A reduced-basis approximation to solve for the electromagnetic scattering from nonpenetrable targets in a frequency band of interest is studied in detail. Perfect electric scatterers in homogeneous media are considered. Even though the frequency behavior can be complicated, the electromagnetic scattering does not arbitrarily change in the frequency band of interest. Thus, instead of using computationally inefficient, large-dimension numerical approximation scenarios, such as the method of moments, to solve for integral equations in the band of interest, a low-dimension reduced-basis space is identified to approximate the smooth evolution of the electromagnetic scattering itself as frequency changes. As a result, the frequency-parameter scattering problem is solved within a reduced-order model approach. The electric field integral equation formulation is addressed and properly selected electric currents are considered to span the reduced-basis space in the frequency band of interest. The involved frequency dependence in the integral equation due to the wave propagation phenomena described in the free-space Green’s function has traditionally limited the applicability of reduced-basis approximations for fast frequency sweep in integral equation methods in electromagnetics. In this article, we focus on this difficulty and propose a physics-based approach where the frequency-parameter dependence shows an affine behavior in the integral equation, without relying on rather complicated interpolation schemes. As a result, a fast frequency sweep for integral equation problems in electromagnetics is proposed. Finally, real-life applications will illustrate the capabilities of this methodology.

中文翻译：

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基于约简基法的非穿透性物体散射的电场积分方程快速扫频

详细研究了用于解决感兴趣频带中不可穿透目标的电磁散射的约基近似。考虑了均匀介质中的完美电散射体。尽管频率行为可能很复杂，但电磁散射不会在感兴趣的频带内任意改变。因此，不是使用计算效率低下的大维数值近似方案（例如矩量法）来求解感兴趣带中的积分方程，而是确定低维缩减基空间来近似平滑演化电磁散射本身随着频率的变化而变化。因此，频率参数散射问题在降阶模型方法中得到解决。寻址和正确选择的电流被认为是正确选择的电流跨越感兴趣的频带中的降低空间。由于自由空间格林函数中描述的波传播现象，积分方程中涉及的频率依赖性传统上限制了电磁学积分方程方法中快速扫频的约基近似的适用性。在本文中，我们专注于这个困难，并提出了一种基于物理的方法，其中频率参数依赖性在积分方程中表现出仿射行为，而不依赖于相当复杂的插值方案。因此，提出了电磁学中积分方程问题的快速频率扫描。最后，