An accurate method for the calculation of singular integrals arising in time-domain integral equation analysis of electromagnetic scattering

Abstract

An accurate method for the evaluation of the Cauchy principal value integrals arising in time-domain electromagnetic wave scattering is presented. This is applied to a boundary integral equation (BIE) method employing quadratic curvilinear surface elements where such singularities do not vanish (as they generally do when simpler but less accurate discretizations are employed). The technique involves weakening the singularity in the original kernel to a degree where conventional integration methods may be employed and transforming the strong singularity to a line integral in a form which allows cancellation of its singular components. The effectiveness of the method is demonstrated by scattering calculations on a variety of targets and the computational cost of the approach is trivial.