Development of Empirical Cubature Method Based on Gappy-POD

Abstract

Among various methods to develop surrogate models of high-fidelity models, reduced-order modeling using proper orthogonal decomposition (POD) is one of promising methods. However, the method has a well-known drawback that the computation of Galerkin projection is heavy, which overshadows the reduction of computational cost for simultaneous equations. To speed up the simulation, a hyper-reduction method, which approximately calculates Galarkin projection, is introduced. A hyper-reduction method allows to avoid the full-domain integration. As a result, a great speed-up is realized. Although several hyper-reduction methods have been proposed, an empirical cubature method (ECM) is widely used. The present study proposed a novel ECM based on Gappy-POD, which is one of the sparse sampling techniques and was originally proposed for image reconstruction. In this study, we applied the proposed method to various types of nonlinear analyses. As a result, we confirmed that the proposed method can provide the effective hyper-reduced-order model in significant reduction of computational time while preserving desired accuracy.