On the Evaluation of Retarded-Time Potentials due to CRWG Functions: Self-Term Case

Abstract

A scheme to evaluate the retarded-time potentials due to curvilinear Rao-Wilton-Glisson (CRWG) functions is presented for the self-term case, i.e., when the observation point is in the source triangle. Using the Radon transform interpretation of the radiation integrals, the surface integral is reduced to a line integral on the intersection of the sphere centered to the observation point and the support of the CRWG function, i.e., high order triangles. The line integral is evaluated using the suitable order Gauss-Legendre quadrature rule (GLQR). It is shown that the kernel of the resulting line integral does not exhibit any singular behavior as time tends to zero. A numerical example is presented to demonstrate the accuracy and validity of the proposed scheme.