Mathew Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

1. Auflage 2008
ISBN: 978-3-540-77209-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 61, 770 Seiten, eBook

Reihe: Lecture Notes in Computational Science and Engineering

Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. The topics discussed include hybrid formulations, Schwarz, substructuring and Lagrange multiplier methods for elliptic equations, computational issues, least squares-control methods, multilevel methods, non-self adjoint problems, parabolic equations, saddle point applications (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 also included.

Zielgruppe

Research

Autoren/Hrsg.

Mathew, Tarek

Inhaltsverzeichnis

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.