Curl-based Electric-Field Boundary Condition for the Accurate and Stable Electromagnetic Scattering Analysis
We introduce a curl-based Electric-Field Integral Equation (Curl-EFIE) for the electromagnetic scattering analysis from perfect electric conductors. The formulation is derived by enforcing a vanishing curl on the EFIE over the boundary manifold, achieved by testing the internal electric field with orthogonal tangent solenoidal disks. We demonstrate that a Method-of-Moments (MoM) discretization of the Curl-EFIE converges to a Galerkin-discretized MFIE as the testing disk dimensions vanish, yielding stable, breakdown-free impedance matrices for low frequencies and dense grids. Unlike the strongly singular kernels of the MFIE, the Curl-EFIE utilizes weakly singular kernels, significantly simplifying source integral evaluations. As a first-kind integral equation, it bypasses the MFIE's Gram matrix requirement, facilitating the analysis of non-matching triangulations. Furthermore, a linear combination of the Curl-EFIE and the conventional EFIE provides an interior-resonance-free formulation analogous to the Combined Field Integral Equation (CFIE). Finally, the Curl-EFIE performs particularly well at capturing the scattering behavior of sharp- edged and cornered geometries.