An overfilled cavity problem for Maxwell's equations
An overfilled cavity problem for Maxwell's equations
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DOI：
10.1002/mma.2562
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发表时间：
2012-11
影响因子：
2.9
通讯作者：
Peijun Li;Haijun Wu;Weiying Zheng
中科院分区：
文献类型：
--
作者：
Peijun Li;Haijun Wu;Weiying Zheng
本文研究了时谐电磁平面波在理想导电无限大地平面中的开孔和满孔散射问题，其中电磁波的传播由麦克斯韦方程组控制。在平坦的地面和空腔的开口之上，假设空间填充有具有恒定介电常数和磁导率的均匀介质，而空腔的内部填充有具有可变介电常数和磁导率的非均匀介质。散射问题被建模为一个有界区域上的边值问题，与透明边界条件的半球包围的不均匀性表示的空腔。利用变分方法证明了该模型问题弱解的存在唯一性。研究了完全匹配层（PML）方法截断无界电磁腔体散射问题。证明了截断PML问题的唯一解。给出了原始散射问题的解与截断PML问题的解之间的显式误差估计。误差估计意味着PML解决方案的原始腔散射问题的指数收敛，无论是通过增加PML介质参数或PML层厚度。该收敛结果对电磁散射计算中PML介质参数的确定具有一定的参考价值。版权所有© 2012约翰威利父子有限公司.
This paper is concerned with the mathematical analysis of the scattering of a time‐harmonic electromagnetic plane wave by an open and overfilled cavity that is embedded in a perfect electrically conducting infinite ground plane, where the electromagnetic wave propagation is governed by the Maxwell equations. Above the flat ground surface and the open aperture of the cavity, the space is assumed to be filled with a homogeneous medium with a constant permittivity and permeability, whereas the interior of the cavity is filled with some inhomogeneous medium with a variable permittivity and permeability. The scattering problem is modeled as a boundary value problem over a bounded domain, with transparent boundary condition proposed on the hemisphere enclosing the inhomogeneity represented by the cavity. The existence and uniqueness of the weak solution for the model problem are established by using a variational approach. The perfectly matched layer (PML) method is investigated to truncate the unbounded electromagnetic cavity scattering problem. It is shown that the truncated PML problem attains a unique solution. An explicit error estimate is given between the solution of the original scattering problem and that of the truncated PML problem. The error estimate implies that the PML solution converges exponentially to the original cavity scattering problem by increasing either the PML medium parameter or the PML layer thickness. The convergence result is expected to be useful for determining the PML medium parameter in the computational electromagnetic scattering problem. Copyright © 2012 John Wiley & Sons, Ltd.