A topologically consistent class of 3-D higher order curvilinear FDTD schemes for dispersion-optimized EMC and material modeling

An enhanced higher order finite-difference time-domain (FDTD) algorithm for the precise analysis of complex 3-D electromagnetic compatibility (EMC) structures and arbitrary interface material distributions in general curvilinear, skewed and stretching lattices is presented in this paper. Introducing a systematic topological tessellation, the novel methodology develops a family of robust higher order non-standard forms, which exactly represent the material properties and significantly suppress the artificial dispersion errors. To handle inherent mesh deficiencies an enhanced low-pass filtering procedure is implemented, while a consistent class of self-adaptive compact operators ensures the correct evaluation of electromagnetic components near boundary walls. Moreover, for more involved media interfaces that do not follow the lines of the grid, a convergent transformation around these discontinuities leads to precise simulations. Therefore, this optimal field-preserving technique along with suitably tuned perfectly matched layers (PMLs), achieve high levels of accuracy, decrease the required number of points per wavelength and provide considerable computational savings, as indicated by extensive numerical results addressing 3-D EMC and hard-to-model material applications.