This paper is concerned with the design of a reduced-order discontinuous Galerkin (DG) method based on proper orthogonal decomposition (POD) method for electromagnetic simulation. A centered flux approximation for surface integral and a second order leap-frog (LF2) scheme for advancing in time are applied in the classical DG method. The POD basis is created by the eigensytem of the correlation matrix, which is generated by the snapshot matrix whose columns are the snapshot vectors extracted from the high fidelity DG simulation. The POD-DGTD formulation with lower dimension and sufficiently high accuracy is established by applying a Galerkin projection for the semi-discrete DG scheme. The overall goal is to reduce the computational cost while maintaining an acceptable level of accuracy. Numerical experiments for electromagnetic problems illustrate the performance of the proposed reduction method.

We present a non-intrusive model order reduction (NIMOR) approach with an offline-online decoupling for the solution of parameterized time-domain Maxwell's equations. During the offline stage, the training parameters are chosen by using Smolyak sparse grid method with an approximation level $ L $ ($ L\geq1 $) over a target parameterized space. For each selected parameter, the snapshot vectors are first produced by a high order discontinuous Galerkin time-domain (DGTD) solver formulated on an unstructured simplicial mesh. In order to minimize the overall computational cost in the offline stage and to improve the accuracy of the NIMOR method, a radial basis function (RBF) interpolation method is then used to construct more snapshot vectors at the sparse grid with approximation level $ L+1 $, which includes the sparse grids from approximation level $ L $. A 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 reduced coefficient matrices of the high-fidelity solutions onto the reduced-order subspace spaned by the POD basis functions are extracted. Moreover, a Gaussian process regression (GPR) method is proposed to approximate the dominating time- and parameter-modes of the reduced coefficient matrices. During the online stage, the reduced-order solutions for new time and parameter values can be rapidly recovered via outputs from the regression models without using the DGTD method. Numerical experiments for the scattering of plane wave by a 2-D dielectric cylinder and a multi-layer heterogeneous medium nicely illustrate the performance of the NIMOR method.