Toward an optimal a priori reduced basis strategy for frictional contact problems with LATIN solver

In this paper, an efficient a priori model reduction strategy for frictional contact problems is presented. We propose to solve this problem by using the finite element method and the non-linear LATIN solver. Basically, this non-linear solver assumes a space-time separated representation presaging nowadays PGD strategies. We extend this family of solvers to frictional engineering applications with reduced subspaces and no prior knowledge about the solution (contrary to a posteriori model reduction techniques). Hereinafter, a hybrid a priori/a posteriori LATIN-PGD formulation for frictional contact problems is proposed. Indeed, the suggested algorithm may or may not start with an initial guess of the reduced basis and is able to enrich the basis in order to reach a given level of accuracy. Moreover, it provides progressively the solution of the considered problem into a quasi-optimal space-time separated form compared to the singular value decomposition (SVD). Some examples are provided in order to illustrate the efficiency and quasi-optimality of the proposed a priori reduced basis LATIN solver.