Robust Algebraic Multilevel Methods and Algorithms

Johannes Kraus; Svetozar Margenov

Published by De Gruyter 2009

Robust Algebraic Multilevel Methods and Algorithms

Johannes Kraus and Svetozar Margenov

Volume 5 in the series Radon Series on Computational and Applied Mathematics

https://doi.org/10.1515/9783110214833

Overview
Contents

About this book

This book deals with algorithms for the solution of linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained after discretization of partial differential equations using finite element methods. The authors provide a systematic presentation of the recent advances in robust algebraic multilevel methods and algorithms, e.g., the preconditioned conjugate gradient method, algebraic multilevel iteration (AMLI) preconditioners, the classical algebraic multigrid (AMG) method and its recent modifications, namely AMG using element interpolation (AMGe) and AMG based on smoothed aggregation.

The first six chapters can serve as a short introductory course on the theory of AMLI methods and algorithms. The next part of the monograph is devoted to more advanced topics, including the description of new generation AMG methods, AMLI methods for discontinuous Galerkin systems, looking-free algorithms for coupled problems etc., ending with important practical issues of implementation and challenging applications. This second part is addressed to some more experienced students and practitioners and can be used to complete a more advanced course on robust AMLI and AMG methods and their efficient application.

This book is intended for mathematicians, engineers, natural scientists etc.

Author information

Johannes Kraus, Radon Institute for Computational and Applied Mathematics, Linz, Austria;
Svetozar Margenov, Institute for Parallel Processing, Sofia, Bulgaria.

Reviews

"The book will nd its readers in the people who are interested in (algebraic) multigrid."
Dietrich Braess in Zentralblatt MATH 1/2010

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	i
Contents Requires Authentication Unlicensed Licensed Download PDF	vii
1. Introduction Requires Authentication Unlicensed Licensed Download PDF	1
2. Algebraic multilevel iteration methods Requires Authentication Unlicensed Licensed Download PDF	29
3. Robust AMLI algorithms: Conforming linear finite elements Requires Authentication Unlicensed Licensed Download PDF	57
4. Robust AMLI algorithms: Nonconforming linear finite elements Requires Authentication Unlicensed Licensed Download PDF	77
5. Schur complement based multilevel preconditioners Requires Authentication Unlicensed Licensed Download PDF	102
6. Algebraic multigrid (AMG) Requires Authentication Unlicensed Licensed Download PDF	117
7. Preconditioning of Rannacher–Turek nonconforming FE systems Requires Authentication Unlicensed Licensed Download PDF	136
8. AMLI algorithms for discontinuous Galerkin FE problems Requires Authentication Unlicensed Licensed Download PDF	164
9. AMLI methods for coupled problems Requires Authentication Unlicensed Licensed Download PDF	196
10. Practical issues Requires Authentication Unlicensed Licensed Download PDF	219
Backmatter Requires Authentication Unlicensed Licensed Download PDF	237

(Deutsch)

Language: English
Publisher: De Gruyter
Audience: Graduate Students of Mathematics, Engineering, and Natural Sciences; Researchers; Academic Libraries
Pages
- Front matter: 10
- Main content: 246
Keywords: Linear Algebra; Multigrid Method; Partial Differential Equation

eBook

Published: September 4, 2009
ISBN: 9783110214833

Hardcover

Published: September 16, 2009
ISBN: 9783110193657