基于旋度的电场边界条件用于精确稳定的电磁散射分析
Curl-based Electric-Field Boundary Condition for the Accurate and Stable Electromagnetic Scattering Analysis
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中文总结 AI 辅助
研究针对完美导体电磁散射分析，提出基于旋度的电场积分方程（Curl-EFIE）。通过矩量法离散，其收敛到伽辽金离散的MFIE，利用弱奇异核简化积分，还能与传统EFIE组合，在捕捉特定几何散射行为上表现出色。
中文摘要 AI 辅助
我们引入一种基于旋度的电场积分方程（Curl-EFIE）用于完美导体的电磁散射分析。该公式通过在边界流形上对EFIE施加零旋度得出，通过用正交切向螺线管盘测试内部电场实现。我们证明，当测试盘尺寸消失时，Curl-EFIE的矩量法（MoM）离散收敛到伽辽金离散的MFIE，为低频和密集网格产生稳定、无击穿的阻抗矩阵。与MFIE的强奇异核不同，Curl-EFIE使用弱奇异核，显著简化源积分评估。作为第一类积分方程，它绕过了MFIE的Gram矩阵要求，便于分析非匹配三角剖分。此外，Curl-EFIE和传统EFIE的线性组合提供了类似于组合场积分方程（CFIE）的无内部共振公式。最后，Curl-EFIE在捕捉尖锐边缘和拐角几何形状的散射行为方面表现特别出色。
英文摘要
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.
