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In this work, solvers and preconditioners based on Gauss-Seidel and Jacobialgorithms are explored for stochastic Galerkin discretization of partialdifferential equations (PDEs) with random input data. Gauss-Seidel and Jacobialgorithms are formulated such that the existing software is leveraged in thecomputational effort. These algorithms are also used as preconditioners toKrylov iterative methods. The solvers and preconditiners are compared withKrylov based iterative methods with the traditional mean-based preconditioner[13] and Kronecker-product preconditioner [17] by solving a steady state stateadvection-diffusion equation, which upon discretization, results in anon-symmetric positive definite matrix on left-hand-side. Numerical resultsshow that an approximate version of Gauss-Seidel algorithm is a goodpreconditioner for GMRES to solve non-symmetric Galerkin system of equations.

Solvers and precondtioners based on Gauss-Seidel and Jacobi algorithms for non-symmetric stochastic Galerkin system of equations