Time-explicit numerical methods for Maxwell’s equation in second-order form

Abstract

This paper postulates three numerical methods solving the second-order Maxwell’s equation on unstructured grids. These numerical methods are derived from the classic finite-volume philosophy and also from the residual distribution approach. Some approximations are performed on the outflow boundary and the transverse electric (TE) mode with a perfect electrical conducting (PEC) material interface to ensure that these numerical methods will work for hyperbolic wave equations. The methods proposed here are simple, compact, second-order-accurate coupled with an explicit time-integration, and can be replicated with the least effort. Results herein include a variety of two and three dimensional problems with good accuracy. Moreover, solving the second-order Maxwell’s equation shows a substantial reduction in computational cost relative to solving the first-order system of Maxwell’s equations. Higher Education