Numerical computation of near-singular and near-hypersingular integrals in higher order method of moments using curved quadrilateral patches

In numerical techniques based on the method of moments (MoM) in the surface integral equation (SIE) formulation in the frequency domain, special attention must be paid to achieving high accuracy, which includes advanced methods for numerical computation of singular and near-singular integrals defined on MoM-SIE patches. The techniques for dealing with such integrals, which arise for zero or small source-to-field distances in computing the MoM matrix entries, can broadly be classified into singularity extraction or subtraction methods and singularity cancellation or coordinate transformation methods. Also, when a MoM-SIE method is aimed at analysis of both metallic and dielectric/magnetic structures, such generality in electromagnetic MoM-SIE simulations increases the singularity of the integral kernel, and requires special treatment of highly singular integrals. Finally, this problem is even more pronounced when higher order basis functions are used for the approximation of electric and magnetic equivalent surface currents in the MoM-SIE method and when such functions are defined on curved patches.