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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]