Author: Jim E. Jones
Publisher:
ISBN:
Category : Anisotropy
Languages : en
Pages : 18
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Book Description
Abstract: "Efficient and robust multigrid solvers for anisotropic problems typically use either semi-coarsened grids or implicit smoothers -- line relaxation in 2D and plane relaxation in 3D. However, both of these may be difficult to implement in codes using multi-block structured grids where there may be no natural definition of a global 'line' or 'plane'. These multi-block structured grids are often used in fluid dynamic applications to capture complex geometries and/or to facilitate parallel processing. In this paper, we investigate the performance of multigrid algorithms using implicit smoothers within the blocks of a such a [sic] grid. By looking at a model problem, the 2-D anisotropic diffusion equation, we show that true multigrid efficiency is achieved only when the block sizes are proportional to the strength of the anisotropy. Further, the blocks must overlap and the size of the overlap must again be proportional to the strength of the anisotropy."
Author: William L. Briggs
Publisher: SIAM
ISBN: 9780898714623
Category : Mathematics
Languages : en
Pages : 318
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Book Description
Mathematics of Computing -- Numerical Analysis.
Author:
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 800
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Book Description
Author: Ignacio M. Llorente
Publisher:
ISBN:
Category :
Languages : en
Pages : 32
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Book Description
Author:
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 148
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Book Description
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 92
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Book Description
Author: Hans-Joachim Bungartz
Publisher: Springer Nature
ISBN: 3030479560
Category : Computers
Languages : en
Pages : 624
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Book Description
This open access book summarizes the research done and results obtained in the second funding phase of the Priority Program 1648 "Software for Exascale Computing" (SPPEXA) of the German Research Foundation (DFG) presented at the SPPEXA Symposium in Dresden during October 21-23, 2019. In that respect, it both represents a continuation of Vol. 113 in Springer’s series Lecture Notes in Computational Science and Engineering, the corresponding report of SPPEXA’s first funding phase, and provides an overview of SPPEXA’s contributions towards exascale computing in today's sumpercomputer technology. The individual chapters address one or more of the research directions (1) computational algorithms, (2) system software, (3) application software, (4) data management and exploration, (5) programming, and (6) software tools. The book has an interdisciplinary appeal: scholars from computational sub-fields in computer science, mathematics, physics, or engineering will find it of particular interest.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 162
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Book Description
Author: Ulrich Trottenberg
Publisher: Academic Press
ISBN: 9780127010700
Category : Mathematics
Languages : en
Pages : 652
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Book Description
Mathematics of Computing -- Numerical Analysis.
Author: Achi Brandt
Publisher: SIAM
ISBN: 9781611970753
Category : Mathematics
Languages : en
Pages : 239
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Book Description
This classic text presents the best practices of developing multigrid solvers for large-scale computational problems in science and engineering. By representing a problem at multiple scales and employing suitable interscale interactions, multigrid avoids slowdown due to stiffness and reduces the computational cost of classical algorithms by orders of magnitude. Starting from simple examples, this book guides the reader through practical stages for developing reliable multigrid solvers, methodically supported by accurate performance predictors. The revised edition presents discretization and fast solution of linear and nonlinear partial differential systems; treatment of boundary conditions, global constraints and singularities; grid adaptation, high-order approximations, and system design optimization; applications to fluid dynamics, from simple models to advanced systems; new quantitative performance predictors, a MATLAB sample code, and more. Readers will also gain access to the Multigrid Guide 2.0 Web site, where updates and new developments will be continually posted, including a chapter on Algebraic Multigrid.
