Generating the Voronoi-Delaunay Dual Diagram for Co-Volume Integration Schemes

Abstract

Advantages of co-volume methods (based on the use of a high quality Voronoi diagram and the dual Delaunay mesh) for two- and three-dimensional computational electromagnetics are well known. The co-volume method is faster than traditional methods for an unstructured mesh and needs less memory. The co-volume integration scheme preserves energy, i.e. gives high accuracy of wave amplitude. It also gives better accuracy if the scattering objects has sharp corners or vertices. However, the co-volume method requires use of high quality unstructured dual Voronoi-Delaunay diagrams which cannot be created by classical mesh generation methods. For two-dimensional problems, a stitching method gives the best mesh quality for a wide variety of domains. Generation of a three-dimensional dual mesh appropriate for the use of a co-volume scheme is a much more difficult issue. Here, an approach is being developed where the main ideas of the stitching method are exploited. Some examples of three-dimensional meshes generated by this new method, as well as the results of the integration of Maxwell's equations on those meshes, are presented.