Domain decomposition methods for the numerical solution of partial differential equations / Tarek P.A. Mathew.

Format:

Book

Author/Creator:

Mathew, Tarek P. A. (Tarek Poonithara Abraham)

Series:

Lecture notes in computational science and engineering ; 61.

Lecture notes in computational science and engineering, 1439-7358 ; 61

Language:

English

Subjects (All):

Decomposition method.

Differential equations, Partial--Numerical solutions.

Differential equations, Partial.

Physical Description:

1 online resource (780 p.)

Edition:

1st ed. 2008.

Place of Publication:

Berlin : Springer, c2008.

Language Note:

English

Summary:

Domain decomposition methods are divide and conquer methods for the parallel and computational solution of partial differential equations of elliptic or parabolic type. They include iterative algorithms for solving the discretized equations, techniques for non-matching grid discretizations and techniques for heterogeneous approximations. This book serves as an introduction to this subject, with emphasis on matrix formulations. The topics studied include Schwarz, substructuring, Lagrange multiplier and least squares-control hybrid formulations, multilevel methods, non-self adjoint problems, parabolic equations, saddle point problems (Stokes, porous media and optimal control), non-matching grid discretizations, heterogeneous models, fictitious domain methods, variational inequalities, maximum norm theory, eigenvalue problems, optimization problems and the Helmholtz scattering problem. Selected convergence theory is included.

Contents:

Decomposition Frameworks

Schwarz Iterative Algorithms

Schur Complement and Iterative Substructuring Algorithms

Lagrange Multiplier Based Substructuring: FETI Method

Computational Issues and Parallelization

Least Squares-Control Theory: Iterative Algorithms

Multilevel and Local Grid Refinement Methods

Non-Self Adjoint Elliptic Equations: Iterative Methods

Parabolic Equations

Saddle Point Problems

Non-Matching Grid Discretizations

Heterogeneous Domain Decomposition Methods

Fictitious Domain and Domain Imbedding Methods

Variational Inequalities and Obstacle Problems

Maximum Norm Theory

Eigenvalue Problems

Optimization Problems

Helmholtz Scattering Problem.

Notes:

Description based upon print version of record.

Includes bibliographical references (p. [711]-760) and index.

ISBN:

9786611512804

9781281512802

128151280X

9783540772095

354077209X

OCLC:

272298809