Exact Evaluation of Time-Domain Physical Optics Integral for High-Order Triangles

Abstract

In this work, a method for the exact evaluation of time domain physical optics (PO) integral on high-order triangles is presented. The presented method is based on the recently developed method for quadratic triangles. Specifically, the PO integral on the surface of the high-order triangle is reduced to a line integral on the intersection of the high-order triangle and the plane formed by the incidence and observation directions in barycentric coordinates of the triangle. Then, the intersecting curve is parametrized in terms of one of the barycentric coordinates of the high-order triangle. At last, the line integral is evaluated exactly using the suitable order Gauss Legendre quadrature rule (GLQR). The validity of the proposed method is demonstrated via analyzing transient scattering from a unit sphere and a flower-shaped scatterer modeled with high-order triangles using PO approximation.