routing node are both involved. Label switch paths are classified into different priorities according to each quality of service. The corresponding routing algorithm, differentiating integrated routing algorithm (DIRA), is proposed and studied. The quality of service (QoS) of a label switch path and the optimization of network resources utilization are taken into account comprehensively in DIRA. A comparison of DIRA with the representative optical routing algorithms via simulation shows that it can reduce the blocking probability of delay-constraint LSP and improve the network throughput.

  1. Numerical Modelling of Volcanic Ash 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.

    2011-12-01

    At the bottom of the world's oceans lies layer after layer of ash deposited from past volcanic eruptions. Correct interpretation of these layers can provide important constraints on the duration and frequency of volcanism, but requires a full understanding of the complex multi-phase settling and deposition process. Analogue experiments of tephra settling through a tank of water demonstrate that small ash particles can either settle individually, or collectively as a gravitationally unstable ash-laden plume. These plumes are generated when the concentration of particles exceeds a certain threshold such that the density of the tephra-water mixture is sufficiently large relative to the underlying particle-free water for a gravitational Rayleigh-Taylor instability to develop. These ash-laden plumes are observed to descend as a vertical density current at a velocity much greater than that of single particles, which has important implications for the emplacement of tephra deposits on the seabed. To extend the results of laboratory experiments to large scales and explore the conditions under which vertical density currents may form and persist, we have developed a multi-phase extension to Fluidity, a combined finite element / control volume CFD code that uses adaptive unstructured meshes. As a model validation, we present two- and three-dimensional simulations of tephra plume formation in a water tank that replicate laboratory experiments (Carey, 1997, doi:10.1130/0091-7613(1997)025<0839:IOCSOT>2.3.CO;2). An inflow boundary condition at the top of the domain allows particles to flux in at a constant rate of 0.472 gm-2s-1, forming a near-surface layer of tephra particles, which initially settle individually at the predicted Stokes velocity of 1.7 mms-1. As more tephra enters the water and the particle concentration increases, the layer eventually becomes unstable and plumes begin to form, descending with velocities more than ten times greater than those of individual

  2. Investigation of instabilities affecting detonations: Improving the resolution using block-structured adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Ravindran, Prashaanth

    The unstable nature of detonation waves is a result of the critical relationship between the hydrodynamic shock and the chemical reactions sustaining the shock. A perturbative analysis of the critical point is quite challenging due to the multiple spatio-temporal scales involved along with the non-linear nature of the shock-reaction mechanism. The author's research attempts to provide detailed resolution of the instabilities at the shock front. Another key aspect of the present research is to develop an understanding of the causality between the non-linear dynamics of the front and the eventual breakdown of the sub-structures. An accurate numerical simulation of detonation waves requires a very efficient solution of the Euler equations in conservation form with detailed, non-equilibrium chemistry. The difference in the flow and reaction length scales results in very stiff source terms, requiring the problem to be solved with adaptive mesh refinement. For this purpose, Berger-Colella's block-structured adaptive mesh refinement (AMR) strategy has been developed and applied to time-explicit finite volume methods. The block-structured technique uses a hierarchy of parent-child sub-grids, integrated recursively over time. One novel approach to partition the problem within a large supercomputer was the use of modified Peano-Hilbert space filling curves. The AMR framework was merged with CLAWPACK, a package providing finite volume numerical methods tailored for wave-propagation problems. The stiffness problem is bypassed by using a 1st order Godunov or a 2nd order Strang splitting technique, where the flow variables and source terms are integrated independently. A linearly explicit fourth-order Runge-Kutta integrator is used for the flow, and an ODE solver was used to overcome the numerical stiffness. Second-order spatial resolution is obtained by using a second-order Roe-HLL scheme with the inclusion of numerical viscosity to stabilize the solution near the discontinuity

  3. MeshEZW: an image coder using mesh and finite elements

    NASA Astrophysics Data System (ADS)

    Landais, Thomas; Bonnaud, Laurent; Chassery, Jean-Marc

    2003-08-01

    In this paper, we present a new method to compress the information in an image, called MeshEZW. The proposed approach is based on the finite elements method, a mesh construction and a zerotree method. The zerotree method is an adaptive of the EZW algorithm with two new symbols for increasing the performance. These steps allow a progressive representation of the image by the automatic construction of a bitstream. The mesh structure is adapted to the image compression domain and is defined to allow video comrpession. The coder is described and some preliminary results are discussed.

  4. Projections of grounding line retreat in West Antarctica carried out with an adaptive mesh model

    NASA Astrophysics Data System (ADS)

    Cornford, Stephen; Payne, Antony; Martin, Daniel; Le Brocq, Anne

    2013-04-01

    Present and future sea level rise associated with mass loss from West Antarctica is typically attributed to marine glaciers retreating in response to a warming ocean. Warmer waters melt the floating ice shelves that restrain some, if not all, marine glaciers, and the glaciers themselves respond by speeding up. That leads to thinning and in turn grounding line retreat. Satellite observations indicate that Amundsen Sea Embayment and, in particular, Pine Island Glacier, are undergoing this kind of dynamic change today. Numerical models, however, struggle to reproduce the observed behavior because either high resolution or some other kind special treatment is required at the grounding line. We present 200-year projections of three major glacier systems of West Antarctica: those that drain into the Amundsen Sea , the Filchner-Ronne Ice Shelf and the Ross Ice shelf. We do so using the newly developed BISICLES ice­ sheet model, which employs adaptive ­mesh refinement to maintain sub-kilometer resolution close to the grounding line and coarser resolution elsewhere. Ice accumulation and ice­ shelf melt-rate are derived from a range of models of the Antarctic atmosphere and ocean forced by the SRES A1B and E1 scenarios. We find that a substantial proportion of the grounding line in West Antarctica retreats, however the total sea level rise is less than 50 mm by 2100, and less than 100 mm by 2200. The lion's share of the mass loss is attributed to Pine Island Glacier, while its immediate neighbor Thwaites Glacier does not retreat until the end of the simulations.

  5. A learning heuristic for space mapping and searching self-organizing systems using adaptive mesh refinement

    NASA Astrophysics Data System (ADS)

    Phillips, Carolyn L.

    2014-09-01

    In a complex self-organizing system, small changes in the interactions between the system's components can result in different emergent macrostructures or macrobehavior. In chemical engineering and material science, such spontaneously self-assembling systems, using polymers, nanoscale or colloidal-scale particles, DNA, or other precursors, are an attractive way to create materials that are precisely engineered at a fine scale. Changes to the interactions can often be described by a set of parameters. Different contiguous regions in this parameter space correspond to different ordered states. Since these ordered states are emergent, often experiment, not analysis, is necessary to create a diagram of ordered states over the parameter space. By issuing queries to points in the parameter space (e.g., performing a computational or physical experiment), ordered states can be discovered and mapped. Queries can be costly in terms of resources or time, however. In general, one would like to learn the most information using the fewest queries. Here we introduce a learning heuristic for issuing queries to map and search a two-dimensional parameter space. Using a method inspired by adaptive mesh refinement, the heuristic iteratively issues batches of queries to be executed in parallel based on past information. By adjusting the search criteria, different types of searches (for example, a uniform search, exploring boundaries, sampling all regions equally) can be flexibly implemented. We show that this method will densely search the space, while preferentially targeting certain features. Using numerical examples, including a study simulating the self-assembly of complex crystals, we show how this heuristic can discover new regions and map boundaries more accurately than a uniformly distributed set of queries.

  6. General relativistic hydrodynamics with Adaptive-Mesh Refinement (AMR) and modeling of accretion disks

    NASA Astrophysics Data System (ADS)

    Donmez, Orhan

    We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.

  7. Adaptive particle-cell algorithm for Fokker-Planck based rarefied gas flow simulations

    NASA Astrophysics Data System (ADS)

    Pfeiffer, M.; Gorji, M. H.

    2017-04-01

    Recently, the Fokker-Planck (FP) kinetic model has been devised on the basis of the Boltzmann equation (Jenny et al., 2010; Gorji et al., 2011). Particle Monte-Carlo schemes are then introduced for simulations of rarefied gas flows based on the FP kinetics. Here the particles follow independent stochastic paths and thus a spatio-temporal resolution coarser than the collisional scales becomes possible. In contrast to the direct simulation Monte-Carlo (DSMC), the computational cost is independent of the Knudsen number resulting in efficient simulations at moderate/low Knudsen flows. In order to further exploit the efficiency of the FP method, the required particle-cell resolutions should be found, and a cell refinement strategy has to be developed accordingly. In this study, an adaptive particle-cell scheme applicable to a general unstructured mesh is derived for the FP model. Virtual sub cells are introduced for the adaptive mesh refinement. Moreover a sub cell-merging algorithm is provided to honor the minimum required number of particles per cell. For assessments, the 70 degree blunted cone reentry flow (Allgre et al., 1997) is studied. Excellent agreement between the introduced adaptive FP method and DSMC is achieved.

  8. An architecture for adaptive algorithmic hybrids.

    PubMed

    Cassimatis, Nicholas; Bignoli, Perrin; Bugajska, Magdalena; Dugas, Scott; Kurup, Unmesh; Murugesan, Arthi; Bello, Paul

    2010-06-01

    We describe a cognitive architecture for creating more robust intelligent systems. Our approach is to enable hybrids of algorithms based on different computational formalisms to be executed. The architecture is motivated by some features of human cognitive architecture and the following beliefs: 1) Most existing computational methods often exhibit some of the characteristics desired of intelligent systems at the cost of other desired characteristics and 2) a system exhibiting robust intelligence can be designed by implementing hybrids of these computational methods. The main obstacle to this approach is that the various relevant computational methods are based on data structures and algorithms that are difficult to integrate into one system. We describe a new method of executing hybrids of algorithms using the focus of attention of multiple modules. The key to this approach is the following two principles: 1) Algorithms based on very different computational frameworks (e.g., logical reasoning, probabilistic inference, and case-based reasoning) can be implemented using the same set of five common functions and 2) each of these common functions can be executed using multiple data structures and algorithms. This approach has been embodied in the Polyscheme cognitive architecture. Systems based on Polyscheme in planning, spatial reasoning, robotics, and information retrieval illustrate that this approach to hybridizing algorithms enables qualitative and measurable quantitative advances in the abilities of intelligent systems.

  9. Adaptive phase aberration correction based on imperialist competitive algorithm.

    PubMed

    Yazdani, R; Hajimahmoodzadeh, M; Fallah, H R

    2014-01-01

    We investigate numerically the feasibility of phase aberration correction in a wavefront sensorless adaptive optical system, based on the imperialist competitive algorithm (ICA). Considering a 61-element deformable mirror (DM) and the Strehl ratio as the cost function of ICA, this algorithm is employed to search the optimum surface profile of DM for correcting the phase aberrations in a solid-state laser system. The correction results show that ICA is a powerful correction algorithm for static or slowly changing phase aberrations in optical systems, such as solid-state lasers. The correction capability and the convergence speed of this algorithm are compared with those of the genetic algorithm (GA) and stochastic parallel gradient descent (SPGD) algorithm. The results indicate that these algorithms have almost the same correction capability. Also, ICA and GA are almost the same in convergence speed and SPGD is the fastest of these algorithms.

