This paper presents a non-intrusive model order reduction (MOR) for the solution of parameterized electromagnetic scattering problems, which needs to prepare a database offline of full-order solution samples (snapshots) at some different parameter locations. The snapshot vectors are produced by a high order discontinuous Galerkin time-domain (DGTD) solver formulated on an unstructured simplicial mesh. Because the second dimension of snapshots matrix is large, 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 (also referred to as the reduced coefficient matrices) of full-order solutions onto the RB subspace are extracted. A cubic spline interpolation-based (CSI) approach is proposed 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. Moreover, a surrogate error model is constructed as an efficient error estimator for the POD-CSI 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 POD-CSI method.

本文提出了一种用于解决参数化电磁散射问题的非侵入式模型降阶（MOR）方法，该算法需要离线准备一个数据库，其中包含一些不同参数位置的全阶解决方案样本（快照）。快照向量由在非结构化简单网格上制定的高阶不连续Galerkin时域（DGTD）求解器生成。由于快照矩阵的第二维较大，因此采用两步或嵌套的固有正交分解（POD）方法来提取与时间和参数无关的POD基函数。通过使用奇异值分解（SVD）方法，提取全阶解在RB子空间上的投影系数矩阵（也称为降系数矩阵）的主成分。提出了一种基于三次样条插值（CSI）的方法来近似降低系数矩阵的主导时间模式和参数模式，而无需借助Galerkin投影。在离线阶段完成了快照向量的生成，POD基函数的构造以及基于CSI方法的约简系数矩阵的逼近。可以通过在线阶段中插值模型的输出快速恢复新时间和参数值的RB解决方案。特别地，所提出的RB方法的离线和在线阶段，称为POD-CSI方法，被完全解耦，这确保了该方法的计算有效性。此外，替代误差模型被构建为POD-CSI方法的有效误差估计器。