An effective 3D leapfrog scheme for electromagnetic modelling of arbitrary shaped dielectric objects using unstructured meshes

Abstract

In computational electromagnetics, the advantages of the standard Yee algorithm are its simplicity and its low computational costs. However, because of the accuracy losses resulting from the staircased representation of curved interfaces, it is normally not the method of choice for modelling electromagnetic interactions with objects of arbitrary shape. For these problems, an unstructured mesh finite volume time domain method is often employed, although the scheme does not satisfy the divergence free condition at the discrete level. In this paper, we generalize the standard Yee algorithm for use on unstructured meshes and solve the problem concerning the loss of accuracy linked to staircasing, while preserving the divergence free nature of the algorithm. The scheme is implemented on high quality primal Delaunay and dual Voronoi meshes. The performance of the approach was validated in previous work by simulating the scattering of electromagnetic waves by spherical 3D PEC objects in free space. In this paper we demonstrate the performance of this scheme for penetration problems in lossy dielectrics using a new averaging technique for Delaunay and Voronoi edges at the interface. A detailed explanation of the implementation of the method, and a demonstration of the quality of the results obtained for transmittance and scattering simulations by 3D objects of arbitrary shapes, are presented.