  10. Optimal Pid Controller Design Using Adaptive Vurpso Algorithm

    NASA Astrophysics Data System (ADS)

    Zirkohi, Majid Moradi

    2015-04-01

    The purpose of this paper is to improve theVelocity Update Relaxation Particle Swarm Optimization algorithm (VURPSO). The improved algorithm is called Adaptive VURPSO (AVURPSO) algorithm. Then, an optimal design of a Proportional-Integral-Derivative (PID) controller is obtained using the AVURPSO algorithm. An adaptive momentum factor is used to regulate a trade-off between the global and the local exploration abilities in the proposed algorithm. This operation helps the system to reach the optimal solution quickly and saves the computation time. Comparisons on the optimal PID controller design confirm the superiority of AVURPSO algorithm to the optimization algorithms mentioned in this paper namely the VURPSO algorithm, the Ant Colony algorithm, and the conventional approach. Comparisons on the speed of convergence confirm that the proposed algorithm has a faster convergence in a less computation time to yield a global optimum value. The proposed AVURPSO can be used in the diverse areas of optimization problems such as industrial planning, resource allocation, scheduling, decision making, pattern recognition and machine learning. The proposed AVURPSO algorithm is efficiently used to design an optimal PID controller.

  11. Self-Adaptive Differential Evolution Algorithm With Zoning Evolution of Control Parameters and Adaptive Mutation Strategies.

    PubMed

    Fan, Qinqin; Yan, Xuefeng

    2016-01-01

    The performance of the differential evolution (DE) algorithm is significantly affected by the choice of mutation strategies and control parameters. Maintaining the search capability of various control parameter combinations throughout the entire evolution process is also a key issue. A self-adaptive DE algorithm with zoning evolution of control parameters and adaptive mutation strategies is proposed in this paper. In the proposed algorithm, the mutation strategies are automatically adjusted with population evolution, and the control parameters evolve in their own zoning to self-adapt and discover near optimal values autonomously. The proposed algorithm is compared with five state-of-the-art DE algorithm variants according to a set of benchmark test functions. Furthermore, seven nonparametric statistical tests are implemented to analyze the experimental results. The results indicate that the overall performance of the proposed algorithm is better than those of the five existing improved algorithms.

  12. Bayesian of inductive cognition algorithm for adaptive classification

    NASA Astrophysics Data System (ADS)

    Jin, Longcun; Wan, Wanggen; Cui, Bin; Wu, Yongliang

    2009-07-01

    In this paper, we proposed a Bayesian of inductive cognition algorithm using in virtual reality multimedia classification. We present a Bayesian of inductive cognition algorithm framework model for adaptively classifying scenes in virtual reality multimedia data. The Multimedia can switch between different shots, the unknown objects can leave or enter the scene at multiple times, and the scenes can be adaptively classified. The proposed algorithm consists of Bayesian inductive cognition part and Dirichlet process part. This algorithm has several advantages over traditional distance-based agglomerative adaptively classifying algorithms. Bayesian of inductive cognition algorithm based on Dirichlet process hypothesis testing is used to decide which merges are advantageous and to output the recommended depth of the scenes. The algorithm can be interpreted as a novel fast bottom-up approximate inference method for a Dirichlet process mixture model. We describe procedures for learning the model hyperparameters, computing the predictive distribution, and extensions to the Bayesian of inductive cognition algorithm. Experimental results on virtual reality multimedia data sets demonstrate useful properties of the Bayesian of inductive cognition algorithm.

  13. An adaptive inverse kinematics algorithm for robot manipulators

    NASA Technical Reports Server (NTRS)

    Colbaugh, R.; Glass, K.; Seraji, H.

    1990-01-01

    An adaptive algorithm for solving the inverse kinematics problem for robot manipulators is presented. The algorithm is derived using model reference adaptive control (MRAC) theory and is computationally efficient for online applications. The scheme requires no a priori knowledge of the kinematics of the robot if Cartesian end-effector sensing is available, and it requires knowledge of only the forward kinematics if joint position sensing is used. Computer simulation results are given for the redundant seven-DOF robotics research arm, demonstrating that the proposed algorithm yields accurate joint angle trajectories for a given end-effector position/orientation trajectory.

  14. Adaptive optimal quantization for 3D mesh representation in the spherical coordinate system

    NASA Astrophysics Data System (ADS)

    Ahn, Jeong-Hwan; Ho, Yo-Sung

    1998-12-01

    In recent days, applications using 3D models are increasing. Since the 3D model contains a huge amount of information, compression of the 3D model data is necessary for efficient storage or transmission. In this paper, we propose an adaptive encoding scheme to compress the geometry information of the 3D model. Using the Levinson-Durbin algorithm, the encoder first predicts vertex positions along a vertex spanning tree. After each prediction error is normalized, the prediction error vector of each vertex point is represented in the spherical coordinate system (r,(theta) ,(phi) ). Each r is then quantizes by an optimal uniform quantizer. A pair of each ((theta) ,(phi) ) is also successively encoded by partitioning the surface of the sphere according to the quantized value of r. The proposed scheme demonstrates improved coding efficiency by exploiting the statistical properties of r and ((theta) ,(phi) ).

  15. Classification of adaptive memetic algorithms: a comparative study.

    PubMed

    Ong, Yew-Soon; Lim, Meng-Hiot; Zhu, Ning; Wong, Kok-Wai

    2006-02-01

    Adaptation of parameters and operators represents one of the recent most important and promising areas of research in evolutionary computations; it is a form of designing self-configuring algorithms that acclimatize to suit the problem in hand. Here, our interests are on a recent breed of hybrid evolutionary algorithms typically known as adaptive memetic algorithms (MAs). One unique feature of adaptive MAs is the choice of local search methods or memes and recent studies have shown that this choice significantly affects the performances of problem searches. In this paper, we present a classification of memes adaptation in adaptive MAs on the basis of the mechanism used and the level of historical knowledge on the memes employed. Then the asymptotic convergence properties of the adaptive MAs considered are analyzed according to the classification. Subsequently, empirical studies on representatives of adaptive MAs for different type-level meme adaptations using continuous benchmark problems indicate that global-level adaptive MAs exhibit better search performances. Finally we conclude with some promising research directions in the area.

  16. The PCNN adaptive segmentation algorithm based on visual perception

    NASA Astrophysics Data System (ADS)

    Zhao, Yanming

    To solve network adaptive parameter determination problem of the pulse coupled neural network (PCNN), and improve the image segmentation results in image segmentation. The PCNN adaptive segmentation algorithm based on visual perception of information is proposed. Based on the image information of visual perception and Gabor mathematical model of Optic nerve cells receptive field, the algorithm determines adaptively the receptive field of each pixel of the image. And determines adaptively the network parameters W, M, and β of PCNN by the Gabor mathematical model, which can overcome the problem of traditional PCNN parameter determination in the field of image segmentation. Experimental results show that the proposed algorithm can improve the region connectivity and edge regularity of segmentation image. And also show the PCNN of visual perception information for segmentation image of advantage.

  17. Adaptively resizing populations: Algorithm, analysis, and first results

    NASA Technical Reports Server (NTRS)

    Smith, Robert E.; Smuda, Ellen

    1993-01-01

    Deciding on an appropriate population size for a given Genetic Algorithm (GA) application can often be critical to the algorithm's success. Too small, and the GA can fall victim to sampling error, affecting the efficacy of its search. Too large, and the GA wastes computational resources. Although advice exists for sizing GA populations, much of this advice involves theoretical aspects that are not accessible to the novice user. An algorithm for adaptively resizing GA populations is suggested. This algorithm is based on recent theoretical developments that relate population size to schema fitness variance. The suggested algorithm is developed theoretically, and simulated with expected value equations. The algorithm is then tested on a problem where population sizing can mislead the GA. The work presented suggests that the population sizing algorithm may be a viable way to eliminate the population sizing decision from the application of GA's.

  18. A Novel Hybrid Self-Adaptive Bat Algorithm

    PubMed Central

    Fister, Iztok; Brest, Janez

    2014-01-01

    Nature-inspired algorithms attract many researchers worldwide for solving the hardest optimization problems. One of the newest members of this extensive family is the bat algorithm. To date, many variants of this algorithm have emerged for solving continuous as well as combinatorial problems. One of the more promising variants, a self-adaptive bat algorithm, has recently been proposed that enables a self-adaptation of its control parameters. In this paper, we have hybridized this algorithm using different DE strategies and applied these as a local search heuristics for improving the current best solution directing the swarm of a solution towards the better regions within a search space. The results of exhaustive experiments were promising and have encouraged us to invest more efforts into developing in this direction. PMID:25187904

  19. An adaptive, lossless data compression algorithm and VLSI implementations

    NASA Technical Reports Server (NTRS)

    Venbrux, Jack; Zweigle, Greg; Gambles, Jody; Wiseman, Don; Miller, Warner H.; Yeh, Pen-Shu

    1993-01-01

    This paper first provides an overview of an adaptive, lossless, data compression algorithm originally devised by Rice in the early '70s. It then reports the development of a VLSI encoder/decoder chip set developed which implements this algorithm. A recent effort in making a space qualified version of the encoder is described along with several enhancements to the algorithm. The performance of the enhanced algorithm is compared with those from other currently available lossless compression techniques on multiple sets of test data. The results favor our implemented technique in many applications.

  20. Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

    NASA Astrophysics Data System (ADS)

    Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert

    2017-04-01

    A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.

  1. Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

    DOE PAGES

    Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert

    2017-01-27

    A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fractionmore » or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.« less

  2. Optimization and Reconfiguration of Advanced Manufacturing Mode Based on Object-Based Knowledge Mesh and Improved Immune Genetic Algorithm

    NASA Astrophysics Data System (ADS)

    Xue, Chaogai; Cao, Haiwang

    This paper deals with an approach to the optimization and reconfiguration of advanced manufacturing mode based on the object-based knowledge mesh (OKM) and improved immune genetic algorithm (IGA). To explore the optimization and reconfiguration of the new OKM by the user's function requirements, an optimization procedure of an OKM aiming at the user's maximum function-satisfaction is proposed. Firstly, based on the definitions of the fuzzy function-satisfaction degree relationships of the users' requirements for the OKM functions and the multiple fuzzy function-satisfaction degrees of the relationships, the optimization model of the OKM multiple set operation expression is constructed. And the OKM multiple set operation expression is optimized by the immune genetic algorithm, with the steps of the OKM optimization presented in detail as well. Based upon the above, the optimization and reconfiguration of an advanced manufacturing mode are illustrated by an actual OKM example. The proposed approach proves to be very effective.

  3. Adaptive Mesh Refinement Cosmological Simulations of Cosmic Rays in Galaxy Clusters

    NASA Astrophysics Data System (ADS)

    Skillman, Samuel William

    2013-12-01

    Galaxy clusters are unique astrophysical laboratories that contain many thermal and non-thermal phenomena. In particular, they are hosts to cosmic shocks, which propagate through the intracluster medium as a by-product of structure formation. It is believed that at these shock fronts, magnetic field inhomogeneities in a compressing flow may lead to the acceleration of cosmic ray electrons and ions. These relativistic particles decay and radiate through a variety of mechanisms, and have observational signatures in radio, hard X-ray, and Gamma-ray wavelengths. We begin this dissertation by developing a method to find shocks in cosmological adaptive mesh refinement simulations of structure formation. After describing the evolution of shock properties through cosmic time, we make estimates for the amount of kinetic energy processed and the total number of cosmic ray protons that could be accelerated at these shocks. We then use this method of shock finding and a model for the acceleration of and radio synchrotron emission from cosmic ray electrons to estimate the radio emission properties in large scale structures. By examining the time-evolution of the radio emission with respect to the X-ray emission during a galaxy cluster merger, we find that the relative timing of the enhancements in each are important consequences of the shock dynamics. By calculating the radio emission expected from a given mass galaxy cluster, we make estimates for future large-area radio surveys. Next, we use a state-of-the-art magnetohydrodynamic simulation to follow the electron acceleration in a massive merging galaxy cluster. We use the magnetic field information to calculate not only the total radio emission, but also create radio polarization maps that are compared to recent observations. We find that we can naturally reproduce Mpc-scale radio emission that resemble many of the known double radio relic systems. Finally, motivated by our previous studies, we develop and introduce a

  4. Modeling gravitational instabilities in self-gravitating protoplanetary disks with adaptive mesh refinement techniques

    NASA Astrophysics Data System (ADS)

    Lichtenberg, Tim; Schleicher, Dominik R. G.

