SIAM/ASA Journal on Uncertainty Quantification, Volume 8, Issue 2, Page 748-774, January 2020.
We consider time-harmonic electromagnetic scattering problems on perfectly conducting scatterers with uncertain shape. Thus, the scattered field will also be uncertain. Based on the knowledge of the two-point correlation of the domain boundary variations around a reference domain, we derive a perturbation analysis for the mean of the scattered field. Therefore, we compute the second shape derivative of the scattering problem for a single perturbation. Taking the mean, this leads to an at least third order accurate approximation with respect to the perturbation amplitude of the domain variations. To compute the required second order correction term, a tensor product equation on the domain boundary has to be solved. We discuss its discretization and efficient solution using boundary integral equations. Numerical experiments in three dimensions are presented.

中文翻译：

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随机域电磁散射问题的高阶摄动方法

SIAM / ASA不确定性量化期刊，第8卷，第2期，第748-774页，2020年1月。
我们考虑形状不确定的完美导电散射体的时谐电磁散射问题。因此，散射场也将是不确定的。基于对参考域周围域边界变化的两点相关性的了解，我们得出了散射场均值的摄动分析。因此，我们为单个摄动计算了散射问题的第二个形状导数。取平均值，这导致关于域变化的扰动幅度的至少三阶精确近似。为了计算所需的二阶校正项，必须求解域边界上的张量积方程。我们讨论使用边界积分方程的离散化和有效解。