Robust Multigrid Smoothers for Three Dimensional Elliptic Equations with Strong Anisotropies PDF Download
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Author: Ignacio M. Llorente
Publisher:
ISBN:
Category : Anisotropy
Languages : en
Pages : 44
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Book Description
Abstract: "We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems."
Author: Ignacio M. Llorente
Publisher:
ISBN:
Category : Anisotropy
Languages : en
Pages : 44
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Book Description
Abstract: "We discuss the behavior of several plane relaxation methods as multigrid smoothers for the solution of a discrete anisotropic elliptic model problem on cell-centered grids. The methods compared are plane Jacobi with damping, plane Jacobi with partial damping, plane Gauss-Seidel, plane zebra Gauss-Seidel, and line Gauss-Seidel. Based on numerical experiments and local mode analysis, we compare the smoothing factor of the different methods in the presence of strong anisotropies. A four-color Gauss-Seidel method is found to have the best numerical and architectural properties of the methods considered in the present work. Although alternating direction plane relaxation schemes are simpler and more robust than other approaches, they are not currently used in industrial and production codes because they require the solution of a two-dimensional problem for each plane in each direction. We verify the theoretical predictions of Thole and Trottenberg that an exact solution of each plane is not necessary and that a single two-dimensional multigrid cycle gives the same result as an exact solution, in much less execution time. Parallelization of the two-dimensional multigrid cycles, the kernel of the three-dimensional implicit solver, is also discussed. Alternating-plane smoothers are found to be highly efficient multigrid smoothers for anisotropic elliptic problems."
Author: Erik Dick
Publisher: Springer Science & Business Media
ISBN: 9783540671572
Category : Mathematics
Languages : en
Pages : 316
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Book Description
This volume contains 39 of the papers presented at the Sixth European Multigrid Conference, held in Gent, Belgium, September 27-30, 1999. The topics treated at the conference cover all aspects of Multigrid Methods: theory, analysis, computer implementation, applications in the fields of physics, chemistry, fluid mechanics, structural mechanics and magnetism.
Author: C.B. Jenssen
Publisher: Gulf Professional Publishing
ISBN: 0080538401
Category : Science
Languages : en
Pages : 601
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Book Description
Parallel CFD 2000, the Twelfth in an International series of meetings featuring computational fluid dynamics research on parallel computers, was held May 22-25, 2000 in Trondheim, Norway.Following the trend of the past conferences, areas such as numerical schemes and algorithms, tools and environments, load balancing, as well as interdisciplinary topics and various kinds of industrial applications were all well represented in the work presented. In addition, for the first time in the Parallel CFD conference series, the organizing committee chose to draw special attention to certain subject areas by organizing a number of special sessions.We feel the emphasis of the papers presented at the conference reflect the direction of the research within parallel CFD at the beginning of the new millennium. It seems to be a clear tendency towards increased industrial exploitation of parallel CFD. Several presentations also demonstrated how new insight is being achieved from complex simulations, and how powerful parallel computers now make it possible to use CFD within a broader interdisciplinary setting.Obviously, successful application of parallel CFD still rests on the underlying fundamental principles. Therefore, numerical algorithms, development tools, and parallelization techniques are still as important as when parallel CFD was in is infancy. Furthermore, the novel concepts of affordable parallel computing as well as metacomputing show that exciting developments are still taking place.As is often pointed out however, the real power of parallel CFD comes from the combination of all the disciplines involved: Physics, mathematics, and computer science. This is probably one of the principal reasons for the continued popularity of the Parallel CFD Conferences series, as well as the inspiration behind much of the excellent work carried out on the subject. We hope that the papers in this book, both on an individual basis and as a whole, will contribute to that inspiration. Further details of Parallel CFD'99, as well as other conferences in this series, are available at http://www.parcfd.org
Author: D. Keyes
Publisher: Elsevier
ISBN: 008053838X
Category : Mathematics
Languages : en
Pages : 477
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Book Description
Contributed presentations were given by over 50 researchers representing the state of parallel CFD art and architecture from Asia, Europe, and North America. Major developments at the 1999 meeting were: (1) the effective use of as many as 2048 processors in implicit computations in CFD, (2) the acceptance that parallelism is now the 'easy part' of large-scale CFD compared to the difficulty of getting good per-node performance on the latest fast-clocked commodity processors with cache-based memory systems, (3) favorable prospects for Lattice-Boltzmann computations in CFD (especially for problems that Eulerian and even Lagrangian techniques do not handle well, such as two-phase flows and flows with exceedingly multiple-connected demains with a lot of holes in them, but even for conventional flows already handled well with the continuum-based approaches of PDEs), and (4) the nascent integration of optimization and very large-scale CFD. Further details of Parallel CFD'99, as well as other conferences in this series, are available at http://www.parcfd.org
Author: Victor Malyshkin
Publisher: Springer
ISBN: 3030256367
Category : Computers
Languages : en
Pages : 452
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Book Description
This book constitutes the proceedings of the 15th International Conference on Parallel Computing Technologies, PaCT 2019, held in Almaty, Kazakhstan, in August 2019. The 24 full papers and 10 short papers presented were carefully reviewed and selected from 72 submissions. The papers are organized in topical sections on Programming Languages and Execution Environments; Methods and Tools for Parallel Solution of Large-Scale Problems; Data Processing; Cellular Automata; and Distributed Algorithms.
Author: IEEE Computer Society
Publisher: Institute of Electrical & Electronics Engineers(IEEE)
ISBN: 9780769505008
Category : Computers
Languages : en
Pages : 436
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Book Description
Proceedings of a January 2000 workshop, covering distributed and I/O systems, applications, web based computing, performance analysis, computer architecture, models and languages, scheduling and mapping, metacomputing, languages and compilers, distributed shared memory systems, and tools and environments. Specific topics include security mechanisms for the MAP agent system, predictability of bulk synchronous programs using MPI, and tailoring a self-distributed architecture to a cluster computer environment. Other subjects are parallel computing with a data driven model, groups in bulk synchronous parallel computing, databases and the web, the parallel cellular programming model, and reusable message passing components. The volume lacks a subject index. Annotation copyrighted by Book News, Inc., Portland, OR.
Author:
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 1154
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Book Description
Author: Jack Dongarra
Publisher: Springer Science & Business Media
ISBN: 3540665498
Category : Computers
Languages : en
Pages : 513
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Book Description
This book constitutes the refereed proceedings of the 6th European Meeting of the Parallel Virtual Machine and Message Passing Interface Users' Group, PVM/MPI '99, held in Barcelona, Spain in September 1999. The 67 revised papers presented were carefully reviewed and selected from a large number of submissions. All current issues of PVM and MPI are addressed. The papers are organized in topical sections on evaluation and performance, extensions and improvements, implementation issues, tools, algorithms, applications in science and engineering, networking, and heterogeneous distributed systems.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 166
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Book Description
Author: Institute for Computer Applications in Science and Engineering
Publisher:
ISBN:
Category :
Languages : en
Pages : 24
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Book Description