    2015-07-01

    The astonishing diversity in the observed planetary population requires theoretical efforts and advances in planet formation theories. The use of numerical approaches provides a method to tackle the weaknesses of current models and is an important tool to close gaps in poorly constrained areas such as the rapid formation of giant planets in highly evolved systems. So far, most numerical approaches make use of Lagrangian-based smoothed-particle hydrodynamics techniques or grid-based 2D axisymmetric simulations. We present a new global disk setup to model the first stages of giant planet formation via gravitational instabilities (GI) in 3D with the block-structured adaptive mesh refinement (AMR) hydrodynamics code enzo. With this setup, we explore the potential impact of AMR techniques on the fragmentation and clumping due to large-scale instabilities using different AMR configurations. Additionally, we seek to derive general resolution criteria for global simulations of self-gravitating disks of variable extent. We run a grid of simulations with varying AMR settings, including runs with a static grid for comparison. Additionally, we study the effects of varying the disk radius. The physical settings involve disks with Rdisk = 10,100 and 300 AU, with a mass of Mdisk ≈ 0.05 M⊙ and a central object of subsolar mass (M⋆ = 0.646 M⊙). To validate our thermodynamical approach we include a set of simulations with a dynamically stable profile (Qinit = 3) and similar grid parameters. The development of fragmentation and the buildup of distinct clumps in the disk is strongly dependent on the chosen AMR grid settings. By combining our findings from the resolution and parameter studies we find a general lower limit criterion to be able to resolve GI induced fragmentation features and distinct clumps, which induce turbulence in the disk and seed giant planet formation. Irrespective of the physical extension of the disk, topologically disconnected clump features are only

  5. Adaptive wavelet transform algorithm for image compression applications

    NASA Astrophysics Data System (ADS)

    Pogrebnyak, Oleksiy B.; Manrique Ramirez, Pablo

    2003-11-01

    A new algorithm of locally adaptive wavelet transform is presented. The algorithm implements the integer-to-integer lifting scheme. It performs an adaptation of the wavelet function at the prediction stage to the local image data activity. The proposed algorithm is based on the generalized framework for the lifting scheme that permits to obtain easily different wavelet coefficients in the case of the (N~,N) lifting. It is proposed to perform the hard switching between (2, 4) and (4, 4) lifting filter outputs according to an estimate of the local data activity. When the data activity is high, i.e., in the vicinity of edges, the (4, 4) lifting is performed. Otherwise, in the plain areas, the (2,4) decomposition coefficients are calculated. The calculations are rather simples that permit the implementation of the designed algorithm in fixed point DSP processors. The proposed adaptive transform possesses the perfect restoration of the processed data and possesses good energy compactation. The designed algorithm was tested on different images. The proposed adaptive transform algorithm can be used for image/signal lossless compression.

  6. Partially Adaptive STAP Algorithm Approaches to functional MRI

    PubMed Central

    Huang, Lejian; Thompson, Elizabeth A.; Schmithorst, Vincent; Holland, Scott K.; Talavage, Thomas M.

    2010-01-01

    In this work, the architectures of three partially adaptive STAP algorithms are introduced, one of which is explored in detail, that reduce dimensionality and improve tractability over fully adaptive STAP when used in construction of brain activation maps in fMRI. Computer simulations incorporating actual MRI noise and human data analysis indicate that element space partially adaptive STAP can attain close to the performance of fully adaptive STAP while significantly decreasing processing time and maximum memory requirements, and thus demonstrates potential in fMRI analysis. PMID:19272913

  7. Anisotropic mesh adaptation for solution of finite element problems using hierarchical edge-based error estimates

    SciTech Connect

    Lipnikov, Konstantin; Agouzal, Abdellatif; Vassilevski, Yuri

    2009-01-01

    We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N{sub h} triangles, the error is proportional to N{sub h}{sup -1} and the gradient of error is proportional to N{sub h}{sup -1/2} which are optimal asymptotics. The methodology is verified with numerical experiments.

  8. A local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems

    NASA Astrophysics Data System (ADS)

    Carpio, Jaime; Prieto, Juan Luis; Vera, Marcos

    2016-02-01

    A novel numerical algorithm for the simulation of transient combustion problems at low Mach and moderately high Reynolds numbers is presented. These problems are often characterized by the existence of a large disparity of length and time scales, resulting in the development of directional flow features, such as slender jets, boundary layers, mixing layers, or flame fronts. This makes local anisotropic adaptive techniques quite advantageous computationally. In this work we propose a local anisotropic refinement algorithm using, for the spatial discretization, unstructured triangular elements in a finite element framework. For the time integration, the problem is formulated in the context of semi-Lagrangian schemes, introducing the semi-Lagrange-Galerkin (SLG) technique as a better alternative to the classical semi-Lagrangian (SL) interpolation. The good performance of the numerical algorithm is illustrated by solving a canonical laminar combustion problem: the flame/vortex interaction. First, a premixed methane-air flame/vortex interaction with simplified transport and chemistry description (Test I) is considered. Results are found to be in excellent agreement with those in the literature, proving the superior performance of the SLG scheme when compared with the classical SL technique, and the advantage of using anisotropic adaptation instead of uniform meshes or isotropic mesh refinement. As a more realistic example, we then conduct simulations of non-premixed hydrogen-air flame/vortex interactions (Test II) using a more complex combustion model which involves state-of-the-art transport and chemical kinetics. In addition to the analysis of the numerical features, this second example allows us to perform a satisfactory comparison with experimental visualizations taken from the literature.

  9. Adaptive GOF residual operation algorithm in video compression

    NASA Astrophysics Data System (ADS)

    Pan, Jiyan; Hu, Bo

    2005-07-01

    Residual operations are introduced in many video compression algorithms to exploit temporal redundancy in video sequences. One of the most effective and computationally simple algorithms is 3D-DWT-SPIHT algorithm. Nevertheless, it only utilizes intra-GOF temporal redundancy. In order to eliminate inter-GOF redundancy, the Simple GOF Residual Operation (SGRO) algorithm was introduced, where residual operations are performed every two GOFs. However, when background mutations occur, the PSNR of reconstructed target GOF significantly drops; on the other hand, when video sequences are temporally stationary, SGRO algorithm fails to fully utilize inter-GOF temporal redundancy due to its imperative insertion of no-residual-operation GOFs. In this paper, we propose a new Adaptive GOF Residual Operation (AGRO) algorithm, based upon a criterion on residual operations, which is derived from an empirical formula of image complexity established by us. AGRO algorithm always selects the best residual operation manner according to the contents of video sequences: by detecting contents of video sequences, it cancels residual operations where background mutations happen, while encouraging residual operations where video sequences are temporally stationary. Therefore, AGRO algorithm prevents the significant drop in compression effects resulted from background mutations, and in the meantime, fully utilizes inter-GOF temporal redundancy. In addition, AGRO algorithm demonstrates an innate error-propagation-resistant property. Numerical results show that AGRO algorithm renders a significant PSNR increase over SGRO algorithm whenever background mutations occur or temporally stationary sequences dominate.

  10. Automatic DarkAdaptation Threshold Detection Algorithm.

    PubMed

    G de Azevedo, Dario; Helegda, Sergio; Glock, Flavio; Russomano, Thais

    2005-01-01

    This paper describes an algorithm used to automatically determine the threshold sensitivity in a new dark adaptometer. The new instrument is controlled by a personal computer and can be used in the investigation of several retinal diseases. The stimulus field is delivered to the eye through the modified optics of a fundus camera. An automated light stimulus source was developed to operate together with this fundus camera. New control parameters were developed in this instrument to improve the traditional Goldmann-Weekers dark adaptometer.

  11. Tomographic mesh generation for OSEM reconstruction of SPECT images

    NASA Astrophysics Data System (ADS)

    Lu, Yao; Yu, Bo; Vogelsang, Levon; Krol, Andrzej; Xu, Yuesheng; Hu, Xiaofei; Feiglin, David

    2009-02-01

    To improve quality of OSEM SPECT reconstruction in the mesh domain, we implemented an adaptive mesh generation method that produces tomographic mesh consisting of triangular elements with size and density commensurate with geometric detail of the objects. Node density and element size change smoothly as a function of distance from the edges and edge curvature without creation of 'bad' elements. Tomographic performance of mesh-based OSEM reconstruction is controlled by the tomographic mesh structure, i.e. node density distribution, which in turn is ruled by the number of key points on the boundaries. A greedy algorithm is used to influence the distribution of nodes on the boundaries. The relationship between tomographic mesh properties and OSEM reconstruction quality has been investigated. We conclude that by selecting adequate number of key points, one can produce a tomographic mesh with lowest number of nodes that is sufficient to provide desired quality of reconstructed images, appropriate for the imaging system properties.

  12. Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation

    NASA Astrophysics Data System (ADS)

    Weller, Hilary; Browne, Philip; Budd, Chris; Cullen, Mike

    2016-03-01

    An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tessellations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.

  13. Dynamic mesh adaptation for front evolution using discontinuous Galerkin based weighted condition number relaxation

    NASA Astrophysics Data System (ADS)

    Greene, Patrick; Schofield, Sam; Nourgaliev, Robert

    2016-11-01

    A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin (DG) projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. The method retains the excellent smoothing capabilities of condition number relaxation, while providing a method for clustering mesh cells near regions of interest. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

  14. Solving Local Minima Problem in Back Propagation Algorithm Using Adaptive Gain, Adaptive Momentum and Adaptive Learning Rate on Classification Problems

    NASA Astrophysics Data System (ADS)

    Hamid, Norhamreeza Abdul; Nawi, Nazri Mohd; Ghazali, Rozaida; Salleh, Mohd Najib Mohd

    This paper presents a new method to improve back propagation algorithm from getting stuck with local minima problem and slow convergence speeds which caused by neuron saturation in the hidden layer. In this proposed algorithm, each training pattern has its own activation functions of neurons in the hidden layer that are adjusted by the adaptation of gain parameters together with adaptive momentum and learning rate value during the learning process. The efficiency of the proposed algorithm is compared with the conventional back propagation gradient descent and the current working back propagation gradient descent with adaptive gain by means of simulation on three benchmark problems namely iris, glass and thyroid.

  15. Industrial OCR approaches: architecture, algorithms, and adaptation techniques

    NASA Astrophysics Data System (ADS)

    Marosi, István

    2007-01-01

    Optical Character Recognition is much more than character classification. An industrial OCR application combines algorithms studied in detail by different researchers in the area of image processing, pattern recognition, machine learning, language analysis, document understanding, data mining, and other, artificial intelligence domains. There is no single perfect algorithm for any of the OCR problems, so modern systems try to adapt themselves to the actual features of the image or document to be recognized. This paper describes the architecture of a modern OCR system with an emphasis on this adaptation process.

