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Towards Robust Algebraic Multigrid Methods for Nonsymmetric Problems

  • JamesĀ Lottes

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-x
  2. James Lottes
    Pages 1-24
  3. James Lottes
    Pages 25-36
  4. James Lottes
    Pages 37-65
  5. James Lottes
    Pages 67-90
  6. James Lottes
    Pages 91-127
  7. James Lottes
    Pages 129-131

About this book

Introduction

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.

Keywords

Algebraic Multigrid (AMG) nonsymmetric problems absolute value iterative methods convergence theory advection-diffusion equation MSC (2010): 65F10, 65N22, 65N55, 65N30, 65J10

Authors and affiliations

  • JamesĀ Lottes
    • 1
  1. 1.Google Inc. Mountain View, Santa ClaraUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-56306-0
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-56305-3
  • Online ISBN 978-3-319-56306-0
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • Buy this book on publisher's site
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