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

Abstract

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.

Efficient hyper reduced-order model (HROM) for parametric studies of the 3D thermo-elasto-plastic calculation

“…Moreover, the orthogonal condition in Eq. (21) does not mean that all the residuals of the equilibrium equations must be equal to zero. In fact, it allows us to introduce a RID only on a part of the global domain.…”

“…Energy measure for displacements: Similar to previous works of Giacoma et al [17,21] and Boucinha et al [22], the energy measure related to displacements is evaluated in order to determine the size of the reduced basis. The energy measure of the displacement field integrated over the considered time domain is defined by…”

An efficient quasi-optimal space-time PGD application to frictional contact mechanics

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“…We suggest to embed into a PGD iteration, one iteration of Algorithm 3 in order to compress progressively the iterated low rank expansion. Doing so, one can expect to make it close to the optimal one and stem inflation of iterated expansion [15].…”

Efficient hyper‐reduced‐order model (HROM) for thermal analysis in the moving frame

“…In addition, various interpolation methods are reported to get the adaptive RB for parametric studies [12,[16][17][18]. However, the accuracy of the ROM strongly depends on the relevancy of the selected RB [15,19,20]. Contrary to the POD-based ROM method, the proper generalized decomposition (PGD)-based ROMs [21] have been more recently generalized to high-dimensional problems [22][23][24][25][26][27].…”