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Product Details
From the back cover: "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.
"The 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."
BRIEF CONTENTS
Preface
Part I. Motivation for Preconditioning
A Finite Element Tutorial
A Main Goal
Part II. Block Factorization Preconditioners
Two-by-Two Block Matrices and Their Factorization
Classical Examples of Block-Factorizations
Multigrid (MG)
Topics on Algebraic Multigrid (AMG)
Domain Decomposition (DD) Methods
Preconditioning Nonsymmetric and Indefinite Matrices
Preconditioning Saddle-Point Matrices
Variable-Step Interative Methods
Preconditioning Nonlinear Problems
Quadratic Constrained Minimization Problems
Part III. Appendices
Generalized Conjugate Gradient Methods
Properties of Finite Element Matrices, Further Details
Computable Scales of Sobolev Norms
Multilevel Algorithms for Boundary Extension Mappings
H01-norm Characterization
MG Convergence Results for Finite Element Problems
