The K-grid Fourier Analysis of Multigrid-type Iterative Methods

The K-grid Fourier Analysis of Multigrid-type Iterative Methods
Author: University of Wisconsin--Madison. Computer Sciences Dept
Publisher:
Total Pages: 59
Release: 1987
Genre: Computer science
ISBN:

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Experiments indicate that a multigrid-type cycle can be used as an efficient preconditioner in the iterative solution of the discrete problem corresponding to a singularly perturbed elliptic boundary value problem. Motivated by a report of Goldstein, we explore the theoretical basis for the efficiency of such a preconditioner when applied to a model problem. The techniques developed are also used to analyze a multigrid V-cycle when used alone as a fast iterative solver. (Author).

Practical Fourier Analysis for Multigrid Methods

Practical Fourier Analysis for Multigrid Methods
Author: Roman Wienands
Publisher: CRC Press
Total Pages: 235
Release: 2004-10-28
Genre: Mathematics
ISBN: 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

An Introduction to Multigrid Methods

An Introduction to Multigrid Methods
Author: Pieter Wesseling
Publisher: R.T. Edwards, Inc.
Total Pages: 300
Release: 2004
Genre: Mathematics
ISBN:

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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.

Multi-Grid Methods and Applications

Multi-Grid Methods and Applications
Author: Wolfgang Hackbusch
Publisher: Springer Science & Business Media
Total Pages: 391
Release: 2013-03-09
Genre: Mathematics
ISBN: 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.

A Multigrid Tutorial

A Multigrid Tutorial
Author: William L. Briggs
Publisher: SIAM
Total Pages: 318
Release: 2000-07-01
Genre: Mathematics
ISBN: 9780898714623

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Mathematics of Computing -- Numerical Analysis.

Multigrid Methods

Multigrid Methods
Author: James H Bramble
Publisher: Routledge
Total Pages: 114
Release: 2019-01-22
Genre: Mathematics
ISBN: 135142985X

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Multigrid methods are among the most efficient iterative methods for the solution of linear systems which arise in many large scale scientific calculations. Every researcher working with the numerical solution of partial differential equations should at least be familiar with this powerful technique. This invaluable book presents results concerning the rates of convergence of multigrid iterations.

Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
Author: Yousef Saad
Publisher: SIAM
Total Pages: 537
Release: 2003-04-01
Genre: Mathematics
ISBN: 0898715342

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Mathematics of Computing -- General.

Iterative Methods for Linear Systems

Iterative Methods for Linear Systems
Author: Maxim A. Olshanskii
Publisher: SIAM
Total Pages: 257
Release: 2014-07-21
Genre: Mathematics
ISBN: 1611973465

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Iterative Methods for Linear Systems?offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.??