Fully Analytical Evaluation of Singular Integrals With RWG and Rooftop Basis Functions

When the method of moments is used to solve surface integral equations, it is inevitable to encounter the problem of singularity because of Green's function in integral kernel. In this article, by expanding Green's function with Taylor series and applying appropriate coordinate transformation, closed-form expression of each term is derived. After proper linear combination, analytical solutions of singular integrals on triangular and rectangular domains with Rao-Wilton-Glisson and rooftop basis function can be achieved. Compared with numerical solutions, this approach is more efficient and can considerably decrease the computational cost, for a given precision.