  16. An hp-Adaptive Discretization Algorithm for Signed Distance Field Generation.

    PubMed

    Koschier, Dan; Deul, Crispin; Brand, Magnus; Bender, Jan

    2017-10-01

    In this paper we present an hp-adaptive algorithm to generate discrete higher-order polynomial Signed Distance Fields (SDFs) on axis-aligned hexahedral grids from manifold polygonal input meshes. Using an orthonormal polynomial basis, we efficiently fit the polynomials to the underlying signed distance function on each cell. The proposed error-driven construction algorithm is globally adaptive and iteratively refines the SDFs using either spatial subdivision ( h-refinement) following an octree scheme or by cell-wise adaption of the polynomial approximation's degree ( p-refinement). We further introduce a novel decision criterion based on an error-estimator in order to decide whether to apply p- or h-refinement. We demonstrate that our method is able to construct more accurate SDFs at significantly lower memory consumption compared to previous approaches. While the cell-wise polynomial approximation will result in highly accurate SDFs, it can not be guaranteed that the piecewise approximation is continuous over cell interfaces. Therefore, we propose an optimization-based post-processing step in order to weakly enforce continuity. Finally, we apply our generated SDFs as collision detector to the physically-based simulation of geometrically highly complex solid objects in order to demonstrate the practical relevance and applicability of our method.

  17. Spatially adaptive regularized iterative high-resolution image reconstruction algorithm

    NASA Astrophysics Data System (ADS)

    Lim, Won Bae; Park, Min K.; Kang, Moon Gi

    2000-12-01

    High resolution images are often required in applications such as remote sensing, frame freeze in video, military and medical imaging. Digital image sensor arrays, which are used for image acquisition in many imaging systems, are not dense enough to prevent aliasing, so the acquired images will be degraded by aliasing effects. To prevent aliasing without loss of resolution, a dense detector array is required. But it may be very costly or unavailable, thus, many imaging systems are designed to allow some level of aliasing during image acquisition. The purpose of our work is to reconstruct an unaliased high resolution image from the acquired aliased image sequence. In this paper, we propose a spatially adaptive regularized iterative high resolution image reconstruction algorithm for blurred, noisy and down-sampled image sequences. The proposed approach is based on a Constrained Least Squares (CLS) high resolution reconstruction algorithm, with spatially adaptive regularization operators and parameters. These regularization terms are shown to improve the reconstructed image quality by forcing smoothness, while preserving edges in the reconstructed high resolution image. Accurate sub-pixel motion registration is the key of the success of the high resolution image reconstruction algorithm. However, sub-pixel motion registration may have some level of registration error. Therefore, a reconstruction algorithm which is robust against the registration error is required. The registration algorithm uses a gradient based sub-pixel motion estimator which provides shift information for each of the recorded frames. The proposed algorithm is based on a technique of high resolution image reconstruction, and it solves spatially adaptive regularized constrained least square minimization functionals. In this paper, we show that the reconstruction algorithm gives dramatic improvements in the resolution of the reconstructed image and is effective in handling the aliased information. The

  18. Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

    NASA Technical Reports Server (NTRS)

    Barth, Timothy J.; Kutler, Paul (Technical Monitor)

    1998-01-01

    Several stabilized demoralization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin demoralization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS, and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobean linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Discrete maximum principle theory will be presented for general finite volume approximations on unstructured meshes. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc, will. be addressed as needed.

  19. A particle-mesh algorithm for advection-reaction-diffusion equations with applications to plankton modeling

    NASA Astrophysics Data System (ADS)

    Paparella, F.; Oliveri, F.

    2009-04-01

    The interplay of advection, reaction and diffusion terms in ADR equations is a rather difficult one to be modeled numerically. The kind of spurious oscillations that is usually harmless for non-reacting scalars is often amplified without bounds by reaction terms. Furthermore, in most biogeochimical applications, such as mesoscale or global-scale plankton modeling, the diffusive fluxes may be smaller than the numerical ones. Inspired by the particle-mesh methods used by cosmologists, we propose to discretize on a grid only the diffusive term of the equation, and solve the advection-reaction terms as ordinary differential equations along the characteristic lines. Diffusion happens by letting the concentration field carried by each particle to relax towards the diffusive field known on the grid, without redistributing the particles. This method, in the limit of vanishing diffusivity and for a fixed mesh size, recovers the advection-reaction solution with no numerical diffusion. We show some example numerical solutions of the ADR equations stemming from a simple predator-prey model.

  20. Adapting Eclat algorithm to parallel environments with Charm++ library

    NASA Astrophysics Data System (ADS)

    Puścian, Marek; Grabski, Waldemar

    2016-09-01

    In this paper we describe Eclat algorithm that is adapted to deal with growing data repositories. The presented solution utilizes Master-Slave scheme to distribute data mining tasks among available computation nodes. Several improvements have been proposed and successfully implemented using Charm++ library. This paper introduces optimization techniques to reduce communication cost and synchronization overhead. It also discusses results of the performance of parallel Eclat algorithm against different databases and compares it with parallel Apriori algorithm. The proposed approach has been illustrated with many experiments and measurements performed using multiprocessor and multithreaded computer platform.

  1. A Demons algorithm for image registration with locally adaptive regularization.

    PubMed

    Cahill, Nathan D; Noble, J Alison; Hawkes, David J

    2009-01-01

    Thirion's Demons is a popular algorithm for nonrigid image registration because of its linear computational complexity and ease of implementation. It approximately solves the diffusion registration problem by successively estimating force vectors that drive the deformation toward alignment and smoothing the force vectors by Gaussian convolution. In this article, we show how the Demons algorithm can be generalized to allow image-driven locally adaptive regularization in a manner that preserves both the linear complexity and ease of implementation of the original Demons algorithm. We show that the proposed algorithm exhibits lower target registration error and requires less computational effort than the original Demons algorithm on the registration of serial chest CT scans of patients with lung nodules.

  2. A novel gradient adaptive step size LMS algorithm with dual adaptive filters.

    PubMed

    Jiao, Yuzhong; Cheung, Rex Y P; Chow, Winnie W Y; Mok, Mark P C

    2013-01-01

    Least mean square (LMS) adaptive filter has been used to extract life signals from serious ambient noises and interferences in biomedical applications. However, a LMS adaptive filter with a fixed step size always suffers from slow convergence rate or large signal distortion due to the diversity of the application environments. An ideal adaptive filtering system should be able to adapt different environments and obtain the useful signals with low distortion. Adaptive filter with gradient adaptive step size is therefore more desirable in order to meet the demands of adaptation and convergence rate, which adjusts the step-size parameter automatically by using gradient descent technique. In this paper, a novel gradient adaptive step size LMS adaptive filter is presented. The proposed algorithm utilizes two adaptive filters to estimate gradients accurately, thus achieves good adaptation and performance. Though it uses two LMS adaptive filters, it has a low computational complexity. An active noise cancellation (ANC) system with two applications for extracting heartbeat and lung sound signals from noises is used to simulate the performance of the proposed algorithm.

  3. Sensitivity-based adaptive mesh refinement collocation method for dynamic optimization of chemical and biochemical processes.

    PubMed

    Xiao, Long; Liu, Ping; Liu, Xinggao; Zhang, Zeyin; Wang, Yalin; Yang, Chunhua; Gui, Weihua; Chen, Xu; Zhu, Bochao

    2017-06-07

    Collocation on finite element (CFE) is an effective simultaneous method of dynamic optimization to increase the profitability or productivity of industrial process. The approach needs to select an optimal mesh of time interval to balance the computational cost with desired solution. A new CFE approach with non-uniform refinement procedure based on the sensitivity analysis for dynamic optimization problems is, therefore, proposed, where a subinterval is further refined if the obtained control parameters have significant effect on the performance index. To improve the efficiency, the sensitivities of state parameters with respect to control parameters are derived from the solution of the discretized dynamic system. The proposed method is illustrated by testing two classic dynamic optimization problems from chemical and biochemical engineering. The detailed comparisons among the proposed method, the CFE with uniform mesh, and other reported methods are also carried out. The research results reveal the effectiveness of the proposed approach.

  4. Composite-Grid Techniques and Adaptive Mesh Refinement in Computational Fluid Dynamics

    DTIC Science & Technology

    1990-01-01

    in scope and in quality, as a dissertation for the degree of Doctor of Philosophy. Joel H . Ferziger (Principal Advisor) I certify that I have read...solution as the mesh size goes to zero. In many engineering applications , however, it is considered desirable that the numerical solution for a finite... Application of the BFG Method , International Journal for Numerical Methods in Fluids, Vol. 6, pp. 529-539, 1986 [HEN85] W.D. Henshaw, Part I: The

  5. Unstructured and Adaptive Mesh Generation for High Reynolds Number Viscous Flows

    DTIC Science & Technology

    1991-02-01

    smoothness of the mesh. This solution has been computed using a previously described finite-element Navier-Stokes solver in conjunction with an algebraic ...Computational Geometry, An introducion , Texts and Monographs in Computer Science, Springer-Verlag, 1985. 13. Dyn, N., Levin, D., and Rippa, S., "Data Dependent...F. Thompson, !"ineridge Press 1:1., 1988, pp. 05.1-03. - 12 - 16(. Nlavrip! is, D). J., " Algebraic Turbulence Modeling for- UnstrUiciured and

  6. Optimization of multiple turbine arrays in a channel with tidally reversing flow by numerical modelling with adaptive mesh.

    PubMed

    Divett, T; Vennell, R; Stevens, C

    2013-02-28

    At tidal energy sites, large arrays of hundreds of turbines will be required to generate economically significant amounts of energy. Owing to wake effects within the array, the placement of turbines within will be vital to capturing the maximum energy from the resource. This study presents preliminary results using Gerris, an adaptive mesh flow solver, to investigate the flow through four different arrays of 15 turbines each. The goal is to optimize the position of turbines within an array in an idealized channel. The turbines are represented as areas of increased bottom friction in an adaptive mesh model so that the flow and power capture in tidally reversing flow through large arrays can be studied. The effect of oscillating tides is studied, with interesting dynamics generated as the tidal current reverses direction, forcing turbulent flow through the array. The energy removed from the flow by each of the four arrays is compared over a tidal cycle. A staggered array is found to extract 54 per cent more energy than a non-staggered array. Furthermore, an array positioned to one side of the channel is found to remove a similar amount of energy compared with an array in the centre of the channel.

  7. High-order accurate solution of acoustic-elastic interface problems on adapted meshes using a discontinuous Galerkin method

    NASA Astrophysics Data System (ADS)

    Wilcox, L. C.; Burstedde, C.; Ghattas, O.; Stadler, G.

    2009-12-01

    Our goal is to develop scalable methods for global full-waveform seismic inversion. The first step we have taken towards this goal is the creation of an accurate solver for the numerical simulation of wave propagation in media with fluid-solid interfaces. We have chosen a high-order discontinuous Galerkin (DG) method to effectively eliminate numerical dispersion, enabling simulation over many wave periods. Our numerical method uses a strain-velocity formulation that enables the solution of acoustic and elastic wave equations within the same framework. Careful attention has been directed at the formulation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities and at fluid-solid interfaces. We use adaptive mesh refinement (AMR) to resolve local variations in wave speeds with appropriate element sizes. To study the numerical accuracy and convergence of the proposed method we compare with reference solutions of classical interface problems, including Raleigh waves, Lamb waves, Stoneley waves, Scholte waves, and Love waves. We report strong and weak parallel scaling results for generation of the mesh and solution of the wave equations on adaptively resolved global Earth models.

  8. A Procedure for Empirical Initialization of Adaptive Testing Algorithms.

    ERIC Educational Resources Information Center

    van der Linden, Wim J.

    In constrained adaptive testing, the numbers of constraints needed to control the content of the tests can easily run into the hundreds. Proper initialization of the algorithm becomes a requirement because the presence of large numbers of constraints slows down the convergence of the ability estimator. In this paper, an empirical initialization of…

  9. Adaptation algorithms for 2-D feedforward neural networks.

    PubMed

    Kaczorek, T

    1995-01-01

    The generalized weight adaptation algorithms presented by J.G. Kuschewski et al. (1993) and by S.H. Zak and H.J. Sira-Ramirez (1990) are extended for 2-D madaline and 2-D two-layer feedforward neural nets (FNNs).

