A kronecker product preconditioner for stochastic galerkin finite eleme nt discretizations

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Abstract

The discretization of linear partial differential equations with random data by means of the stochastic Galerkin finite element method results in general in a large coupled linear system of equations. Using the stochastic diffusion equation as a model problem, we introduce and study a symmetric positive definite Kronecker product preconditioner for the Galerkin matrix. We compare the popular mean-based preconditioner with the proposed preconditioner which-in contrast to the mean-based construction-makes use of the entire information contained in the Galerkin matrix. We report on results of test problems, where the random diffusion coefficient is given in terms of a truncated Karhunen-Loeve expansion or is a lognormal random field.

Original languageEnglish
Pages (from-to)923-946
Number of pages24
JournalSIAM Journal on Scientific Computing
Volume32
Issue number2
DOIs
StatePublished - 2010
Externally publishedYes

Keywords

  • Karhunen-Loève expansion
  • Kronecker product preconditioner
  • Lognormal random field
  • Polynomial chaos expansion
  • Stochastic Galerkin finite element method

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