Spatio-temporal basis-based parametric non-intrusive reduced order modeling for time-domain Maxwell's equations

This study proposes a spatio-temporal basis-based non-intrusive model order reduction (NIMOR) method based on a fully decoupled offline-online framework for solving parameterized electromagnetic wave propagation problems. By employing a nested proper orthogonal decomposition (POD) method, a set of spatial and temporal reduced basis (RB) functions are derived from a collection of high-fidelity (HF) solutions or snapshots, which are generated by a high-order discontinuous Galerkin time-domain (DGTD) solver on a properly chosen training parameter set. To better approximate the mapping from parameter to reduced order combination coefficient matrix, the CANDECOMP/PARAFAC (CP) method based on an alternating least squares (ALS) method is firstly used to decompose a third-order tensor formed by concatenating all reduced order combination coefficient matrices associated with the parameters. After that, some rank-one tensors or vectors are approximated by the Gaussian process regression (GPR) method, instead of directly regressing the mapping. The offline stage involves several key steps, i.e., generating snapshots, extracting RB functions, and regressing reduced order combination coefficient matrices. Once this stage is completed, the RB solutions for some new parameter values can be quickly recovered solely through the outputs of the matrix regression models during the online stage. This decoupling of the offline and online stages in the proposed NIMOR method, known as the POD-CP-GPR method, ensures the computational efficiency and validity of the approach. To verify the effectiveness of the proposed NIMOR method, some numerical experiments on 2-D problems, including the scattering of a plane wave by a dielectric disk and by a multi-layer heterogeneous medium, are presented. These numerical results fully demonstrate the performance of the proposed method.