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Regularization of the Combined Field Integral Equation on Parametric Surface for EM Scattering Problems

Self- and near-singularities have been an important issue in evaluating and filling matrix elements in the method of moments (MoM) procedure for solving integral equations. In this paper, the combined field integral equation (CFIE) is employed to solve the electromagnetic (EM) scattering problem from conductive objects and a general deductive method for extracting the self- and near-singularities of integral kernels is presented. Moreover, a new set of analytical expressions for the singular terms in the Green's function and its gradient is obtained on parametric surface by using the singularity extraction procedure. Finally, some numerical results are carried out based on the rooftop basis functions, to validate the obtained results and to demonstrate further the accuracy of these expressions in terms of regularizing self- and near-singularities in the integral kernels.