Radial-angular singularity cancellation transformations derived by variable separation

The variable separation method is utilized to construct new radial-angular-Rⁿ coordinate transformation schemes for the singularity cancellation technique. Derived from the concept of achieving an ideal Jacobian of the transformations and with different parameter settings in the variable separation method, a new augmented radial-angular-R¹ transformation, new radial-angular-R², and radial-angular-R²-cosh transformations, as well as a new radial-angular-R³, an augmented radial-angular-R³ and an arcsinh-R³ transformation are introduced. The proposed R² and R³ transformations are efficient and applicable to all types of near-singular kernels occurring in the method of moments (MoM) solution of electromagnetic surface integral equations, whereas the R¹ transformation is only suitable for the first-order singular integrals. The newly proposed transformation schemes are verified and they are also applied to deformed triangles, where good performances are still achieved.