Overview
- Nominated as an outstanding Ph.D. thesis by the University of Oxford, UK
- Provides a concise and self-contained introduction to multigrid for a simple model problem
- Presents a new absolute value concept that naturally extends the energy norm to the nonsymmetric case
- Presents a novel general convergence theory for two-level methods, the first to treat interpolation and restriction independently, by making use of the new absolute value
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Theses (Springer Theses)
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Table of contents (6 chapters)
Keywords
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems
Authors: James Lottes
Series Title: Springer Theses
DOI: https://doi.org/10.1007/978-3-319-56306-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-56305-3Published: 01 April 2017
Softcover ISBN: 978-3-319-85881-4Published: 25 July 2018
eBook ISBN: 978-3-319-56306-0Published: 24 March 2017
Series ISSN: 2190-5053
Series E-ISSN: 2190-5061
Edition Number: 1
Number of Pages: X, 131
Number of Illustrations: 6 b/w illustrations, 15 illustrations in colour
Topics: Computational Mathematics and Numerical Analysis, Operator Theory, Partial Differential Equations