Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

Tarek Poonithara Abraham Mathew (auth.)9783540772057, 9783540772095, 3540772057, 354077209X

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.

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Table of contents :
Front Matter….Pages I-XIII
Decomposition Frameworks….Pages 1-46
Schwarz Iterative Algorithms….Pages 47-105
Schur Complement and Iterative Substructuring Algorithms….Pages 107-230
Lagrange Multiplier Based Substructuring: FETI Method….Pages 231-262
Computational Issues and Parallelization….Pages 263-294
Least Squares-Control Theory: Iterative Algorithms….Pages 295-312
Multilevel and Local Grid Refinement Methods….Pages 313-331
Non-Self Adjoint Elliptic Equations: Iterative Methods….Pages 333-376
Parabolic Equations….Pages 377-416
Saddle Point Problems….Pages 417-513
Non-Matching Grid Discretizations….Pages 515-573
Heterogeneous Domain Decomposition Methods….Pages 575-606
Fictitious Domain and Domain Imbedding Methods….Pages 607-619
Variational Inequalities and Obstacle Problems….Pages 621-646
Maximum Norm Theory….Pages 647-678
Eigenvalue Problems….Pages 679-687
Optimization Problems….Pages 689-698
Helmholtz Scattering Problem….Pages 699-709
Back Matter….Pages 711-764