Chapter

Domain Decomposition Methods in Science and Engineering XX

Volume 91 of the series Lecture Notes in Computational Science and Engineering pp 27-38

Date:

Symbolic Techniques for Domain Decomposition Methods

  • T. CluzeauAffiliated withUniversité de Limoges ; CNRS ; XLIM UMR 6172 Email author 
  • , V. DoleanAffiliated withLaboratoire J.A. Dieudonné, CNRS UMR 6621
  • , F. NatafAffiliated withLaboratoire J.L. Lions, CNRS UMR 7598, Université Pierre et Marie Curie
  • , A. QuadratAffiliated withINRIA Saclay-Île-de-France, DISCO Project, Supélec, L2S

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Abstract

Some algorithmic aspects of systems of PDEs based simulations can be better clarified by means of symbolic computation techniques. This is very important since numerical simulations heavily rely on solving systems of PDEs. For the large-scale problems we deal with in today’s standard applications, it is necessary to rely on iterative Krylov methods that are scalable (i.e., weakly dependent on the number of degrees on freedom and number of subdomains) and have limited memory requirements.