Radial-Angular Singularity Cancellation Transformations Derived by Variable Separation

The variable separation method is utilized to construct new radial-angular-R n 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-R 1 transformation, new radial-angular-R 2 , and radial-angular-R 2 -cosh transformations, as well as a new radial-angular-R 3 , an augmented radial-angular-R 3 and an arcsinh-R 3 transformation are introduced. The proposed R 2 and R 3 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 R 1 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.