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Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

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Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equati... Weiterlesen
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Beschreibung

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. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.



Klappentext
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.


Inhalt
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.

Produktinformationen

Titel: Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations
Autor:
EAN: 9783540772095
ISBN: 978-3-540-77209-5
Digitaler Kopierschutz: Wasserzeichen
Format: E-Book (pdf)
Herausgeber: Springer
Genre: Grundlagen
Anzahl Seiten: 770
Veröffentlichung: 25.06.2008
Jahr: 2008
Untertitel: Englisch
Dateigrösse: 5.8 MB

Weitere Bände aus der Buchreihe "Lecture Notes in Computational Science and Engineering"