Schwarz preconditioner for the stochastic finite element method

The intrusive polynomial chaos approach for uncertainty quantification in numerous engineering problems constitutes a computationally challenging task. Indeed, Galerkin projection in the spectral stochastic finite element method (SSFEM) leads to a large-scale linear system for the polynomial chaos coefficients of the solution process. The development of robust and efficient solution strategies for the resulting linear system therefore is of paramount importance for the applicability of the SSFEM to practical engineering problems. The solution algorithms should be parallel and scalable in order to exploit the available multiprocessor supercomputers. Therefore, we formulate a two-level Schwarz preconditioner for the polynomial chaos based uncertainty quantification of large-scale computational models.