  10. Adaptive wavelet transform algorithm for lossy image compression

    NASA Astrophysics Data System (ADS)

    Pogrebnyak, Oleksiy B.; Ramirez, Pablo M.; Acevedo Mosqueda, Marco Antonio

    2004-11-01

    A new algorithm of locally adaptive wavelet transform based on the modified lifting scheme is presented. It performs an adaptation of the wavelet high-pass filter at the prediction stage to the local image data activity. The proposed algorithm uses the generalized framework for the lifting scheme that permits to obtain easily different wavelet filter coefficients in the case of the (~N, N) lifting. Changing wavelet filter order and different control parameters, one can obtain the desired filter frequency response. It is proposed to perform the hard switching between different wavelet lifting filter outputs according to the local data activity estimate. The proposed adaptive transform possesses a good energy compaction. The designed algorithm was tested on different images. The obtained simulation results show that the visual and quantitative quality of the restored images is high. The distortions are less in the vicinity of high spatial activity details comparing to the non-adaptive transform, which introduces ringing artifacts. The designed algorithm can be used for lossy image compression and in the noise suppression applications.

  11. An Adaptive Tradeoff Algorithm for Multi-issue SLA Negotiation

    NASA Astrophysics Data System (ADS)

    Son, Seokho; Sim, Kwang Mong

    Since participants in a Cloud may be independent bodies, mechanisms are necessary for resolving different preferences in leasing Cloud services. Whereas there are currently mechanisms that support service-level agreement negotiation, there is little or no negotiation support for concurrent price and timeslot for Cloud service reservations. For the concurrent price and timeslot negotiation, a tradeoff algorithm to generate and evaluate a proposal which consists of price and timeslot proposal is necessary. The contribution of this work is thus to design an adaptive tradeoff algorithm for multi-issue negotiation mechanism. The tradeoff algorithm referred to as "adaptive burst mode" is especially designed to increase negotiation speed and total utility and to reduce computational load by adaptively generating concurrent set of proposals. The empirical results obtained from simulations carried out using a testbed suggest that due to the concurrent price and timeslot negotiation mechanism with adaptive tradeoff algorithm: 1) both agents achieve the best performance in terms of negotiation speed and utility; 2) the number of evaluations of each proposal is comparatively lower than previous scheme (burst-N).

  12. An Adaptive Homomorphic Aperture Photometry Algorithm for Merging Galaxies

    NASA Astrophysics Data System (ADS)

    Huang, J. C.; Hwang, C. Y.

    2017-03-01

    We present a novel automatic adaptive aperture photometry algorithm for measuring the total magnitudes of merging galaxies with irregular shapes. First, we use a morphological pattern recognition routine for identifying the shape of an irregular source in a background-subtracted image. Then, we extend the shape of the source by using the Dilation image operation to obtain an aperture that is quasi-homomorphic to the shape of the irregular source. The magnitude measured from the homomorphic aperture would thus have minimal contamination from the nearby background. As a test of our algorithm, we applied our technique to the merging galaxies observed by the Sloan Digital Sky Survey and the Canada–France–Hawaii Telescope. Our results suggest that the adaptive homomorphic aperture algorithm can be very useful for investigating extended sources with irregular shapes and sources in crowded regions.

  13. Flight data processing with the F-8 adaptive algorithm

    NASA Technical Reports Server (NTRS)

    Hartmann, G.; Stein, G.; Petersen, K.

    1977-01-01

    An explicit adaptive control algorithm based on maximum likelihood estimation of parameters has been designed for NASA's DFBW F-8 aircraft. To avoid iterative calculations, the algorithm uses parallel channels of Kalman filters operating at fixed locations in parameter space. This algorithm has been implemented in NASA/DFRC's Remotely Augmented Vehicle (RAV) facility. Real-time sensor outputs (rate gyro, accelerometer and surface position) are telemetered to a ground computer which sends new gain values to an on-board system. Ground test data and flight records were used to establish design values of noise statistics and to verify the ground-based adaptive software. The software and its performance evaluation based on flight data are described

  14. An Adaptive Immune Genetic Algorithm for Edge Detection

    NASA Astrophysics Data System (ADS)

    Li, Ying; Bai, Bendu; Zhang, Yanning

    An adaptive immune genetic algorithm (AIGA) based on cost minimization technique method for edge detection is proposed. The proposed AIGA recommends the use of adaptive probabilities of crossover, mutation and immune operation, and a geometric annealing schedule in immune operator to realize the twin goals of maintaining diversity in the population and sustaining the fast convergence rate in solving the complex problems such as edge detection. Furthermore, AIGA can effectively exploit some prior knowledge and information of the local edge structure in the edge image to make vaccines, which results in much better local search ability of AIGA than that of the canonical genetic algorithm. Experimental results on gray-scale images show the proposed algorithm perform well in terms of quality of the final edge image, rate of convergence and robustness to noise.

  15. Adaptive process control using fuzzy logic and genetic algorithms

    NASA Technical Reports Server (NTRS)

    Karr, C. L.

    1993-01-01

    Researchers at the U.S. Bureau of Mines have developed adaptive process control systems in which genetic algorithms (GA's) are used to augment fuzzy logic controllers (FLC's). GA's are search algorithms that rapidly locate near-optimum solutions to a wide spectrum of problems by modeling the search procedures of natural genetics. FLC's are rule based systems that efficiently manipulate a problem environment by modeling the 'rule-of-thumb' strategy used in human decision making. Together, GA's and FLC's possess the capabilities necessary to produce powerful, efficient, and robust adaptive control systems. To perform efficiently, such control systems require a control element to manipulate the problem environment, and a learning element to adjust to the changes in the problem environment. Details of an overall adaptive control system are discussed. A specific laboratory acid-base pH system is used to demonstrate the ideas presented.

  16. Adaptive Process Control with Fuzzy Logic and Genetic Algorithms

    NASA Technical Reports Server (NTRS)

    Karr, C. L.

    1993-01-01

    Researchers at the U.S. Bureau of Mines have developed adaptive process control systems in which genetic algorithms (GA's) are used to augment fuzzy logic controllers (FLC's). GA's are search algorithms that rapidly locate near-optimum solutions to a wide spectrum of problems by modeling the search procedures of natural genetics. FLC's are rule based systems that efficiently manipulate a problem environment by modeling the 'rule-of-thumb' strategy used in human decision-making. Together, GA's and FLC's possess the capabilities necessary to produce powerful, efficient, and robust adaptive control systems. To perform efficiently, such control systems require a control element to manipulate the problem environment, an analysis element to recognize changes in the problem environment, and a learning element to adjust to the changes in the problem environment. Details of an overall adaptive control system are discussed. A specific laboratory acid-base pH system is used to demonstrate the ideas presented.

  17. A new adaptive GMRES algorithm for achieving high accuracy

    SciTech Connect

    Sosonkina, M.; Watson, L.T.; Kapania, R.K.; Walker, H.F.

    1996-12-31

    GMRES(k) is widely used for solving nonsymmetric linear systems. However, it is inadequate either when it converges only for k close to the problem size or when numerical error in the modified Gram-Schmidt process used in the GMRES orthogonalization phase dramatically affects the algorithm performance. An adaptive version of GMRES (k) which tunes the restart value k based on criteria estimating the GMRES convergence rate for the given problem is proposed here. The essence of the adaptive GMRES strategy is to adapt the parameter k to the problem, similar in spirit to how a variable order ODE algorithm tunes the order k. With FORTRAN 90, which provides pointers and dynamic memory management, dealing with the variable storage requirements implied by varying k is not too difficult. The parameter k can be both increased and decreased-an increase-only strategy is described next followed by pseudocode.

  18. Adaptive bad pixel correction algorithm for IRFPA based on PCNN

    NASA Astrophysics Data System (ADS)

    Leng, Hanbing; Zhou, Zuofeng; Cao, Jianzhong; Yi, Bo; Yan, Aqi; Zhang, Jian

    2013-10-01

    Bad pixels and response non-uniformity are the primary obstacles when IRFPA is used in different thermal imaging systems. The bad pixels of IRFPA include fixed bad pixels and random bad pixels. The former is caused by material or manufacture defect and their positions are always fixed, the latter is caused by temperature drift and their positions are always changing. Traditional radiometric calibration-based bad pixel detection and compensation algorithm is only valid to the fixed bad pixels. Scene-based bad pixel correction algorithm is the effective way to eliminate these two kinds of bad pixels. Currently, the most used scene-based bad pixel correction algorithm is based on adaptive median filter (AMF). In this algorithm, bad pixels are regarded as image noise and then be replaced by filtered value. However, missed correction and false correction often happens when AMF is used to handle complex infrared scenes. To solve this problem, a new adaptive bad pixel correction algorithm based on pulse coupled neural networks (PCNN) is proposed. Potential bad pixels are detected by PCNN in the first step, then image sequences are used periodically to confirm the real bad pixels and exclude the false one, finally bad pixels are replaced by the filtered result. With the real infrared images obtained from a camera, the experiment results show the effectiveness of the proposed algorithm.

  19. Adaptive optics image restoration algorithm based on wavefront reconstruction and adaptive total variation method

    NASA Astrophysics Data System (ADS)

    Li, Dongming; Zhang, Lijuan; Wang, Ting; Liu, Huan; Yang, Jinhua; Chen, Guifen

    2016-11-01

    To improve the adaptive optics (AO) image's quality, we study the AO image restoration algorithm based on wavefront reconstruction technology and adaptive total variation (TV) method in this paper. Firstly, the wavefront reconstruction using Zernike polynomial is used for initial estimated for the point spread function (PSF). Then, we develop our proposed iterative solutions for AO images restoration, addressing the joint deconvolution issue. The image restoration experiments are performed to verify the image restoration effect of our proposed algorithm. The experimental results show that, compared with the RL-IBD algorithm and Wiener-IBD algorithm, we can see that GMG measures (for real AO image) from our algorithm are increased by 36.92%, and 27.44% respectively, and the computation time are decreased by 7.2%, and 3.4% respectively, and its estimation accuracy is significantly improved.

  20. Adaptive Flocking of Robot Swarms: Algorithms and Properties

    NASA Astrophysics Data System (ADS)

    Lee, Geunho; Chong, Nak Young

    This paper presents a distributed approach for adaptive flocking of swarms of mobile robots that enables to navigate autonomously in complex environments populated with obstacles. Based on the observation of the swimming behavior of a school of fish, we propose an integrated algorithm that allows a swarm of robots to navigate in a coordinated manner, split into multiple swarms, or merge with other swarms according to the environment conditions. We prove the convergence of the proposed algorithm using Lyapunov stability theory. We also verify the effectiveness of the algorithm through extensive simulations, where a swarm of robots repeats the process of splitting and merging while passing around multiple stationary and moving obstacles. The simulation results show that the proposed algorithm is scalable, and robust to variations in the sensing capability of individual robots.

