A new family of radial angular transformations for the near-singularity cancellation technique

A new family of radial-angular-Rⁿ transformation formulas are proposed for the singularity cancellation technique. To cancel out the singularity in the integral kernels, an ideal Jacobian of the coordinate transformations is required. For the first order of singular coupling integral kernels, a new augmented radial-angular-R¹ transformation is proposed. For the second order of singular coupling integral kernels, new radial-angular-R² and radial-angular-R²-cosh transformations are developed. Finally, for the third order of singular coupling integral kernels, a new group of radial-angular-R³, arcsinh-R³ and augmented radial-angular-R³ transformations are designed. The higher order singularity cancellation schemes are also effective for the lower orders of singular kernels. The proposed R² and R³ transformation schemes are efficient and applicable to all mutual couplings for in electromagnetics integral equations.