Advertisement

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

  • Authors
  • Tarek Poonithara Abraham Mathew

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 61)

About this book

Introduction

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.

Keywords

algorithm algorithms differential equation finite elements linear algebra numerical analysis optimization parallelization partial differential equation partial differential equations scientific computing

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-77209-5
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-77205-7
  • Online ISBN 978-3-540-77209-5
  • Series Print ISSN 1439-7358
  • Buy this book on publisher's site