ON THE COMPUTATION OF SINGULAR INTEGRALS OVER TRIANGULAR SURFACES IN R3

Abstract

Various integral equation formulations and the related numerical solutions either via Boundary Element Method (BEM) or Method of Moments (MoM) require tedious calculation of double surface integrals arising from the use of vector triangular basis functions. This paper presents an accurate technique for computation of these integrals by first converting the surface integrals to contour integrals facilitating the decomposition of boundary integral to the sum of line integrals over triangle edges. It was shown that application of this technique to a Laplace type of equations yields expressions having analytical solutions. Moreover, although the same was not possible to achieve in case of integrals involving Helmholtz kernels, nonetheless, the technique enabled the computation of surface integrals to a machine accuracy by employing the adaptive quadrature rules. This approach could be found useful in the high frequency computational dosimetry.