Orthogonal Basis Functions in Discrete-Time Electromagnetics and Their Implementation to Compute the Matrix-Type UTD Transition Function for PEC Wedge Diffractions

A set of orthogonal global time-domain (TD) basis functions of numerical robust is presented and examined for the applications of discrete time electromagnetics (DT-EM). The matrix equations or integrals arising from the expansion of TD field signals by this basis set can be effectively computed since they can be diagonalized by eigenvalue and vector decomposition method. This characteristic is particularly useful in the computation of TD solutions transformed from the corresponding frequency domain formulations such as in the computation of transition functions for the implementation of DT uniform geometrical theory of diffraction (DT-UTD). It may not only avoid the TD field signal divergence along propagation, but also simplify the computational complexity by avoiding the numerical integration of matrix integral. In this paper, the characteristics are examined via the implementation of plane wave propagation and DT-UTD for the diffraction from curved wedges. Numerical examples are presented to demonstrate their validity in DT-EM applications.