A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but modifies the reduced order model so that the appropriate Hamiltonian structure is preserved. However, its computational complexity for online simulations is still high if the Hamiltonian involves non-polynomial nonlinearities. In this paper, we apply the discrete empirical interpolation method to improve the online efficiency of the structure-preserving reduced order simulations. Since the reduced basis truncation can degrade the Hamiltonian approximation, we propose to use the basis obtained from shifted snapshots. A nonlinear wave equation is used as a test bed and the numerical results illustrate the efficacy of the proposed method.
翻译:汉密尔顿系统在[Gong等人,2017年]为汉密尔顿系统开发了一种结构,保持适当的正正正分解减序模型模型,该结构使用传统的基于Galerkin预测的减序模型框架,但修改了降序模型,以保持适当的汉密尔顿结构;然而,如果汉密尔顿人涉及非球系非线性,其在线模拟的计算复杂性仍然很高。在本文件中,我们采用离散经验性内插法,以提高结构保全减序模拟的在线效率。由于减少基次脱轨可以降低汉密尔顿近似值,我们提议使用从转移的快照中获得的基础。使用非线性波方程式作为测试床,数字结果说明拟议方法的功效。