A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations

The standard SSOR preconditioner is ineffective for the iterative solution of the symmetric indefinite linear systems arising from finite element discretization of the Biot’s consolidation equations. In this paper, a modified block SSOR preconditioner combined with the Eisenstat-trick implementation is proposed. For actual implementation, a pointwise variant of this modified block SSOR preconditioner is highly recommended to obtain a compromise between simplicity and effectiveness. Numerical experiments show that the proposed modified SSOR preconditioned symmetric QMR solver can achieve faster convergence than several effective preconditioners published in the recent literature in terms of total runtime. Moreover, the proposed modified SSOR preconditioners can be generalized to non-symmetric Biot’s systems