Ebook: Domain Decomposition Methods — Algorithms and Theory

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)

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The purpose of this text is to offer a comprehensive and self-contained presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. Strong emphasis is placed on both algorithmic and mathematical aspects. Some important methods such FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods, not treated previously in any monograph, are covered in detail.

Winner of the 2005 Award for Excellence in Professional and Scholarly Publishing - Mathematics/Statistics - of the Association of American Publishers

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The purpose of this text is to offer a comprehensive and self-contained presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. Strong emphasis is placed on both algorithmic and mathematical aspects. Some important methods such FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods, not treated previously in any monograph, are covered in detail.

Winner of the 2005 Award for Excellence in Professional and Scholarly Publishing - Mathematics/Statistics - of the Association of American Publishers
Content:
Front Matter....Pages I-XV
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 ; ?) and H (curl ; ?)....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
Back Matter....Pages 413-450

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The purpose of this text is to offer a comprehensive and self-contained presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. Strong emphasis is placed on both algorithmic and mathematical aspects. Some important methods such FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods, not treated previously in any monograph, are covered in detail.

Winner of the 2005 Award for Excellence in Professional and Scholarly Publishing - Mathematics/Statistics - of the Association of American Publishers
Content:
Front Matter....Pages I-XV
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 ; ?) and H (curl ; ?)....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
Back Matter....Pages 413-450
....