Three-dimensional time-domain method for solving Maxwell's equations based on circumcenters of elements

The finite-difference time-domain (FD-TD) method, based on the traditional Yee (1966) algorithm, has been successfully applied to the analysis of many problems of interest. A three-dimensional time-domain method for solving Maxwell's equations is developed by using non-cubic cells. The advantage of this formulation is that it is free from a volume integration since updating equations are directly obtained from Faraday and Ampere's laws. The faces of tetrahedral elements and the polygons of their Voronoi diagram are chosen as integral surfaces for Faraday and Ampere's laws, respectively. From the calculation of the scattering of the plane wave by a cylinder, it is found that this formulation is valid for curved surfaces.