期刊
SIAM JOURNAL ON SCIENTIFIC COMPUTING
卷 32, 期 2, 页码 923-946出版社
SIAM PUBLICATIONS
DOI: 10.1137/080742853
关键词
stochastic Galerkin finite element method; lognormal random field; polynomial chaos expansion; Karhunen-Loeve expansion; Kronecker product preconditioner
资金
- DFG [1324]
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.
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