时域中完美导体电磁散射的域导数
A Domain Derivative for Electromagnetic Scattering by Perfect Conductors in the Time Domain
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中文总结 AI 辅助
该研究为时域完美导体电磁散射建立域导数，通过拉普拉斯域推导频率界，证明时间半离散化与空间伽辽金法结合的收敛性，并应用于迭代形状重建，数值实验验证了算法在噪声下的鲁棒性。
中文摘要 AI 辅助
针对完美导体的时变电磁散射，建立了域导数。通过拉普拉斯域进行推导，得到了麦克斯韦方程解的频率相关界。这些界既用于建立域导数的时间正则性性质，也用于证明所提出的龙格-库塔卷积求积时间半离散化的收敛性。当该时间离散化与空间中的伽辽金方法结合时，还对域导数的点评估进行了完整的收敛性分析。最终，该域导数被应用于迭代形状重建算法中，其中在远离完美导体的若干接收器位置测量电场近场。数值示例显示了该算法的可行性，并特别强调了当对数据施加额外噪声时其鲁棒性。
英文摘要
A domain derivative for time-dependent electromagnetic scattering from perfect conductors is established. By proceeding through the Laplace domain, frequency-dependent bounds on solutions to Maxwell's equations are derived. These bounds are used both for establishing time regularity properties of the domain derivative and for proving convergence of the proposed Runge--Kutta convolution quadrature semi-discretization in time. A full convergence analysis is also carried out for pointwise evaluations of the domain derivative, when this time discretization is combined with a Galerkin method in space. Eventually, the domain derivative is applied in an iterative shape reconstruction algorithm, in which measurements of the electric near field at some receiver positions, away from the perfect conductor are measured. Numerical examples show the feasibility of this algorithm and in particular highlight its robustness, when additional noise is applied to the data.
发表机构
- Department of Mathematics and Statistics, University of Helsinki（赫尔辛基大学数学与统计系）
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