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

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. Result s 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 (c) 2020 Elsevier Inc. All rights reserved.