Multilevel block factorization preconditioners: matrix-based analysis and algorithms for solving finite element equations

Panayot S. Vassilevski (auth.)0387715649, 0387715630, 9780387715643, 9780387715636

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.

Table of contents :
Front Matter….Pages i-xiv
A Finite Element Tutorial….Pages 3-47
A Main Goal….Pages 49-51
Two-by-Two Block Matrices and Their Factorization….Pages 55-88
Classical Examples of Block-Factorizations….Pages 89-127
Multigrid (MG)….Pages 129-197
Topics on Algebraic Multigrid (AMG)….Pages 199-261
Domain Decomposition (DD) Methods….Pages 263-318
Preconditioning Nonsymmetric and Indefinite Matrices….Pages 319-325
Preconditioning Saddle-Point Matrices….Pages 327-361
Variable-Step Iterative Methods….Pages 363-375
Preconditioning Nonlinear Problems….Pages 377-383
Quadratic Constrained Minimization Problems….Pages 385-403
Back Matter….Pages 405-529