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Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems

Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems

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Part of the Springer Theses series

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Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems Synopsis

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.

About This Edition

ISBN: 9783319563053
Publication date:
Author: James Lottes
Publisher: Springer an imprint of Springer International Publishing
Format: Hardback
Pagination: 131 pages
Series: Springer Theses
Genres: Numerical analysis
Functional analysis and transforms
Differential calculus and equations

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