A Simple Transformation for Near-Singular Integrals on Curvilinear Elements

It is difficult to evaluate the near-singular four-dimensional integrals in the Galerkin magnetic-field integral equations (MFIE), especially for the curvilinear elements. This communication presents a hyperbolic transformation to cancel the near singularities in the 1/R² kernel on curved quadrilateral elements, which is addressed theoretically and numerically. This method has a much simpler formula than the so-called DIRECTFN method, and its convergence rate may be much faster than the latter. This is demonstrated by evaluating the near-singular integral of a sharp-edged structure composed of two curvilinear quadrilaterals.