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This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
List of contents
Abstract Theory of Schwarz Methods.- Two-Level Overlapping Methods.- Substructuring Methods: Introduction.- Primal Iterative Substructuring Methods.- Neumann-Neumann and FETI Methods.- Spectral Element Methods.- Linear Elasticity.- Preconditioners for Saddle Point Problems.- Problems in H (div ; ?) and H (curl ; ?).- Indefinite and Nonsymmetric Problems.- Elliptic Problems and Sobolev Spaces.- Galerkin Approximations.- Solution of Algebraic Linear Systems.
Summary
This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
Additional text
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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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)
