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

Abstract : 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.
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https://hal.inria.fr/hal-01973540
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Submitted on : Tuesday, January 8, 2019 - 1:13:04 PM
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Kun Li, Ting-Zhu Huang, Liang Li, Stéphane Lanteri. A reduced-order DG formulation based on POD method for the time-domain Maxwell’s equations in dispersive media. Journal of Computational and Applied Mathematics, Elsevier, 2018, 336, pp.249-266. ⟨10.1016/j.cam.2017.12.051⟩. ⟨hal-01973540⟩

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