A Preconditioned Recycling GMRES Solver for Stochastic Helmholtz Problems

Abstract

We present a parallel Schwarz type domain decomposition preconditioned recycling Krylov subspace method for the numerical solution of stochastic indefinite elliptic equations with two random coefficients. Karhunen-Loeve expansions are used to represent the stochastic variables and the stochastic Galerkin method with dou- ble orthogonal polynomials is used to derive a sequence of uncoupled deterministic equations. We show numerically that the Schwarz preconditioned recycling GMRES method is an effective technique for solving the entire family of linear systems and, in particular, the use of recycled Krylov subspaces is the key element of this successful approach.