A modified SSOR preconditioner for sparse symmetric indefinite linear systems of equations. (English) Zbl 1114.74056

Summary: The standard SSOR preconditioner is ineffective for iterative solution of symmetric indefinite linear systems arising from finite element discretization of Biot’s consolidation equations. In this paper, we propose a modified block SSOR preconditioner combined with the Eisenstat-trick implementation [S. C. Eisenstat, SIAM J. Sci. Stat. Comput. 2, 1–4 (1981; Zbl 0474.65020)]. 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 in terms of total runtime than several effective preconditioners published in the recent literature. Moreover, the proposed modified SSOR preconditioners can be generalized to non-symmetric Biot’s systems.


74S05 Finite element methods applied to problems in solid mechanics
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74L10 Soil and rock mechanics
65F50 Computational methods for sparse matrices


Zbl 0474.65020


Full Text: DOI


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