  We present a computational study of several preconditioning techniques for
the GMRES algorithm applied to the stochastic diffusion equation with a
lognormal coefficient discretized with the stochastic Galerkin method. The
clear block structure of the system matrix arising from this type of
discretization motivates the analysis of preconditioners designed according to
a field-splitting strategy of the stochastic variables. This approach is
inspired by a similar procedure used within the framework of physics based
preconditioners for deterministic problems, and its application to stochastic
PDEs represents the main novelty of this work. Our numerical investigation
highlights the superior properties of the field-split type preconditioners over
other existing strategies in terms of computational time and stochastic
parameter dependence.
