Evaluation of the Retarded-Time Potentials Due to an Impulsively Excited Curvilinear RWG Function

A scheme to evaluate the retarded-time potentials due to impulsively excited curvilinear Rao–Wilton–Glisson (CRWG) functions, defined on a pair of high-order triangles, is presented. The scheme is presented for the self-term case, i.e., when the observation point is in the source triangle, then extended to the non-self-term cases. To develop the scheme, first, the retarded-time potential integrals on the high-order triangles are reduced to a line integral, which is formed by the intersection of the high-order triangle and a sphere centered at the observation point, then suitable order Gauss–Legendre quadrature rule (GLQR) is applied to evaluate the line integral. It is shown that the resulting scheme does not require any singularity treatment since the integrand of the line integral does not exhibit any singular behavior as time tends to zero. Numerical examples demonstrate the validity and accuracy of the proposed scheme by comparing the time samples of the retarded-time potentials obtained using the proposed scheme and samples obtained in the frequency domain (FD) and then inverse Fourier transformed to the time domain. It is also shown that using suitable order GLQR, retarded-time potentials can be evaluated in machine precision.