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Abstract: The aim of this paper is to implement an asymptotically optimal diagonal preconditioner for the linear system stemming from the discretization of the three fields formulation. In order to apply the preconditioner based on wavelets, by introducing multiresolution analysis (MRA) for L 2(0,2) and using MRA on the unitary interval, we construct a MRA on the skeleton arising from a certain domain decomposition. Extensive numerical tests performed on a model problem confirm the optimality of the diagonal preconditioner. [Copyright &y& Elsevier]

Abstract: There are two approaches for applying substructuring preconditioner for the linear system corresponding to the discrete Steklov–Poincaré operator arising in the three fields domain decomposition method for elliptic problems. One of them is to apply the preconditioner in a common way, i.e. using an iterative method such as preconditioned conjugate gradient method [S. Bertoluzza, Substructuring preconditioners for the three fields domain decomposition method, I.A.N.-C.N.R, 2000] and the other one is to apply iterative methods like for instance bi-conjugate gradient method, conjugate gradient square and etc. which are efficient for nonsymmetric systems (the preconditioned system will be nonsymmetric). In this paper, second approach will be followed and extensive numerical tests will be presented which imply that the considered iterative methods are efficient. [Copyright &y& Elsevier]