Efficient Solvers for a Linear Stochastic Galerkin Mixed Formulation of Diffusion Problems with Random Data

Ernst, O.G. and Powell, C.E and Silvester, D.J. and Ullmann, E. (2009) Efficient Solvers for a Linear Stochastic Galerkin Mixed Formulation of Diffusion Problems with Random Data. SIAM Journal of Scientific Computing, 31 (2). pp. 1424-1447.

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Abstract

We introduce a stochastic Galerkin mixed formulation of the steady-state diffusion equation and focus on the efficient iterative solution of the saddle-point systems obtained by combining standard finite element discretisations with two distinct types of stochastic basis functions. So-called mean-based preconditioners, based on fast solvers for scalar diffusion problems, are introduced for use with the minimum residual method. We derive eigenvalue bounds for the preconditioned system matrices and report on the efficiency of the chosen preconditioning schemes with respect to all the discretisation parameters

Item Type:	Article
Subjects:	MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory MSC 2010, the AMS's Mathematics Subject Classification > 65 Numerical analysis
Depositing User:	Dr C.E. Powell
Date Deposited:	11 Feb 2009
Last Modified:	20 Oct 2017 14:12
URI:	https://eprints.maths.manchester.ac.uk/id/eprint/1229

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