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A popular strategy for the numerical solution to contact problems is based on Finite Elements with the contact constraints enforced by a penalty formulation. The resulting linearized system, however, can prove severely ill-conditioned, with the iterative solution to large 3D problems requiring expensive ILU-type preconditioners to converge. In the present communication a novel block preconditioner is proposed to reduce the spectral conditioning number of the preconditioned matrix and hence to accelerate convergence independently of the penalty values. [ABSTRACT FROM AUTHOR]

The repeated solution in time of the linear system arising from the Finite Element (FE) integration of coupled consolidation equations is often a major computational effort. This system can be written in either a symmetric or unsymmetric form, thus calling for the implementation of different preconditioners and Krylov subspace solvers. The present communication investigates the performance of ad hoc block preconditioners used with either SQMR or Bi-CGSTAB. The symmetric and unsymmetric forms of the FE consolidation equations prove to be almost equivalent as to the convergence rate of SQMR and Bi-CGSTAB, respectively, with block preconditioners usually outperforming traditional ILU-based preconditioners. [ABSTRACT FROM AUTHOR]