A Reduced-Order Discontinuous Galerkin Method Based on POD for Electromagnetic Simulation

Abstract

This paper is concerned with the design of a reduced-order discontinuous Galerkin (DG) method based on the proper orthogonal decomposition (POD) method for electromagnetic simulation. A centered flux approximation for surface integral and a second-order leap-frog scheme for advancing in time are applied in the classical DG method. The POD basis is created by the eigensystem 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 discontinuous Galerkin time-domain formulation with lower dimension and sufficiently high accuracy is established by applying a Galerkin projection for the semidiscrete 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.