A reduced-order DG formulation based on POD method for the time-domain Maxwell's equations in dispersive media

作者：Li, Kun; Huang, Ting-Zhu^*; Li, Liang^*; Lanteri, Stephane

来源：Journal of Computational and Applied Mathematics, 2018, 336: 249-266.

DOI：10.1016/j.cam.2017.12.051

• Time-domain Maxwell equations
• Dispersive media
• Discontinuous Galerkin method
• Model order reduction
• Proper orthogonal decomposition

In this work, a proper orthogonal decomposition (POD) method is applied to time-domain Maxwell's equations coupled to a Drude dispersion model, which are discretized in space by a discontinuous Galerkin (DG) method. An auxiliary differential equation (ADE) method is used to represent the constitutive relation for the dispersive medium. A POD-DGTD formulation with lower dimension and sufficiently high accuracy is established, together with the description of the POD reduced-order basis, its construction from a snapshot set, and its application to the solution of the time-domain Maxwell's equations. The overall goal is to reduce the computational time while maintaining an acceptable level of accuracy, in order to obtain an efficient time-domain solver to be used as a starting point for an optimization strategy. We provide results from numerical experiments for two-dimensional problems that illustrate the capabilities of the proposed POD-DGTD formulation and assess its efficiency.

• 出版日期2018-7
• 单位INRIA; 电子科技大学