Discontinuous Galerkin time-domain solution of the purely hyperbolic maxwell equations

摘要

In the numerical solution of Maxwell's equations, we usually consider only Faraday's and Ampere's laws, and assume the two Gauss' laws are satisfied automatically. This will cause a significant numerical error in a self-consistent simulation of a particle-wave interaction. To remove the numerical error that comes from the violation of Gauss' laws, divergence cleaning techniques have been introduced. In this paper, the purely hyperbolic Maxwell (PHM) equations that can eliminate the numerical errors of both Gauss' laws are presented. The discontinuous Galerkin time-domain method is then applied to the numerical solution of the PHM equations, with the intermediate states and the numerical fluxes derived by solving the Riemann problem.