A new radial-angular-R2 transformation for singular integrals on triangular meshes

A new radial-angular-R² singularity cancellation transformation is proposed. The accuracy of this transformation is not associated with the height of the observation point above the plane of the source domain. When the height tends to zero, the corresponding limit of the transformation turns out to be a new well-behaved transformation within the plane of the source domain, which is also very efficient for accurate singular integral computations. Common Green's functions and its gradients require first and second order transformations for singularity cancellation. However, the proposed second order transformation is also effective for the lower order singular integrals and it is, thus, applicable for all forms of singular integrals in electromagnetic boundary integral equation formulations.