SIAM Journal on Matrix Analysis and Applications
A Kronecker Product Preconditioner for Stochastic Galerkin Finite Element Discretizations
SIAM Journal on Scientific Computing
Spectral Methods for Parameterized Matrix Equations
SIAM Journal on Matrix Analysis and Applications
Preconditioning Stochastic Galerkin Saddle Point Systems
SIAM Journal on Matrix Analysis and Applications
SIAM Journal on Scientific Computing
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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 discretizations 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 discretization parameters.