Mesh sampling and weighting for the hyperreduction of nonlinear Petrov–Galerkin reduced?order models with local reduced?order bases

The energy-conserving sampling and weighting (ECSW) method is a hyper-reduction originally developed for accelerating the performance of Galerkin projection-based reduced-order models (PROMs) associated with large-scale finite element models, when underlying projected operators need to be frequently recomputed as in parametric and/or nonlinear problems. In this paper, extended Petrov–Galerkin PROMs where high-dimensional can arbitrary element, volume, difference semi-discretization methods. Its scope also cover local based on piecewise-affine approximation subspaces, such those designed mitigating Kolmogorov n-width barrier issue convection-dominated flow resulting ECSW shown paper robust accurate. particular, its offline phase fast parallelizable, potential online applications industrial relevance demonstrated turbulent problems O(107) O(108) degrees freedom. For problems, part proposed enable wall-clock time CPU speedup factors several orders magnitude while delivering exceptional accuracy.