A Preconditioned Recycling GMRES Solver for Stochastic Helmholtz Problems (Communications in Computational Physics, 2018)
We present a parallel Schwarz type domain decomposition preconditionedrecycling Krylov subspace method for the numerical solution of stochastic indefiniteelliptic equations with two random coefficients. Karhunen-Loève expansions are usedto represent the stochastic variables and the stochastic Galerkin method with doubleorthogonal polynomials is used to derive a sequence of uncoupled deterministicequations. We show numerically that the Schwarz preconditioned recycling GMRESmethod is an effective technique for solving the entire family of linear systems and, inparticular, the use of recycled Krylov subspaces is the key element of this successfulapproach.