What question did this study set out to answer?

The research aims to develop a higher-order FDTD technique for modeling complex waveguides using nonorthogonal curvilinear coordinates.

April 3, 2026Open Access

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

NKNikolaos KantartzisAristotle University of Thessaloniki TTTheodoros D. TsiboukisAristotle University of Thessaloniki TKTheodoros KosmanisInternational Hellenic University

Key Points

The research aims to develop a higher-order FDTD technique for modeling complex waveguides using nonorthogonal curvilinear coordinates.
Utilized a higher-order FDTD approach based on covariant and contravariant vector components.
Implemented a spatially-localized Wavelet-Galerkin formulation to handle fast field variations.
Combined the method with pulsed excitation and enhanced unsplit-field PMLs.
Achieved significant accuracy in modeling waveguides.
Suppressed discretization errors effectively.
Reduced computational resource demands compared to conventional methods.

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

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