  1. An adaptive multimeme algorithm for designing HIV multidrug therapies.

    PubMed

    Neri, Ferrante; Toivanen, Jari; Cascella, Giuseppe Leonardo; Ong, Yew-Soon

    2007-01-01

    This paper proposes a period representation for modeling the multidrug HIV therapies and an Adaptive Multimeme Algorithm (AMmA) for designing the optimal therapy. The period representation offers benefits in terms of flexibility and reduction in dimensionality compared to the binary representation. The AMmA is a memetic algorithm which employs a list of three local searchers adaptively activated by an evolutionary framework. These local searchers, having different features according to the exploration logic and the pivot rule, have the role of exploring the decision space from different and complementary perspectives and, thus, assisting the standard evolutionary operators in the optimization process. Furthermore, the AMmA makes use of an adaptation which dynamically sets the algorithmic parameters in order to prevent stagnation and premature convergence. The numerical results demonstrate that the application of the proposed algorithm leads to very efficient medication schedules which quickly stimulate a strong immune response to HIV. The earlier termination of the medication schedule leads to lesser unpleasant side effects for the patient due to strong antiretroviral therapy. A numerical comparison shows that the AMmA is more efficient than three popular metaheuristics. Finally, a statistical test based on the calculation of the tolerance interval confirms the superiority of the AMmA compared to the other methods for the problem under study.

  2. An Adaptive Hybrid Genetic Algorithm for Improved Groundwater Remediation Design

    NASA Astrophysics Data System (ADS)

    Espinoza, F. P.; Minsker, B. S.; Goldberg, D. E.

    2001-12-01

    Identifying optimal designs for a groundwater remediation system is computationally intensive, especially for complex, nonlinear problems such as enhanced in situ bioremediation technology. To improve performance, we apply a hybrid genetic algorithm (HGA), which is a two-step solution method: a genetic algorithm (GA) for global search using the entire population and then a local search (LS) to improve search speed for only a few individuals in the population. We implement two types of HGAs: a non-adaptive HGA (NAHGA), whose operations are invariant throughout the run, and a self-adaptive HGA (SAHGA), whose operations adapt to the performance of the algorithm. The best settings of the two HGAs for optimal performance are then investigated for a groundwater remediation problem. The settings include the frequency of LS with respect to the normal GA evaluation, probability of individual selection for LS, evolution criterion for LS (Lamarckian or Baldwinian), and number of local search iterations. A comparison of the algorithms' performance under different settings will be presented.

  3. Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

    NASA Technical Reports Server (NTRS)

    Barth, Timothy; Chancellor, Marisa K. (Technical Monitor)

    1997-01-01

    Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.

  4. An adaptive grid algorithm for one-dimensional nonlinear equations

    NASA Technical Reports Server (NTRS)

    Gutierrez, William E.; Hills, Richard G.

    1990-01-01

    Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and

  5. Efficient implementation of the adaptive scale pixel decomposition algorithm

    NASA Astrophysics Data System (ADS)

    Zhang, L.; Bhatnagar, S.; Rau, U.; Zhang, M.

    2016-08-01

    Context. Most popular algorithms in use to remove the effects of a telescope's point spread function (PSF) in radio astronomy are variants of the CLEAN algorithm. Most of these algorithms model the sky brightness using the delta-function basis, which results in undesired artefacts when used to image extended emission. The adaptive scale pixel decomposition (Asp-Clean) algorithm models the sky brightness on a scale-sensitive basis and thus gives a significantly better imaging performance when imaging fields that contain both resolved and unresolved emission. Aims: However, the runtime cost of Asp-Clean is higher than that of scale-insensitive algorithms. In this paper, we identify the most expensive step in the original Asp-Clean algorithm and present an efficient implementation of it, which significantly reduces the computational cost while keeping the imaging performance comparable to the original algorithm. The PSF sidelobe levels of modern wide-band telescopes are significantly reduced, allowing us to make approximations to reduce the computational cost, which in turn allows for the deconvolution of larger images on reasonable timescales. Methods: As in the original algorithm, scales in the image are estimated through function fitting. Here we introduce an analytical method to model extended emission, and a modified method for estimating the initial values used for the fitting procedure, which ultimately leads to a lower computational cost. Results: The new implementation was tested with simulated EVLA data and the imaging performance compared well with the original Asp-Clean algorithm. Tests show that the current algorithm can recover features at different scales with lower computational cost.

  6. Estimating meme fitness in adaptive memetic algorithms for combinatorial problems.

    PubMed

    Smith, J E

    2012-01-01

    Among the most promising and active research areas in heuristic optimisation is the field of adaptive memetic algorithms (AMAs). These gain much of their reported robustness by adapting the probability with which each of a set of local improvement operators is applied, according to an estimate of their current value to the search process. This paper addresses the issue of how the current value should be estimated. Assuming the estimate occurs over several applications of a meme, we consider whether the extreme or mean improvements should be used, and whether this aggregation should be global, or local to some part of the solution space. To investigate these issues, we use the well-established COMA framework that coevolves the specification of a population of memes (representing different local search algorithms) alongside a population of candidate solutions to the problem at hand. Two very different memetic algorithms are considered: the first using adaptive operator pursuit to adjust the probabilities of applying a fixed set of memes, and a second which applies genetic operators to dynamically adapt and create memes and their functional definitions. For the latter, especially on combinatorial problems, credit assignment mechanisms based on historical records, or on notions of landscape locality, will have limited application, and it is necessary to estimate the value of a meme via some form of sampling. The results on a set of binary encoded combinatorial problems show that both methods are very effective, and that for some problems it is necessary to use thousands of variables in order to tease apart the differences between different reward schemes. However, for both memetic algorithms, a significant pattern emerges that reward based on mean improvement is better than that based on extreme improvement. This contradicts recent findings from adapting the parameters of operators involved in global evolutionary search. The results also show that local reward schemes

  7. PHURBAS: AN ADAPTIVE, LAGRANGIAN, MESHLESS, MAGNETOHYDRODYNAMICS CODE. I. ALGORITHM

    SciTech Connect

    Maron, Jason L.; McNally, Colin P.; Mac Low, Mordecai-Mark E-mail: cmcnally@amnh.org

    2012-05-01

    We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial interpolations (Moving Least Squares interpolations) are calculated from the field values of neighboring particles to obtain field values and spatial derivatives at the particle position. Field values and particle positions are advanced in time with a second-order predictor-corrector scheme. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is implemented to ensure the particles fill the computational volume, which gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. Particle addition and deletion is based on a local void and clump detection algorithm. Dynamic artificial viscosity fields provide stability to the integration. The resulting algorithm provides a robust solution for modeling flows that require Lagrangian or adaptive discretizations to resolve. This paper derives and documents the Phurbas algorithm as implemented in Phurbas version 1.1. A following paper presents the implementation and test problem results.

  8. Modelling of fluid-solid interactions using an adaptive mesh fluid model coupled with a combined finite-discrete element model

    NASA Astrophysics Data System (ADS)

    Viré, Axelle; Xiang, Jiansheng; Milthaler, Frank; Farrell, Patrick Emmet; Piggott, Matthew David; Latham, John-Paul; Pavlidis, Dimitrios; Pain, Christopher Charles

    2012-12-01

    Fluid-structure interactions are modelled by coupling the finite element fluid/ocean model `Fluidity-ICOM' with a combined finite-discrete element solid model `Y3D'. Because separate meshes are used for the fluids and solids, the present method is flexible in terms of discretisation schemes used for each material. Also, it can tackle multiple solids impacting on one another, without having ill-posed problems in the resolution of the fluid's equations. Importantly, the proposed approach ensures that Newton's third law is satisfied at the discrete level. This is done by first computing the action-reaction force on a supermesh, i.e. a function superspace of the fluid and solid meshes, and then projecting it to both meshes to use it as a source term in the fluid and solid equations. This paper demonstrates the properties of spatial conservation and accuracy of the method for a sphere immersed in a fluid, with prescribed fluid and solid velocities. While spatial conservation is shown to be independent of the mesh resolutions, accuracy requires fine resolutions in both fluid and solid meshes. It is further highlighted that unstructured meshes adapted to the solid concentration field reduce the numerical errors, in comparison with uniformly structured meshes with the same number of elements. The method is verified on flow past a falling sphere. Its potential for ocean applications is further shown through the simulation of vortex-induced vibrations of two cylinders and the flow past two flexible fibres.

  9. Landsat ecosystem disturbance adaptive processing system (LEDAPS) algorithm description

    USGS Publications Warehouse

    Schmidt, Gail; Jenkerson, Calli; Masek, Jeffrey; Vermote, Eric; Gao, Feng

    2013-01-01

    The Landsat Ecosystem Disturbance Adaptive Processing System (LEDAPS) software was originally developed by the National Aeronautics and Space Administration–Goddard Space Flight Center and the University of Maryland to produce top-of-atmosphere reflectance from LandsatThematic Mapper and Enhanced Thematic Mapper Plus Level 1 digital numbers and to apply atmospheric corrections to generate a surface-reflectance product.The U.S. Geological Survey (USGS) has adopted the LEDAPS algorithm for producing the Landsat Surface Reflectance Climate Data Record.This report discusses the LEDAPS algorithm, which was implemented by the USGS.

  10. 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.

  11. Self-adaptive incremental Newton-Raphson algorithms

    NASA Technical Reports Server (NTRS)

    Padovan, J.

    1980-01-01

    Multilevel self-adaptive Newton-Raphson type strategies are developed to improve the solution efficiency of nonlinear finite element simulations of statically loaded structures. The overall strategy involves three basic levels. The first level involves preliminary solution tunneling via primative operators. Secondly, the solution is constantly monitored via quality/convergence/nonlinearity tests. Lastly, the third level involves self-adaptive algorithmic update procedures aimed at improving the convergence characteristics of the Newton-Raphson strategy. Numerical experiments are included to illustrate the results of the procedure.

  12. Algorithms for Zonal Methods and Development of Three Dimensional Mesh Generation Procedures.

    DTIC Science & Technology

    1984-02-01

    zonal methods and 4D-grid generation procedures for application of finite difference methods to solve complex aircraft con- figurations. For the task...this research has been to further develop grid generation procedures and zonal methods so as to extend the applications of nonlinear finite difference ...C - - A CHIMERA GRID SCHEME .................... 51 APPENDIX D - - A CONSERVATIVE FINITE DIFFERENCE ALGORITHM FOR THE UNSTEADY TRANSONIC POTENTIAL

  13. Implementation of Interaction Algorithm to Non-Matching Discrete Interfaces Between Structure and Fluid Mesh

    NASA Technical Reports Server (NTRS)

    Chen, Shu-Po

    1999-01-01

    This paper presents software for solving the non-conforming fluid structure interfaces in aeroelastic simulation. It reviews the algorithm of interpolation and integration, highlights the flexibility and the user-friendly feature that allows the user to select the existing structure and fluid package, like NASTRAN and CLF3D, to perform the simulation. The presented software is validated by computing the High Speed Civil Transport model.

  14. A Novel Adaptive Frequency Estimation Algorithm Based on Interpolation FFT and Improved Adaptive Notch Filter

    NASA Astrophysics Data System (ADS)

    Shen, Ting-ao; Li, Hua-nan; Zhang, Qi-xin; Li, Ming

    2017-02-01

    The convergence rate and the continuous tracking precision are two main problems of the existing adaptive notch filter (ANF) for frequency tracking. To solve the problems, the frequency is detected by interpolation FFT at first, which aims to overcome the convergence rate of the ANF. Then, referring to the idea of negative feedback, an evaluation factor is designed to monitor the ANF parameters and realize continuously high frequency tracking accuracy. According to the principle, a novel adaptive frequency estimation algorithm based on interpolation FFT and improved ANF is put forward. Its basic idea, specific measures and implementation steps are described in detail. The proposed algorithm obtains a fast estimation of the signal frequency, higher accuracy and better universality qualities. Simulation results verified the superiority and validity of the proposed algorithm when compared with original algorithms.

  15. Application of Quaternions for Mesh

    NASA Technical Reports Server (NTRS)

    Samareh, Jamshid A.

