Analysis and augmentation of the Duffy transformation for near-singular integrals

This paper presents a singularity cancellation transformation for dealing with weak, near-singular integral kernels on triangular surface domains, as encountered in the method of moments (MoM). The main benefit of singularity cancellation quadrature schemes is that it is purely numerical, with no analytical evaluations of integrals required. The transformation presented here is based on augmenting the well-known Duffy transformation in a systematic way, such that its shortcomings are addressed. This augmented Duffy transformation performs very well in comparison to other, existing methods.