On the Near-Interaction Elements in Integral Equation Solvers for Electromagnetic Scattering by Three-Dimensional Thin Objects

The accuracy of near-interaction (NI) evaluation is investigated for hypersingular and strongly singular kernels in solving electromagnetic (EM) integral equations. We first define the NI between a field point and a source triangular patch using a nearness factor (
NF
) and show the accuracy of numerical integrations for the NI integrals with hypersingular or strongly singular kernels. It is found that there exists a transition area or turning point before and after which the convergence behaviors of those integrations are greatly different. We define the
NF
value at the 1% relative error as the turning point
NF

₀
and define
NF
les
NF

₀
as the NI range. We find that
NF

₀
=1.4 could be a bound of NI range for the triangles with a quality factor
q
> 0.35 and analytical formulas should be used in evaluating NI elements within the bound. Numerical examples for EM scattering by three-dimensional (3D) thin objects are used to demonstrate the significance of NI treatments for the accurate solutions.