    2002-01-01

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

  16. N-body simulations for f(R) gravity using a self-adaptive particle-mesh code

    SciTech Connect

    Zhao Gongbo; Koyama, Kazuya; Li Baojiu

    2011-02-15

    We perform high-resolution N-body simulations for f(R) gravity based on a self-adaptive particle-mesh code MLAPM. The chameleon mechanism that recovers general relativity on small scales is fully taken into account by self-consistently solving the nonlinear equation for the scalar field. We independently confirm the previous simulation results, including the matter power spectrum, halo mass function, and density profiles, obtained by Oyaizu et al.[Phys. Rev. D 78, 123524 (2008)] and Schmidt et al.[Phys. Rev. D 79, 083518 (2009)], and extend the resolution up to k{approx}20 h/Mpc for the measurement of the matter power spectrum. Based on our simulation results, we discuss how the chameleon mechanism affects the clustering of dark matter and halos on full nonlinear scales.

  17. THREE-DIMENSIONAL ADAPTIVE MESH REFINEMENT SIMULATIONS OF LONG-DURATION GAMMA-RAY BURST JETS INSIDE MASSIVE PROGENITOR STARS

    SciTech Connect

    Lopez-Camara, D.; Lazzati, Davide; Morsony, Brian J.; Begelman, Mitchell C.

    2013-04-10

    We present the results of special relativistic, adaptive mesh refinement, 3D simulations of gamma-ray burst jets expanding inside a realistic stellar progenitor. Our simulations confirm that relativistic jets can propagate and break out of the progenitor star while remaining relativistic. This result is independent of the resolution, even though the amount of turbulence and variability observed in the simulations is greater at higher resolutions. We find that the propagation of the jet head inside the progenitor star is slightly faster in 3D simulations compared to 2D ones at the same resolution. This behavior seems to be due to the fact that the jet head in 3D simulations can wobble around the jet axis, finding the spot of least resistance to proceed. Most of the average jet properties, such as density, pressure, and Lorentz factor, are only marginally affected by the dimensionality of the simulations and therefore results from 2D simulations can be considered reliable.

  18. Advanced Dynamically Adaptive Algorithms for Stochastic Simulations on Extreme Scales

    SciTech Connect

    Xiu, Dongbin

    2016-06-21

    The focus of the project is the development of mathematical methods and high-performance com- putational tools for stochastic simulations, with a particular emphasis on computations on extreme scales. The core of the project revolves around the design of highly e cient and scalable numer- ical algorithms that can adaptively and accurately, in high dimensional spaces, resolve stochastic problems with limited smoothness, even containing discontinuities.

  19. Adaptive primal-dual genetic algorithms in dynamic environments.

    PubMed

    Wang, Hongfeng; Yang, Shengxiang; Ip, W H; Wang, Dingwei

    2009-12-01

    Recently, there has been an increasing interest in applying genetic algorithms (GAs) in dynamic environments. Inspired by the complementary and dominance mechanisms in nature, a primal-dual GA (PDGA) has been proposed for dynamic optimization problems (DOPs). In this paper, an important operator in PDGA, i.e., the primal-dual mapping (PDM) scheme, is further investigated to improve the robustness and adaptability of PDGA in dynamic environments. In the improved scheme, two different probability-based PDM operators, where the mapping probability of each allele in the chromosome string is calculated through the statistical information of the distribution of alleles in the corresponding gene locus over the population, are effectively combined according to an adaptive Lamarckian learning mechanism. In addition, an adaptive dominant replacement scheme, which can probabilistically accept inferior chromosomes, is also introduced into the proposed algorithm to enhance the diversity level of the population. Experimental results on a series of dynamic problems generated from several stationary benchmark problems show that the proposed algorithm is a good optimizer for DOPs.

  20. Progress report on the wisker weaving all-hexahedral meshing algorithm

    SciTech Connect

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

    1996-02-01

    In this paper, a review of the Spatial Twist Contiuum and the basic whisker weaving algorithm are given. Progress in the detection and resolution of several types of degeneracies formed by whisker weaving are discussed. These examples include so-called knife doublets, triple doublets, through-cells and through-chords. Knife doublets and triple doublets are resolved by preventing their formation a-priori, which forces whisker weaving to remove the element(s) causing the degeneracy. Through-chords and through-cells are left in the weave and resolved after the weave has been closed. The paper concludes with three examples of geometries ``closed`` by whisker weaving.

  1. Adaptive Load-Balancing Algorithms Using Symmetric Broadcast Networks

    NASA Technical Reports Server (NTRS)

    Das, Sajal K.; Biswas, Rupak; Chancellor, Marisa K. (Technical Monitor)

    1997-01-01

    In a distributed-computing environment, it is important to ensure that the processor workloads are adequately balanced. Among numerous load-balancing algorithms, a unique approach due to Dam and Prasad defines a symmetric broadcast network (SBN) that provides a robust communication pattern among the processors in a topology-independent manner. In this paper, we propose and analyze three novel SBN-based load-balancing algorithms, and implement them on an SP2. A thorough experimental study with Poisson-distributed synthetic loads demonstrates that these algorithms are very effective in balancing system load while minimizing processor idle time. They also compare favorably with several other existing load-balancing techniques. Additional experiments performed with real data demonstrate that the SBN approach is effective in adaptive computational science and engineering applications where dynamic load balancing is extremely crucial.

  2. Adaptive Firefly Algorithm: Parameter Analysis and its Application

    PubMed Central

    Shen, Hong-Bin

    2014-01-01

    As a nature-inspired search algorithm, firefly algorithm (FA) has several control parameters, which may have great effects on its performance. In this study, we investigate the parameter selection and adaptation strategies in a modified firefly algorithmadaptive firefly algorithm (AdaFa). There are three strategies in AdaFa including (1) a distance-based light absorption coefficient; (2) a gray coefficient enhancing fireflies to share difference information from attractive ones efficiently; and (3) five different dynamic strategies for the randomization parameter. Promising selections of parameters in the strategies are analyzed to guarantee the efficient performance of AdaFa. AdaFa is validated over widely used benchmark functions, and the numerical experiments and statistical tests yield useful conclusions on the strategies and the parameter selections affecting the performance of AdaFa. When applied to the real-world problem — protein tertiary structure prediction, the results demonstrated improved variants can rebuild the tertiary structure with the average root mean square deviation less than 0.4Å and 1.5Å from the native constrains with noise free and 10% Gaussian white noise. PMID:25397812

  3. An adaptive gyroscope-based algorithm for temporal gait analysis.

    PubMed

    Greene, Barry R; McGrath, Denise; O'Neill, Ross; O'Donovan, Karol J; Burns, Adrian; Caulfield, Brian

    2010-12-01

    Body-worn kinematic sensors have been widely proposed as the optimal solution for portable, low cost, ambulatory monitoring of gait. This study aims to evaluate an adaptive gyroscope-based algorithm for automated temporal gait analysis using body-worn wireless gyroscopes. Gyroscope data from nine healthy adult subjects performing four walks at four different speeds were then compared against data acquired simultaneously using two force plates and an optical motion capture system. Data from a poliomyelitis patient, exhibiting pathological gait walking with and without the aid of a crutch, were also compared to the force plate. Results show that the mean true error between the adaptive gyroscope algorithm and force plate was -4.5 ± 14.4 ms and 43.4 ± 6.0 ms for IC and TC points, respectively, in healthy subjects. Similarly, the mean true error when data from the polio patient were compared against the force plate was -75.61 ± 27.53 ms and 99.20 ± 46.00 ms for IC and TC points, respectively. A comparison of the present algorithm against temporal gait parameters derived from an optical motion analysis system showed good agreement for nine healthy subjects at four speeds. These results show that the algorithm reported here could constitute the basis of a robust, portable, low-cost system for ambulatory monitoring of gait.

  4. Adaptive firefly algorithm: parameter analysis and its application.

    PubMed

    Cheung, Ngaam J; Ding, Xue-Ming; Shen, Hong-Bin

    2014-01-01

    As a nature-inspired search algorithm, firefly algorithm (FA) has several control parameters, which may have great effects on its performance. In this study, we investigate the parameter selection and adaptation strategies in a modified firefly algorithm - adaptive firefly algorithm (AdaFa). There are three strategies in AdaFa including (1) a distance-based light absorption coefficient; (2) a gray coefficient enhancing fireflies to share difference information from attractive ones efficiently; and (3) five different dynamic strategies for the randomization parameter. Promising selections of parameters in the strategies are analyzed to guarantee the efficient performance of AdaFa. AdaFa is validated over widely used benchmark functions, and the numerical experiments and statistical tests yield useful conclusions on the strategies and the parameter selections affecting the performance of AdaFa. When applied to the real-world problem - protein tertiary structure prediction, the results demonstrated improved variants can rebuild the tertiary structure with the average root mean square deviation less than 0.4Å and 1.5Å from the native constrains with noise free and 10% Gaussian white noise.

  5. Generalized pattern search algorithms with adaptive precision function evaluations

    SciTech Connect

    Polak, Elijah; Wetter, Michael

    2003-05-14

    In the literature on generalized pattern search algorithms, convergence to a stationary point of a once continuously differentiable cost function is established under the assumption that the cost function can be evaluated exactly. However, there is a large class of engineering problems where the numerical evaluation of the cost function involves the solution of systems of differential algebraic equations. Since the termination criteria of the numerical solvers often depend on the design parameters, computer code for solving these systems usually defines a numerical approximation to the cost function that is discontinuous with respect to the design parameters. Standard generalized pattern search algorithms have been applied heuristically to such problems, but no convergence properties have been stated. In this paper we extend a class of generalized pattern search algorithms to a form that uses adaptive precision approximations to the cost function. These numerical approximations need not define a continuous function. Our algorithms can be used for solving linearly constrained problems with cost functions that are at least locally Lipschitz continuous. Assuming that the cost function is smooth, we prove that our algorithms converge to a stationary point. Under the weaker assumption that the cost function is only locally Lipschitz continuous, we show that our algorithms converge to points at which the Clarke generalized directional derivatives are nonnegative in predefined directions. An important feature of our adaptive precision scheme is the use of coarse approximations in the early iterations, with the approximation precision controlled by a test. Such an approach leads to substantial time savings in minimizing computationally expensive functions.

  6. G/SPLINES: A hybrid of Friedman's Multivariate Adaptive Regression Splines (MARS) algorithm with Holland's genetic algorithm

    NASA Technical Reports Server (NTRS)

    Rogers, David

    1991-01-01

    G/SPLINES are a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm with Holland's Genetic Algorithm. In this hybrid, the incremental search is replaced by a genetic search. The G/SPLINE algorithm exhibits performance comparable to that of the MARS algorithm, requires fewer least squares computations, and allows significantly larger problems to be considered.

  7. Using Subdivision Surfaces and Adaptive Surface Simplification Algorithms for Modeling Chemical Heterogeneities in Geophysical Flows

    NASA Astrophysics Data System (ADS)

    Schmalzl, J.

