Generating the VoronoDual Diagram for Co-Volume Integration Schemes

Advantages of co-volume methods (based on the use of a high quality Voronodiagram and the dual Delaunay mesh) for two- and three-dimensional computational electromag- netics 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 en- ergy, i.e. gives high accuracy of wave amplitude. It also gives better accuracy if the scattering objects has sharp cor- ners or vertices. However, the co-volume method requires use of high quality unstructured dual Voronodi- agrams which cannot be created by classical mesh gener- ation methods. For two-dimensional problems, a stitching method gives the best mesh quality for a wide variety of do- mains. Generation of a three-dimensional dual mesh appro- priate for the use of a co-volume scheme is a much more dif- ficult issue. Here, an approach is being developed where the main ideas of the stitching method are exploited. Some ex- amples 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. ments. Nevertheless, despite the fact that real progress has been achieved in unstructured mesh generation methods, co- volume approaches for simulation involving complex shape domains have not been widely applied. This is due to the difficulties encountered when attempting to generate high quality dual diagrams, satisfying the requirements neces- sary for the use of the co-volume solution schemes. In the present work, we list the requirements for the mesh appropriate for the use with co-volume schemes. We demonstrate that current mesh generating methods cannot produce the required mesh for general 3D geometries. We consider a new approach to mesh generation, based on the experience obtained in generating 2D meshes. Some nu- merical examples of a propagating and scattered EM wave are described that demonstrate the effectiveness of the ap- proach for use with co-volume integration schemes.