POD-based model order reduction with an adaptive snapshot selection for a discontinuous Galerkin approximation of the time-domain Maxwell's equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:396

Article

Li, Kun¹  Huang, Ting-Zhu¹  Li, Liang¹  Lanteri, Stephane² 

[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

[2] INRIA, 2004 Route Lucioles,BP 93, F-06902 Sophia Antipolis, France

关键词: Time-domain Maxwell's equations;    Discontinuous Galerkin method;    Model order reduction;    Proper orthogonal decomposition;    Adaptive snapshot selection algorithm;   

DOI  :  10.1016/j.jcp.2019.05.051

来源: Elsevier

【 摘 要 】

In this work we report on a reduced-order model (ROM) for the system of time-domain Maxwell's equations discretized by a discontinuous Galerkin (DG) method. We leverage previous results on proper orthogonal decomposition (POD) [1,2], in particular for the wave equation [3], to propose a POD-based ROM with an adaptive snapshot selection strategy where the snapshots are produced by a high order discontinuous Galerkin time-domain (DGTD) solver. The latter is formulated on an unstructured simplicial mesh, and combines a centered scheme for the definition of the numerical fluxes of the electric and magnetic fields at element interfaces with a second order leap-frog (LF2) time scheme for the time integration of the associated semi-discrete equations. The POD-based ROM is established by projecting (Galerkin projection) the global semi-discrete DG scheme onto a low-dimensional space generated by the POD basis vectors. Inspired from the approach followed in [2,3], we derive error bounds for the POD-based ROM that is adapted to our particular modeling and discretization settings. The adaptive snapshot selection algorithm exploits the results of this analysis to measure the control error. A snapshot choosing rule aiming at keeping the error estimate close to a target selection error tolerance is proposed, which is similar to the standard rules found in adaptive time-stepping ordinary differential equations (ODEs) solvers. An incremental singular value decomposition (ISVD) algorithm is used to update the SVD on-the-fly when a new snapshot is available. The purpose of this adaptive selection strategy is to save memory without storing snapshots, while producing a smaller error. Numerical experiments for the 2-D time-domain Maxwell's equations nicely illustrate the performance of the resulting POD-based ROM with adaptive snapshot selection. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

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