Reduced-order modeling
for the time-domain Maxwell equations

We study non-intrusive model order reduction (MOR) for the solution of parameterized time-domain electromagnetic wave propagation problems. The proposed MOR technique relies on a offline/online approach. The offline approach aims at building a database of high fidelity solution samples (snapshots) at some different parameter locations. These snapshot vectors are produced by a high order discontinuous Galerkin time-domain (DGTD) solver. a two-step or nested proper orthogonal decomposition (POD) method is employed to extract time- and parameter-independent POD basis functions. By using the singular value decomposition (SVD) method, the principal components of the projection coefficient matrices of high fidelity solutions onto the RB subspace are extracted. A cubic spline interpolation-based (CSI) approach is adopted to approximate the dominating time- and parameter-modes of the reduced coefficient matrices without resorting to Galerkin projection. The generation of snapshot vectors, the construction of POD basis functions and the approximation of reduced coefficient matrices based on the CSI method are completed during the offline stage. The RB solutions for new time and parameter values can be rapidly recovered via outputs from the interpolation models in the online stage. In particular, the offline and online stages of the proposed RB method, termed as the POD-CSI method, are completely decoupled, which ensures the computational validity of the method. This study is conducted in collaboration with Kun Li (School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, china), Ting-Zhu Huanga and Liang Li (School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu).

Scattering of plane wave by a dielectric cylinder: 1D plots of the real part of DGTD and POD-CSI solutions (discrete Fourier transform) (top), and bistatic RCS based on Mie series, DGTD and POD-CSI solutions (bottom).