Springer Theses

Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems

Authors: Lottes, James

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  • 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
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eBook $89.00
price for USA in USD
  • ISBN 978-3-319-56306-0
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  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
Softcover $119.99
price for USA in USD
About this book

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.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-3-319-56306-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
Softcover $119.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems
Authors
Series Title
Springer Theses
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-56306-0
DOI
10.1007/978-3-319-56306-0
Hardcover ISBN
978-3-319-56305-3
Softcover ISBN
978-3-319-85881-4
Series ISSN
2190-5053
Edition Number
1
Number of Pages
X, 131
Number of Illustrations
6 b/w illustrations, 15 illustrations in colour
Topics