使用反射广义源的良态电场表面积分方程
Well-conditioned Electric Field Surface Integral Equations using Reflective Generalized Sources
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中文总结 AI 辅助
研究利用广义源方法开发无内部共振的良态积分算子，通过增强EFIE核添加辅助贡献得GSIEs核，研究其谱特性，表明该算子有良好谱特性且可压缩，二维结果为扩展到三维问题及更广泛辅助核奠定基础。
中文摘要 AI 辅助
本文采用广义源方法开发了一类无内部共振的良态积分算子，无需组合公式。通过增强传统电场积分方程（EFIE）核并添加辅助贡献来提高相应矩矩阵块的秩亏，得到广义源积分方程（GSIEs）核。首次研究了内部散射凸屏蔽产生的辅助核的GSIE算子谱。对于同心圆形散射体和屏蔽，表明合适屏蔽参数下，横向磁（TM）和横向电（TE）-GSIE算子无内部固有和准共振。辅助分量是其EFIE对应物的紧扰动，GSIEs继承其密集离散化崩溃问题，可通过卡尔德隆型预处理解决。高频崩溃机制受辅助分量影响，有时具有更大弹性。对于GSIE对偶和汤川核预条件器，公式具有良好谱特性并保持可压缩性，对快速迭代求解器设计有吸引力。二维屏蔽基算子结果为扩展到三维问题和更广泛几何适用性的辅助核奠定基础。
英文摘要
This work uses the generalized source approach to develop a class of well-conditioned integral operators that are free of internal resonance, without the need for combined formulations. The Generalized source integral equations (GSIEs) kernels are obtained by augmenting the conventional electric field integral equation (EFIE) kernel with auxiliary contributions to enhance the rank deficiency of the corresponding moment matrix blocks. This paper presents the first investigation of the spectra of GSIE operators for auxiliary kernels produced by internal scattering convex shields. Using closed-form expressions for concentric circular scatterers and shields, it is shown that, with shield parameters that are suitable for enhanced compressibility, the transverse magnetic (TM)- and transverse electric (TE)-GSIE operators are free of internal proper and quasi-resonances. The auxiliary components are shown to be compact perturbations of their EFIE counterparts. Hence these GSIESs inherit their dense-discretization breakdown, which remains curable via Calderón-type preconditioning. The mechanisms that govern the high-frequency breakdown are shown to be influenced by the auxiliary component, leading, in some cases, to greater resilience. These observations are shown to remain valid for moment matrices and GSIEs designed with non-circular stencil shields. For both GSIE-dual and Yukawa-kernel preconditioners, the formulations exhibit favorable spectral properties while maintaining their compressibility. This makes the formulations attractive for the design of fast iterative solvers. The results on the two-dimensional shield-based operators provide a foundation for extending the approach to three-dimensional problems and to auxiliary kernels with broader geometric applicability.