    2003-04-01

    Convective flows govern much of the dynamics of the Earth. Examples of such flows are convection in the Earth's mantle, convection in magma chambers and much of the dynamics of the world oceans. Nowadays these time-dependent flows are often studied by means of three dimensional (3D) numerical models which solve the equations for the transport of heat and momentum alternatingly. These flows are often driven by a temperature difference. But for many flows there is also an active or passive chemical component that has to be considered. One characteristics of these flows is that the chemical diffusivity is very small. Implementing such a chemical field with a very low diffusivity into a numerical model using a field approach is difficult due to numerical diffusion introduced by the Eulerian schemes. Using Lagrangian tracers is also difficult in 3D flow since a massive amount of tracers is needed. We therefore have implemented a tracer-mesh method which tracks only the position of the interface between the two different components. Compared to a 2D tracer-line the insertion of new 3D surface-elements in highly deformed regions is however more complex. This is due to the topology of the mesh which changes because of the adaptive refinement. Luckily the refinement of polygonal meshes is a very active field of research in computer graphics and has been termed "Subdivision Surfaces". There is a wealth of different subdivision schemes with different properties. We applied the Butterfly scheme and the Loop scheme for the refinement of tracer meshes. When a density difference is connected to a chemical component it often acts as a restoring force. In many cases, the governing flow is spatially heterogenous and the spatial location of the heterogeneities is varying in time (e.g. the location of an upwelling plume). The restoring force of the density contrast may result in a situation where a highly deformed, and therefore highly refined region, returns to a simple geometry. In

  8. Using Subdivision Surfaces and Adaptive Surface Simplification Algorithms for Modeling Chemical Heterogeneities in Geophysical Flows

    NASA Astrophysics Data System (ADS)

    Schmalzl, J.; Loddoch, A.

    2003-12-01

    Convective flows govern much of the dynamics of the Earth. Examples of such flows are convection in the Earth's mantle, convection in magma chambers and much of the dynamics of the world oceans. Nowadays these time-dependent flows are often studied by means of three dimensional (3D) numerical models which solve the equations for the transport of heat and momentum alternatingly. These flows are often driven by a temperature difference. But for many flows there is also an active or passive chemical component that has to be considered. One characteristics of these flows is that the chemical diffusivity is very small. Implementing such a chemical field with a very low diffusivity into a numerical model using a field approach is difficult due to numerical diffusion introduced by the Eulerian schemes. Using Lagrangian tracers is also difficult in 3D flow since a massive amount of tracers is needed. We therefore have implemented a tracer-mesh method which tracks only the position of the interface between the two different components. Compared to a 2D tracer-line the insertion of new 3D surface-elements in highly deformed regions is however more complex. This is due to the topology of the mesh which changes because of the adaptive refinement. Luckily the refinement of polygonal meshes is a very active field of research in computer graphics and has been termed "Subdivision Surfaces". There is a wealth of different subdivision schemes with different properties. We applied the Butterfly scheme and the Loop scheme for the refinement of tracer meshes. When a density difference is connected to a chemical component it often acts as a restoring force. In many cases, the governing flow is spatially heterogenous and the spatial location of the heterogeneities is varying in time (e.g. the location of an upwelling plume). The restoring force of the density contrast may result in a situation where a highly deformed, and therefore highly refined region, returns to a simple geometry. In

  9. Polyhedral shape model for terrain correction of gravity and gravity gradient data based on an adaptive mesh

    NASA Astrophysics Data System (ADS)

    Guo, Zhikui; Chen, Chao; Tao, Chunhui

    2016-04-01

    Since 2007, there are four China Da yang cruises (CDCs), which have been carried out to investigate polymetallic sulfides in the southwest Indian ridge (SWIR) and have acquired both gravity data and bathymetry data on the corresponding survey lines(Tao et al., 2014). Sandwell et al. (2014) published a new global marine gravity model including the free air gravity data and its first order vertical gradient (Vzz). Gravity data and its gradient can be used to extract unknown density structure information(e.g. crust thickness) under surface of the earth, but they contain all the mass effect under the observation point. Therefore, how to get accurate gravity and its gradient effect of the existing density structure (e.g. terrain) has been a key issue. Using the bathymetry data or ETOPO1 (http://www.ngdc.noaa.gov/mgg/global/global.html) model at a full resolution to calculate the terrain effect could spend too much computation time. We expect to develop an effective method that takes less time but can still yield the desired accuracy. In this study, a constant-density polyhedral model is used to calculate the gravity field and its vertical gradient, which is based on the work of Tsoulis (2012). According to gravity field attenuation with distance and variance of bathymetry, we present an adaptive mesh refinement and coarsening strategies to merge both global topography data and multi-beam bathymetry data. The local coarsening or size of mesh depends on user-defined accuracy and terrain variation (Davis et al., 2011). To depict terrain better, triangular surface element and rectangular surface element are used in fine and coarse mesh respectively. This strategy can also be applied to spherical coordinate in large region and global scale. Finally, we applied this method to calculate Bouguer gravity anomaly (BGA), mantle Bouguer anomaly(MBA) and their vertical gradient in SWIR. Further, we compared the result with previous results in the literature. Both synthetic model

  10. A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries

    NASA Astrophysics Data System (ADS)

    Nivarti, Girish V.; Salehi, M. Mahdi; Bushe, W. Kendal

    2015-01-01

    A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton order curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.

  11. A general boundary capability embedded in an orthogonal mesh

    SciTech Connect

    Hewett, D.W.; Yu-Jiuan Chen

    1995-07-01

    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.

  12. 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.

  13. 3-D grid refinement using the University of Michigan adaptive mesh library for a pure advective test

    NASA Astrophysics Data System (ADS)

    Oehmke, R.; Vandenberg, D.; Andronova, N.; Penner, J.; Stout, Q.; Zubov, V.; Jablonowski, C.

    2008-05-01

    The numerical representation of the partial differential equations (PDE) for high resolution atmospheric dynamical and physical features requires division of the atmospheric volume into a set of 3D grids, each of which has a not quite rectangular form. Each location on the grid contains multiple data that together represent the state of Earth's atmosphere. For successful numerical integration of the PDEs the size of each grid box is used to define the Courant-Friedrichs-Levi criterion in setting the time step. 3D adaptive representations of a sphere are needed to represent the evolution of clouds. In this paper we present the University of Michigan adaptive mesh library - a library that supports the production of parallel codes with use of adaptation on a sphere. The library manages the block-structured data layout, handles ghost cell updates among neighboring blocks and splits blocks 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. Users provide data manipulation functions for performing interpolation of user data when refining blocks. We rigorously test the library using refinement of the modeled vertical transport of a tracer with prescribed atmospheric sources and sinks. It is both a 2 and a 3D test, and bridges the performance of the model's dynamics and physics needed for inclusion of cloud formation.

  14. Analysis of adaptive algorithms for an integrated communication network

    NASA Technical Reports Server (NTRS)

    Reed, Daniel A.; Barr, Matthew; Chong-Kwon, Kim

    1985-01-01

    Techniques were examined that trade communication bandwidth for decreased transmission delays. When the network is lightly used, these schemes attempt to use additional network resources to decrease communication delays. As the network utilization rises, the schemes degrade gracefully, still providing service but with minimal use of the network. Because the schemes use a combination of circuit and packet switching, they should respond to variations in the types and amounts of network traffic. Also, a combination of circuit and packet switching to support the widely varying traffic demands imposed on an integrated network was investigated. The packet switched component is best suited to bursty traffic where some delays in delivery are acceptable. The circuit switched component is reserved for traffic that must meet real time constraints. Selected packet routing algorithms that might be used in an integrated network were simulated. An integrated traffic places widely varying workload demands on a network. Adaptive algorithms were identified, ones that respond to both the transient and evolutionary changes that arise in integrated networks. A new algorithm was developed, hybrid weighted routing, that adapts to workload changes.

  15. Medical case-based retrieval: integrating query MeSH terms for query-adaptive multi-modal fusion

    NASA Astrophysics Data System (ADS)

    Seco de Herrera, Alba G.; Foncubierta-Rodríguez, Antonio; Müller, Henning

    2015-03-01

    Advances in medical knowledge give clinicians more objective information for a diagnosis. Therefore, there is an increasing need for bibliographic search engines that can provide services helping to facilitate faster information search. The ImageCLEFmed benchmark proposes a medical case-based retrieval task. This task aims at retrieving articles from the biomedical literature that are relevant for differential diagnosis of query cases including a textual description and several images. In the context of this campaign many approaches have been investigated showing that the fusion of visual and text information can improve the precision of the retrieval. However, fusion does not always lead to better results. In this paper, a new query-adaptive fusion criterion to decide when to use multi-modal (text and visual) or only text approaches is presented. The proposed method integrates text information contained in MeSH (Medical Subject Headings) terms extracted and visual features of the images to find synonym relations between them. Given a text query, the query-adaptive fusion criterion decides when it is suitable to also use visual information for the retrieval. Results show that this approach can decide if a text or multi{modal approach should be used with 77.15% of accuracy.

  16. Constrained-Transport Magnetohydrodynamics with Adaptive-Mesh-Refinement in CHARM

    SciTech Connect

    Miniatii, Francesco; Martin, Daniel

    2011-05-24

    We present the implementation of a three-dimensional, second order accurate Godunov-type algorithm for magneto-hydrodynamic (MHD), in the adaptivemesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit Corner-Transport-Upwind (CTU) scheme. Thefluid quantities are cell-centered and are updated using the Piecewise-Parabolic- Method (PPM), while the magnetic field variables are face-centered and areevolved through application of the Stokes theorem on cell edges via a Constrained- Transport (CT) method. The so-called ?multidimensional MHD source terms?required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracyor robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These includeface-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. Thecode is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests,a three-dimensional shock-cloud interaction problem and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence isshown to remain negligible throughout. Subject headings: cosmology: theory - methods: numerical

  17. Statistical behaviour of adaptive multilevel splitting algorithms in simple models

    NASA Astrophysics Data System (ADS)

    Rolland, Joran; Simonnet, Eric

    2015-02-01

    Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to direct transitions from one metastable state to another. The algorithm is based on successive selection-mutation steps performed on the system in a controlled way. It has two intrinsic parameters, the number of particles/trajectories and the reaction coordinate used for discriminating good or bad trajectories. We investigate first the convergence in law of the algorithm as a function of the timestep for several simple stochastic models. Second, we consider the average duration of reactive trajectories for which no theoretical predictions exist. The most important aspect of this work concerns some systems with two degrees of freedom. They are studied in detail as a function of the reaction coordinate in the asymptotic regime where the number of trajectories goes to infinity. We show that during phase transitions, the statistics of the algorithm deviate significatively from known theoretical results when using non-optimal reaction coordinates. In this case, the variance of the algorithm is peaking at the transition and the convergence of the algorithm can be much slower than the usual expected central limit behaviour. The duration of trajectories is affected as well. Moreover, reactive trajectories do not correspond to the most probable ones. Such behaviour disappears when using the optimal reaction coordinate called committor as predicted by the theory. We finally investigate a three-state Markov chain which reproduces this phenomenon and show logarithmic convergence of the trajectory durations.

  18. Statistical behaviour of adaptive multilevel splitting algorithms in simple models

    SciTech Connect

    Rolland, Joran Simonnet, Eric

    2015-02-15

    Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to direct transitions from one metastable state to another. The algorithm is based on successive selection–mutation steps performed on the system in a controlled way. It has two intrinsic parameters, the number of particles/trajectories and the reaction coordinate used for discriminating good or bad trajectories. We investigate first the convergence in law of the algorithm as a function of the timestep for several simple stochastic models. Second, we consider the average duration of reactive trajectories for which no theoretical predictions exist. The most important aspect of this work concerns some systems with two degrees of freedom. They are studied in detail as a function of the reaction coordinate in the asymptotic regime where the number of trajectories goes to infinity. We show that during phase transitions, the statistics of the algorithm deviate significatively from known theoretical results when using non-optimal reaction coordinates. In this case, the variance of the algorithm is peaking at the transition and the convergence of the algorithm can be much slower than the usual expected central limit behaviour. The duration of trajectories is affected as well. Moreover, reactive trajectories do not correspond to the most probable ones. Such behaviour disappears when using the optimal reaction coordinate called committor as predicted by the theory. We finally investigate a three-state Markov chain which reproduces this phenom