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Block preconditioning of systems of PDEs

  • Kent-Andre Mardal
  • Joachim Berdal Haga
Chapter
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 84)

Abstract

In this chapter, we describe the implementation of block preconditioned Krylov solvers for systems of partial differential equations (PDEs) using CBC.Block and the Python interfaces of DOLFIN and Trilinos. We start by reviewing the abstract theory of constructing preconditioners by considering the differential operators as mappings in properly chosen Sobolev spaces, before giving a short overview of CBC.Block. We then present several examples, namely the Poisson problem, the Stokes problem, the time-dependent Stokes problem and finally a mixed formulation of the Hodge Laplacian.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Kent-Andre Mardal
    • 1
    • 2
  • Joachim Berdal Haga
    • 1
  1. 1.Center for Biomedical Computing at Simula Research LaboratoryOsloNorway
  2. 2.Department of InformaticsUniversity of OsloOsloNorway

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