A lean and efficient snapshot generation technique for the Hyper-Reduction of nonlinear structural dynamics

Model Order Reduction based on subspace projection can lead to impressive speedups, as the number of dofs can be drastically reduced. However, the computation of the nonlinear forces, which is performed in the unreduced physical domain, becomes the dominating bottleneck for nonlinear systems. This issue is addressed by Hyper-Reduction, which is the approximate but inexpensive computation of the nonlinear forces in a reduced basis model. The established Hyper-Reduction methods require training sets which are usually obtained by a training simulation of the full, unreduced model resulting in immense offline costs. To reduce the offline-costs, so-called Nonlinear Stochastic Krylov Training Sets (NSKTS) are proposed in this paper. These training sets are obtained by solving a number of nonlinear static problems where the force is constructed by stochastically weighted forces of a Krylov force subspace. The feasibility of NSKTS as training sets for the Energy Conserving Mesh Sampling and Weighting (ECSW) Hyper-Reduction method is demonstrated on a geometrically nonlinear rubber boot example exhibiting excellent results in terms of accuracy, speedup and robustness.