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arXiv · 1006.3053

Factorizing the Stochastic Galerkin System

Paul G. Constantine·David F. Gleich·Gianluca Iaccarino
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Abstract

Recent work has explored solver strategies for the linear system of equations arising from a spectral Galerkin approximation of the solution of PDEs with parameterized (or stochastic) inputs. We consider the related problem of a matrix equation whose matrix and right hand side depend on a set of parameters (e.g. a PDE with stochastic inputs semidiscretized in space) and examine the linear system arising from a similar Galerkin approximation of the solution. We derive a useful factorization of this system of equations, which yields bounds on the eigenvalues, clues to preconditioning, and a flexible implementation method for a wide array of problems. We complement this analysis with (i) a numerical study of preconditioners on a standard elliptic PDE test problem and (ii) a fluids application using existing CFD codes; the MATLAB codes used in the numerical studies are available online.

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Paul G. Constantine, David F. Gleich, Gianluca Iaccarino. 2010-06-15. Factorizing the Stochastic Galerkin System. https://doi.org/10.1137/100799046

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