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A structure preserving proper orthogonal decomposition reduce-order modelingapproach has been developed in [Gong et al. 2017] for the Hamiltonian system,which uses the traditional framework of Galerkin projection-based modelreduction but modifies the reduced order model so that the appropriateHamiltonian structure is preserved. However, its computational complexity foronline simulations is still high if the Hamiltonian involves non-polynomialnonlinearities. In this paper, we apply the discrete empirical interpolationmethod to improve the online efficiency of the structure-preserving reducedorder simulations. Since the reduced basis truncation can degrade theHamiltonian approximation, we propose to use the basis obtained from shiftedsnapshots. A nonlinear wave equation is used as a test bed and the numericalresults illustrate the efficacy of the proposed method.

Structure-Preserving Galerkin POD-DEIM Reduced-Order Modeling of Hamiltonian Systems