波数侧的简化矢量亥姆霍兹波动方程分析

R. Ott
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引用次数: 0

摘要

预解式有助于求解在所有波数空间上定义的PDE。几乎所有的电磁散射问题都在空间方面得到了解决,并使用了空间格林函数方法。这项工作的动机是解决傅立叶侧的EM问题,以便将预解式和格林函数联系起来。使用的方法包括矩阵理论、傅立叶变换和格林函数。在Dirichlet边界条件下,导出了电磁Helmholtz约化矢量波方程预解式的一个闭合形式。然后使用预解式导出EM波方程解的表达式,并提供解的Sobolev估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Reduced Vector Helmholtz Wave Equation Analysis on the Wave-Number Side
The resolvent helps solve a PDE defined on all of wave-number space, . Almost all electromagnetic scattering problems have been solved on the spatial side and use the spatial Green’s function approach. This work is motivated by solving an EM problem on the Fourier side in order to relate the resolvent and the Green’s function. Methods used include Matrix Theory, Fourier Transforms, and Green’s function. A closed form of the resolvent is derived for the electromagnetic Helmholtz reduced vector wave equation, with Dirichlet boundary conditions. The resolvent is then used to derive expressions for the solution of the EM wave equation and provide Sobolev estimates for the solution.
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