Derivation of radial-angular singularity cancellation transformations by the variable separation method

The variable separation method is utilized to derive a family of radial-angular-Rⁿ transformation schemes for singularity cancellation. The variables, the angle and the radius in polar coordinates derived from the Cartesian coordinates, are utilized by the variable separation method. General solutions to the differential equations derived from the variable separation method are proposed. A new family of radial-angular-R¹, -R² and -R³ transformation schemes is designed for the singularity cancellation technique. The proposed transformation schemes are applicable to all types of singular kernels in the Method of Moments (MoM) as found in electromagnetic surface integral equations.