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Multigrid Techniques

Author: Achi Brandt

Publisher: SIAM

Published: 2011-01-01

Total Pages: 239

ISBN-13: 9781611970753

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.

A Multigrid Tutorial

Author: William L. Briggs

Publisher: SIAM

Published: 2000-07-01

Total Pages: 318

ISBN-13: 9780898714623

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Mathematics of Computing -- Numerical Analysis.

Multi-Grid Methods and Applications

Author: Wolfgang Hackbusch

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 391

ISBN-13: 3662024276

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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.

Multigrid Methods

Author: Ulrich Trottenberg

Publisher: Academic Press

Published: 2001

Total Pages: 652

ISBN-13: 9780127010700

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Mathematics of Computing -- Numerical Analysis.

Multigrid Techniques

Author: Achi Brandt

Publisher: SIAM

Published: 2011-07-07

Total Pages: 217

ISBN-13: 1611970741

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This revised edition of a classic text presents the best practices of developing multigrid solvers for large-scale computational problems. This book will be useful to practitioners and researchers, as well as students and instructors, in many areas of computational science and engineering, applied mathematics and numerical analysis.

Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems

Author: James Lottes

Publisher: Springer

Published: 2017-03-24

Total Pages: 138

ISBN-13: 3319563068

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This thesis presents a rigorous, abstract analysis of multigrid methods for positive nonsymmetric problems, particularly suited to algebraic multigrid, with a completely new approach to nonsymmetry which is based on a new concept of absolute value for nonsymmetric operators. Multigrid, and in particular algebraic multigrid, has become an indispensable tool for the solution of discretizations of partial differential equations. While used in both the symmetric and nonsymmetric cases, the theory for the nonsymmetric case has lagged substantially behind that for the symmetric case. This thesis closes some of this gap, presenting a major and highly original contribution to an important problem of computational science. The new approach to nonsymmetry will be of interest to anyone working on the analysis of discretizations of nonsymmetric operators, even outside the context of multigrid. The presentation of the convergence theory may interest even those only concerned with the symmetric case, as it sheds some new light on and extends existing results.

Multigrid Methods

Author: Stephen F. McCormick

Publisher: SIAM

Published: 1987-12-01

Total Pages: 292

ISBN-13: 1611971888

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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.

Multigrid Methods

Author: W. Hackbusch

Publisher: Springer

Published: 2006-11-15

Total Pages: 664

ISBN-13: 354039544X

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Practical Fourier Analysis for Multigrid Methods

Author: Roman Wienands

Publisher: CRC Press

Published: 2004-10-28

Total Pages: 235

ISBN-13: 1420034995

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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

multigrid methods

Author: Stephen F. Mccormick

Publisher: CRC Press

Published: 2020-08-12

Total Pages: 668

ISBN-13: 1000147223

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This book is a collection of research papers on a wide variety of multigrid topics, including applications, computation and theory. It represents proceedings of the Third Copper Mountain Conference on Multigrid Methods, which was held at Copper Mountain, Colorado.