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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
