Stabilized DG-PSTD Method With Nonconformal Meshes for Electromagnetic Waves

Abstract

We present a node-based discontinuous Galerkin (DG) pseudospectral time domain (PSTD) algorithm, with adaptive nonconformal unstructured meshes, for 3-D large-scale Maxwell’s equations. This algorithm is a combination of a new DG algorithm and a PSTD method, where spectral accuracy is achieved via the PSTD algorithm, while the DG serves as a stable coupling for multiple domains with unstructured hexahedra. Time marching is efficient because the mass matrix in the DG-PSTD algorithm is exactly diagonal. The scheme is low-storage and scalable because the stiffness matrix is localized into a small shared matrix. Furthermore, arbitrary nonconformal meshes can be adaptively realized, increasing the flexibility of complex media modeling. Our numerical results corroborate the long-time stability, high efficiency, and high-order accuracy of the proposed solver. Finally, an adaptive application of 5G electromagnetic signal propagation demonstrates the efficiency and capability of the proposed high-order solver.