Global energy preserving model reduction for multi-symplectic PDEs

作者：

Highlights：

• Preservation of the global energy of multi-symplectic PDEs by reducedorder modeling.

• The reduced approximations of the KdV and NLS equations are almost identical with full solutions.

• Offline-online decomposition of the full-order and reduced-order models demonstrate the computational efficiency of the approach.

• The oscillatory behavior of the reduced global energy over time without any drift guarantees the stability of the solution in the context of geometric integration.

摘要

•Preservation of the global energy of multi-symplectic PDEs by reducedorder modeling.•The reduced approximations of the KdV and NLS equations are almost identical with full solutions.•Offline-online decomposition of the full-order and reduced-order models demonstrate the computational efficiency of the approach.•The oscillatory behavior of the reduced global energy over time without any drift guarantees the stability of the solution in the context of geometric integration.

论文关键词：model reduction,proper orthogonal decomposition,discrete empirical interpolation method,Hamiltonian PDE,multi-symplecticity,energy preservation

论文评审过程：Received 13 February 2022, Revised 10 August 2022, Accepted 14 August 2022, Available online 28 August 2022, Version of Record 28 August 2022.

论文官网地址：https://doi.org/10.1016/j.amc.2022.127483