均匀可穿透散射体的一种广义源积分方程
A Generalized Source Integral Equation for Homogeneous Penetrable Scatterers
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中文总结 AI 辅助
本文扩展广义源积分方程（GSIE）至均匀可穿透散射体，通过降低波相互作用维度增强矩量矩阵的低秩可压缩性，并在有损及慢背景介质中实现显著成本节省，经TM散射问题验证。
中文摘要 AI 辅助
广义源积分方程（GSIE）方法被扩展，以增强对本质凸均匀可穿透散射体的矩量矩阵的可压缩性。在所提出的间接表面积分方程（SIE）公式中，散射场表示使用单一分布的广义源，这些源仅弱辐射到散射体内部。内部场则使用单独分布的常规源来表示。通过广义核的表面子域之间的波相互作用具有降低的有效维度。相应的外部积分算子矩量矩阵块表现出增强的秩亏缺。对于有损散射体，这确保了整个系统的分层矩阵结构的低秩（LR）可压缩性。对于处于慢得多的背景介质中的散射体，可以实现显著的成本节省，且渐近成本缩放延迟。GSIE是针对横磁（TM）散射问题制定的。它通过代表性示例得到验证，并展示了其优越的可压缩性。
英文摘要
The generalized source integral equation (GSIE)approach is extended to enhance the compressibility of moment matrices for essentially-convex homogeneous penetrable scatterers. In the proposed indirect surface integral equation (SIE) formulation, the scattered field representations use a single distribution of generalized sources that radiate only weakly into the scatterer. A separate distribution of conventional sources is used for representing the interior fields. The wave interactions between surface subdomains via the generalized kernel are of a reduced effective dimensionality. The corresponding exterior integral operator moment matrix blocks exhibit enhanced rank deficiency. For lossy scatterers, this secures the low-rank (LR) compressibility of hierarchical matrix structures for the full system. For scatterers in a much slower background medium, significant savings with very delayed asymptotic scaling of the costs can be achieved. The GSIE is formulated for the transverse magnetic (TM) scattering problem. It is validated for representative examples and its superior compressibility is demonstrated.
发表机构
- School of Electrical and Computer Engineering, Ben-Gurion University of the Negev（内盖夫本-古里安大学电气与计算机工程学院）
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