Duffy Method for Evaluation of Weakly Singular SIE Potential Integrals Over Curved Quadrilaterals With Higher Order Basis Functions

A Duffy method for singularity cancellation is proposed for evaluation of weakly singular potential integrals defined on generalized curved parametric quadrilateral patches with polynomial basis functions. Such integrals arise in evaluation of Galerkin matrix elements in method-of-moments analysis of antennas and scatterers in cases of coincident source and test elements. Examples demonstrate that the proposed Duffy method is more accurate, more rapidly converging with the increase of orders of Gauss-Legendre integration formulas, and faster to execute than four other methods for singularity treatment considered in the study.