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We present a computational study of several preconditioning techniques forthe GMRES algorithm applied to the stochastic diffusion equation with alognormal coefficient discretized with the stochastic Galerkin method. Theclear block structure of the system matrix arising from this type ofdiscretization motivates the analysis of preconditioners designed according toa field-splitting strategy of the stochastic variables. This approach isinspired by a similar procedure used within the framework of physics basedpreconditioners for deterministic problems, and its application to stochasticPDEs represents the main novelty of this work. Our numerical investigationhighlights the superior properties of the field-split type preconditioners overother existing strategies in terms of computational time and stochasticparameter dependence.

A computational study of preconditioning techniques for the stochastic diffusion equation with lognormal coefficient