Block preconditioning for the FE solution to contact problems.

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.