Sparse POD modal subsets for reduced-order nonlinear explicit dynamics

Projected reduced order methods (PROM) such as the proper orthogonal decomposition (POD) rely on the quality of the underlying reduced basis (RB) used to approximate the solution. The RB is generally constructed by the low-rank approximation of a set of observations, taken from full-scale simulations, through truncated singular value decomposition (SVD) of the snapshot matrix. This paper revisits the selection criterion of the RB functions in the study of dynamical systems. In opposition to truncating the set of left singular vectors, taken consecutively in decreasing order of associated singular values, the proposed method takes temporality into account, resulting in a compact, sparse subset of RB functions. Selection strategies, implemented in the reduced-order version of a legacy nonlinear explicit dynamics finite element (FE) code, are compared in both offline and online phases in terms of work of internal forces reconstruction error.