Convergence Analysis of a Multigrid Method for Convection Diffusion Equations PDF Download
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Author: Arnold Reusken
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Author: Arnold Reusken
Publisher:
ISBN:
Category :
Languages : en
Pages : 22
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Book Description
Author: Wolfgang Hackbusch
Publisher: Springer Science & Business Media
ISBN: 3662024276
Category : Mathematics
Languages : en
Pages : 391
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Book Description
Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in multi-grid methods will benefit from this book as well as readers with a more theoretical interest.
Author: Mohamed Benbourenane
Publisher:
ISBN:
Category :
Languages : en
Pages : 288
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Book Description
Author: Pieter Wesseling
Publisher: R.T. Edwards, Inc.
ISBN:
Category : Mathematics
Languages : en
Pages : 300
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Book Description
Introduces the principles, techniques, applications and literature of multigrid methods. Aimed at an audience with non-mathematical but computing-intensive disciplines and basic knowledge of analysis, partial differential equations and numerical mathematics, it is packed with helpful exercises, examples and illustrations.
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: Maksim A. Olšanskij
Publisher:
ISBN:
Category :
Languages : en
Pages : 29
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Book Description
Author: Roman Wienands
Publisher: CRC Press
ISBN: 1420034995
Category : Mathematics
Languages : en
Pages : 235
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Book Description
Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detaile
Author: Klas Samuelsson
Publisher:
ISBN:
Category : Green's functions
Languages : en
Pages : 47
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Book Description
Abstract: "We prove two theorems on the residual damping in multigrid methods solving convection dominated diffusion equations and shock wave problems, discretized by the streamline diffusion finite element method. The first theorem shows that a V-cycle, including sufficiently many pre and post smoothing steps, damps the residual in L[superscript loc]1 for a constant coefficient convection problem with small diffusion in two space dimensions, without the assumption that the coarse grid is sufficiently fine. The proof is based on discrete Green's functions related to the smoothing and correction operators. The second theorem proves a similar result for a certain continuous version of a two grid method, with isotropic artificial diffusion, applied to a two dimensional Burgers shock wave problem. We also present numerical experiments that verify the residual damping dependence on the equation, the choice of artificial diffusion and the number of smoothing steps."
Author: Ignacio M. Llorente
Publisher:
ISBN:
Category : Boundary value problems
Languages : en
Pages : 36
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Book Description
Multigrid algorithms are known to be highly efficient in solving systems of elliptic equations. However, standard multi grid algorithms fail to achieve optimal grid-independent convergence rates in solving non-elliptic problems. In many practical cases, the non-elliptic part of a problem is represented by the convection operator. Downstream marching, when it is viable, is the simplest and most efficient way to solve this operator. However, in a parallel setting, the sequential nature of marching degrades the efficiency of the algorithm. The aim of this report is to present, evaluate and analyze an alternative highly parallel multi grid method for 3-D convection-dominated problems. This method employs semi coarsening, a four-color plane-implicit smoother, and discretization rules allowing the same cross-characteristic interactions on all the grids involved to be maintained. The resulting multigrid solver exhibits a fast grid-independent convergence rate for solving the convection-diffusion operator on cell-centered grids with stretching. The load imbalance below the critical level is the main source of inefficiency in its parallel implementation. A hybrid smoother that degrades the convergence properties of the method but improves its granularity has been found to be the best choice in a parallel setting. The numerical and parallel properties of the multi grid algorithm with the four-color and hybrid smoothers are studied on SGI Origin 2000 and Cray T3E systems.
Author: Stephen F. McCormick
Publisher: SIAM
ISBN: 1611971888
Category : Mathematics
Languages : en
Pages : 292
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Book Description
A thoughtful consideration of the current level of development of multigrid methods, this volume is a carefully edited collection of papers that addresses its topic on several levels. The first three chapters orient the reader who is familiar with standard numerical techniques to multigrid methods, first by discussing multigrid in the context of standard techniques, second by detailing the mechanics of use of the method, and third by applying the basic method to some current problems in fluid dynamics. The fourth chapter provides a unified development, complete with theory, of algebraic multigrid (AMG), which is a linear equation solver based on multigrid principles. The last chapter is an ambitious development of a very general theory of multigrid methods for variationally posed problems. Included as an appendix is the latest edition of the Multigrid Bibliography, an attempted compilation of all existing research publications on multigrid.
