Domain Decomposition Methods — Algorithms and Theory

Andrea Toselli, Olof B. Widlund (auth.)3540206965, 9783540206965

From the reviews of the first edition:

“This book unifies the results from a number of papers by the authors and their coworkers over the past two decades, and complements them by new insights and some background. The distinguishing feature of this book is a comprehensive and rigorous treatment of convergence bounds based on the theory of infinite elements. … The bibliography is quite complete for the fields covered … . The book belongs on the desk of all specialists involved in domain decomposition and substructuring … .” (Jan Mandel, Zentralblatt MATH, Vol. 1069, 2005)

Table of contents :
Introduction….Pages 1-34
Abstract Theory of Schwarz Methods….Pages 35-53
Two-Level Overlapping Methods….Pages 54-85
Substructuring Methods: Introduction….Pages 86-112
Primal Iterative Substructuring Methods….Pages 113-129
Neumann-Neumann and FETI Methods….Pages 131-191
Spectral Element Methods….Pages 193-215
Linear Elasticity….Pages 217-229
Preconditioners for Saddle Point Problems….Pages 231-270
Problems in H (div ; ω ) and H (curl ; ω )….Pages 271-309
Indefinite and Nonsymmetric Problems….Pages 311-335
Elliptic Problems and Sobolev Spaces….Pages 337-370
Galerkin Approximations….Pages 371-393
Solution of Algebraic Linear Systems….Pages 395-411