Comparison of MSSOR versus ILU(0) preconditioners for Biot's FEM consolidation equations

Abstract

Numerical performance of two different preconditioning approaches, modified SSOR (MSSOR) preconditioner and incomplete factorization with zero fill-in (ILU0) preconditioner, is compared for the iterative solution of symmetric indefinite linear systems arising from finite element discretization of the Biot's consolidation equations. Numerical results show that the nodal ordering affect the performance of ILU0 whereas MSSOR is less affected. The statistics proposed by Chow and Saad (1997) is demonstrated to be useful in diagnosing the failure of ILU factorization. The stabilized ILU0 coupled with symmetric quasi-minimal residual (SQMR) method is about 10-50% efficient time-wise (especially in the heterogeneous soil condition) than MSSOR-preconditioned system. However, the determination of a proper stabilization parameter (thresh value) for the replacement of smaller pivots is largely problem dependant. The optimal balance can only be identified through numerical experiments - a luxury that practitioners can ill-afford and completely self-defeating if the goal is to solve a problem in a shortest time.