Parallel Adaptive Mesh Refinement Algorithms For Unstructured 2d Meshes
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Parallel Adaptive Mesh Refinement Algorithms For Unstructured 2d Meshes
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Author : Mustafa Keskin
language : en
Publisher:
Release Date : 1994
Parallel Adaptive Mesh Refinement Algorithms For Unstructured 2d Meshes written by Mustafa Keskin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Adaptive Mesh Refinement Algorithms For Parallel Unstructured Finite Element Codes
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Author : J. M. Solberg
language : en
Publisher:
Release Date : 2006
Adaptive Mesh Refinement Algorithms For Parallel Unstructured Finite Element Codes written by J. M. Solberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
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.
Parallel Algorithms For The Adaptive Refinement And Partitioning Of Unstructured Meshes
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Author :
language : en
Publisher:
Release Date : 1994
Parallel Algorithms For The Adaptive Refinement And Partitioning Of Unstructured Meshes written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
The efficient solution of many large-scale scientific calculations depends on adaptive mesh strategies. In this paper we present new parallel algorithms to solve two significant problems that arise in this context: the generation of the adaptive mesh and the mesh partitioning. The crux of our refinement algorithm is the identification of independent sets of elements that can be refined in parallel. The objective of our partitioning heuristic is to construct partitions with good aspect rations. We present run-time bounds and computational results obtained on the Intel DELTA for these algorithms. These results demonstrate that the algorithms exhibit scalable performance and have run-times small in comparison with other aspects of the computation.
Parallel Adaptive Mesh Refinement And Redistribution On Distributed Memory Computers
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Author :
language : en
Publisher:
Release Date : 1993
Parallel Adaptive Mesh Refinement And Redistribution On Distributed Memory Computers written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
A procedure to support parallel refinement and redistribution of two dimensional unstructured finite element meshes on distributed memory computers is presented. The procedure uses the mesh topological entity hierarchy as the underlying data structures to easily support the required adjacency information. Mesh refinement is done by employing links back to the geometric representation to place new nodes on the boundary of the domain directly on the curved geometry. The refined mesh is then redistributed by an iterative heuristic based on the Leiss/Reddy 9 load balancing criteria. A fast parallel tree edge-coloring algorithm is used to pair processors having adjacent partitions and forming a tree structure as a result of Leiss/Reddy load request criteria. Excess elements are iteratively migrated from heavily loaded to less loaded processors until load balancing is achieved. The system is implemented on a massively parallel MasPar MP-1 system with a SIMD style of computation and uses message passing primitives to migrate elements during the mesh redistribution phase. Performance results of the redistribution heuristics on various test meshes are given.
Adaptive Mesh Refinement Theory And Applications
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Author : Tomasz Plewa
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-20
Adaptive Mesh Refinement Theory And Applications written by Tomasz Plewa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-20 with Mathematics categories.
Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.
Parallel Adaptive Mesh Refinement
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Author :
language : en
Publisher:
Release Date : 2005
Parallel Adaptive Mesh Refinement written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
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 ability of both meshing methods to resolve simulation details by varying the local grid spacing.
Adaptive Mesh Refinement Algorithm Development And Dissemination
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Author :
language : en
Publisher:
Release Date : 1997
Adaptive Mesh Refinement Algorithm Development And Dissemination written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The project objective was to develop and disseminate adaptive mesh refinement (AMR) algorithms for structured and unstructured meshes. Development of ARM algorithms will continue along several directions. These directions include algorithms for parallel architectures, techniques for the solution of partial differential equations on adaptive meshes, mesh generation, and algorithms for nontraditional or generic applications of AMR. Dissemination of AMR algorithms is also a goal of the project. AMR algorithms are perceived as difficult to meld to current algorithms. The authors are developing tools that diminish this perception and allow more computational scientists to use AMR within their own work.
Parallel Algorithms For Adaptive Mesh Refinement
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Author :
language : en
Publisher:
Release Date : 1997
Parallel Algorithms For Adaptive Mesh Refinement written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
Computational methods based on the use of adaptively constructed nonuniform meshes reduce the amount of computation and storage necessary to perform many scientific calculations. The adaptive construction of such nonuniform meshes is an important part of these methods. In this paper, the authors present a parallel algorithm for adaptive mesh refinement that is suitable for implementation on distributed-memory parallel computers. Experimental results obtained on the Intel DELTA are presented to demonstrate that, for scientific computations involving the finite element method, the algorithm exhibits scalable performance and has a small run time in comparison with other aspects of the scientific computations examined. It is also shown that the algorithm has a fast expected running time under the P-RAM computation model.
A Parallel Adaptive Mesh Refinement Algorithm
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Author : James J. Quirk
language : en
Publisher:
Release Date : 1993
A Parallel Adaptive Mesh Refinement Algorithm written by James J. Quirk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
A Parallel Adaptive Discontinuous Galerkin Method For Hyperbolic Problems On Unstructured Meshes
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Author : Andrew Giuliani
language : en
Publisher:
Release Date : 2018
A Parallel Adaptive Discontinuous Galerkin Method For Hyperbolic Problems On Unstructured Meshes written by Andrew Giuliani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Conservation laws (Mathematics) categories.
This thesis is concerned with the parallel, adaptive solution of hyperbolic conservation laws on unstructured meshes. First, we present novel algorithms for cell-based adaptive mesh refinement (AMR) on unstructured meshes of triangles on graphics processing units (GPUs). Our implementation makes use of improved memory management techniques and a coloring algorithm for avoiding race conditions. The algorithm is entirely implemented on the GPU, with negligible communication between device and host. We show that the overhead of the AMR subroutines is small compared to the high-order solver and that the proportion of total run time spent adaptively refining the mesh decreases with the order of approximation. We apply our code to a number of benchmarks as well as more recently proposed problems for the Euler equations that require extremely high resolution. We present the solution to a shock reflection problem that addresses the von Neumann triple point paradox. We also study the problem of shock disappearance and self-similar diffraction of weak shocks around thin films. Next, we analyze the stability and accuracy of second-order limiters for the discontinuous Galerkin method on unstructured triangular grids. We derive conditions for a limiter such that the numerical solution preserves second order accuracy and satisfies the local maximum principle. This leads to a new measure of cell size that is approximately twice as large as the radius of the inscribed circle. It is shown with numerical experiments that the resulting bound on the time step is tight. We also consider various combinations of limiting points and limiting neighborhoods and present numerical experiments comparing the accuracy, stability, and efficiency of the corresponding limiters. We show that the theory for strong stability preserving (SSP) time stepping methods employed with the method of lines-type discretizations of hyperbolic conservation laws may result in overly stringent time step restrictions. We analyze a fully discrete finite volume method with slope reconstruction and a second order SSP Runge-Kutta time integrator to show that the maximum stable time step can be increased over the SSP limit. Numerical examples show that this result extends to two-dimensional problems on triangular meshes. Finally, we propose a moment limiter for the discontinuous Galerkin method applied to hyperbolic conservation laws in two and three dimensions. The limiter works by finding directions in which the solution coefficients can be separated and limits them independently of one another by comparing to forward and backward reconstructed differences. The limiter has a precomputed stencil of constant size, which provides computational advantages in terms of implementation and runtime. We provide examples that demonstrate stability and second order accuracy of solutions.