球形几何中 PEC 电磁散射问题的组合纯场边界积分方程

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Luiz Maltez-Faria, Carlos Pérez-Arancibia, Catalin Turc
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引用次数: 0

摘要

SIAM 应用数学杂志》第 84 卷第 1 期第 19-38 页,2024 年 2 月。 摘要。我们分析了完全导电球的频域电磁散射的某些纯场边界积分方程(BIE)的好求性。从(1)散射电场的三个分量[math]和(2)标量[math]是亥姆霍兹方程的辐射解这两个观察结果出发,我们发现,利用应用于上述量的格林等式和散射体表面的边界条件,可以推导出完全导电障碍物电磁散射的新边界积分方程公式。这些公式的未知量是散射电场三个分量的法向导数和散射体表面上散射电场的法向分量,因此这些公式被称为纯场边界积分方程。在本文中,我们在纯场 BIE 方法中使用了 Burton 和 Miller 的组合场方法,并推导出了新的边界积分公式,其特点是只有 Helmholtz 边界积分算子。根据亥姆霍兹边界积分算子在球形几何中的频谱特性,我们证明在球形几何情况下,组合的纯场边界积分算子是可对角的,并且其特征值在所有频率下都不为零。此外,我们还证明,对于球面几何,本文所考虑的其中一种纯场积分公式的特征值聚集在1处--这一性质类似于第二类积分方程。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Combined Field-Only Boundary Integral Equations for PEC Electromagnetic Scattering Problem in Spherical Geometries
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 19-38, February 2024.
Abstract. We analyze the well-posedness of certain field-only boundary integral equations (BIEs) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting from the observations that (1) the three components of the scattered electric field [math] and (2) scalar quantity [math] are radiative solutions of the Helmholtz equation, we see that novel boundary integral equation formulations of electromagnetic scattering from perfectly conducting obstacles can be derived using Green’s identities applied to the aforementioned quantities and the boundary conditions on the surface of the scatterer. The unknowns of these formulations are the normal derivatives of the three components of the scattered electric field and the normal component of the scattered electric field on the surface of the scatterer, and thus these formulations are referred to as field-only BIEs. In this paper we use the combined field methodology of Burton and Miller within the field-only BIE approach, and we derive new boundary integral formulations that feature only Helmholtz boundary integral operators, which we subsequently show to be well posed for all positive frequencies in the case of spherical scatterers. Relying on the spectral properties of Helmholtz boundary integral operators in spherical geometries, we show that the combined field-only boundary integral operators are diagonalizable in the case of spherical geometries and their eigenvalues are nonzero for all frequencies. Furthermore, we show that for spherical geometries one of the field-only integral formulations considered in this paper exhibits eigenvalues clustering at one—a property similar to second-kind integral equations.
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
期刊介绍: SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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