Application of Hybridized Discontinuous Galerkin Time Domain Method into the Solution of Multiscale Electromagnetic Problems

Abstract

In this paper, a hybridized discontinuous Galerkin time domain method consisting of interior penalty discontinuous Galerkin (IPDG) time domain based on Helmholtz vector wave equation and discontinuous Galerkin time domain (DGTD) method based on Maxwell’s equations has been developed to solve the multiscale problems. The IPDG method solves the vector wave equation for the electric field E and meanwhile the magnetic field H is flexibly solved according to an auxiliary equation. The E and H are simultaneously solved by the DGTD method. With the use of the upwind flux, the IPDG and the DGTD is hybridized. With a local time stepping scheme (LTS) based on a simple interpolation technique, the different time steps restricted by the CFL stability can be used in multiple subdomains with arbitrary mesh size ratio, and thus the computational efficiency can be greatly improved. In order to accelerate the solution of the proposed hybridization method, the graphical processing units (GPU) based on compute unified device architecture (CUDA) are introduced. Some numerical examples are given to show good performance of the proposed hybrid method in the solution of multiscale problems.