A nonorthogonal higher-order wavelet-oriented FDTD technique for 3-D waveguide structures on generalized curvilinear grids

Abstract

A generalized higher-order FDTD rendition of the covariant and contravariant vector component theory for the accurate modeling of complex waveguides in 3-D nonorthogonal curvilinear coordinates, is presented in this paper. The novel algo- rithm, which postulates conventional and nonstandard concepts, embodies a spatially-localized Wavelet-Galerkin formulation in order to efficiently deal with fast field variations in the vicinity of arbitrarily-angled wedges. The proposed method is combined with a pulsed excitation and enhanced unsplit-field PMLs thus, achieving significant accuracy and suppression of all discretiza- tion errors with a simultaneous diminishment of computational resources, as indicated by various numerical results. Index Terms— Curvilinear nonorthogonal coordinates, FDTD methods, higher-order schemes, waveguides, wavelet transforms