Multilevel Block Factorization Preconditioners

Matrix-based Analysis and Algorithms for Solving Finite Element Equations

  • Panayot S. Vassilevski

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Motivation for Preconditioning

    1. Pages 49-51
  3. Block Factorization Preconditioners

  4. Back Matter
    Pages 405-529

About this book

Introduction

This monograph is the first to provide a comprehensive, self-contained and rigorous presentation of some of the most powerful preconditioning methods for solving finite element equations in a common block-matrix factorization framework.

Topics covered include the classical incomplete block-factorization preconditioners and the most efficient methods such as the multigrid, algebraic multigrid, and domain decomposition. Additionally, the author discusses preconditioning of saddle-point, nonsymmetric and indefinite problems, as well as preconditioning of certain nonlinear and quadratic constrained minimization problems that typically arise in contact mechanics. The book presents analytical as well as algorithmic aspects.

This text can serve as an indispensable reference for researchers, graduate students, and practitioners. It can also be used as a supplementary text for a topics course in preconditioning and/or multigrid methods at the graduate level.

Keywords

Matrix Panayot algebra algorithms mechanics

Authors and affiliations

  • Panayot S. Vassilevski
    • 1
  1. 1.Center for Applied Scientific ComputingLawrence Livermore National LaboratoryLivermore

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-71564-3
  • Copyright Information Springer New York 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-71563-6
  • Online ISBN 978-0-387-71564-3
  • About this book