Tailoring unstructured meshes for use with a 3D time domain co‐volume algorithm for computational electromagnetics

Abstract

AbstractThe Yee algorithm is a highly efficient time domain co‐volume method for computational electromagnetics using a pair of staggered orthogonal cartesian meshes. An equivalent unstructured mesh process is readily implemented on a primal Delaunay tetrahedral mesh and its orthogonal Voronoï dual. The difficulty, for practical applications, is ensuring that both the Delaunay and the Voronoï meshes possess the necessary properties to enable an accurate and efficient solution to be obtained by this approach. This is a mesh generation problem and it is addressed here by using a combination of a point distribution provided by an ideal tetrahedral mesh, a constrained centroidal Voronoï tessellation method and a mesh quality optimization procedure. For the selected application area of electromagnetic wave scattering problems, the computational efficiency is enhanced by using a hybrid primal mesh, consisting of tetrahedral elements in the vicinity of the scatterer and hexahedral elements elsewhere. Three examples are included to demonstrate the viability of the proposed approach and to indicate the numerical performance that can be achieved. Copyright © 2010 John Wiley & Sons, Ltd.