A stable interpolation technique for FDTD on non-orthogonal grids

The application of the FDTD algorithm on generalized non-orthogonal meshes, following the basic ideas of Holland (1983), has been investigated by many authors for several years now, and detailed dispersion analysis as well as convergence studies have been published. Already in 1992 also a general st ability criterion was given for the time integration using the standard lea p-frog scheme (Lee et al.). Many authors, however, still propose some dampe d time stepping algorithms to work around unexpected instabilities in the d iscretization method. In this paper the origin of this type of instability is revealed. and a technique to obtain a stable discretization of Maxwell's equations on non-orthogonal grids is proposed. To obtain more insight into the stability properties of the method, it is reformulated according to th e matrix-vector notation of the Finite Integration Technique. (C) 1998 John Wiley & Sons, Ltd.