Geometric model reduction of forced and dissipative Hamiltonian systems

摘要

In this paper, a geometric model reduction method, the proper symplectic decomposition (PSD) with structure-preserving projection, is proposed for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD)-Galerkin method, PSD is designed to build a symplectic subspace to fit empirical data, while the structure-preserving projection is developed to reconstruct reduced systems while simultaneously preserving the symplectic and forced structure. In a special case when the external force is described by the Rayleigh dissipative function, the proposed method automatically preserves the dissipativity of the original system. The stability, accuracy, and efficiency of the proposed method are illustrated through numerical simulations of a dissipative wave equation.