A novel class of explicit divergence-free time-domain methods for efficiently solving Maxwell's equations

Abstract

In electrical engineering and physics, Maxwell's equations play a very important role and have a variety of applications. In this paper, we propose and analyse a novel class of time domain conservative schemes in rectangular coordinate to solve Maxwell's equations with periodic boundary conditions. This class of methods is explicit and easy to implement with low computational cost and memory storage. The error estimates presented in this paper demonstrate that the numerical solutions obtained by this class of conservative schemes can achieve arbitrarily high-order accuracy. The discrete divergences in numerical experiments motivate us to show that the conservative scheme is divergence-free by the rigorous numerical analysis, which is of great importance in the sense of geometric numerical integration. The discrete energy monitors give light to the statement that the conservative scheme can keep the linear relationship among some qualitative features of the underlying Maxwell's equations.