Electromagnetic wave scattering by random surfaces: Shape holomorphy
Electromagnetic wave scattering by random surfaces: Shape holomorphy
复制标题
DOI：
10.1142/s0218202517500439
复制
发表时间：
2017-11-01
影响因子：
3.5
通讯作者：
Zech, Jakob
中科院分区：
文献类型：
--
作者：
Jerez-Hanckes, Carlos;Schwab, Christoph;Zech, Jakob
对于被完全导电或介电有界障碍物散射的时谐电磁波，我们证明了其场全纯依赖于散射体的形状。在随机几何扰动存在的情况下，我们的结果表明，在散射体外部的加权空间中，场具有很强的可测量性。这些发现是证明多项式混沌型稀疏逼近技术在计算不确定性正反量化中的维无关收敛速率的关键。此外，我们的形状全纯结果暗示了相应参数解族的简约近似表示，例如，由贪婪策略（如模型阶约化或约基近似）产生。最后，本文证明的形状全纯结果暗示了定幅域扰动远场图形的形状Taylor展开在标称域附近的收敛性，从而扩展了一阶、二阶矩域不确定性量化中广泛使用的渐近线性化方法。
For time-harmonic electromagnetic waves scattered by either perfectly conducting or dielectric bounded obstacles, we show that the fields depend holomorphically on the shape of the scatterer. In the presence of random geometrical perturbations, our results imply strong measurability of the fields, in weighted spaces in the exterior of the scatterer. These findings are key to prove dimension-independent convergence rates of sparse approximation techniques of polynomial chaos type for forward and inverse computational uncertainty quantification. Also, our shape-holomorphy results imply parsimonious approximate representations of the corresponding parametric solution families, which are produced, for example, by greedy strategies such as model order reduction or reduced basis approximations. Finally, the presently proved shape holomorphy results imply convergence of shape Taylor expansions of far-field patterns for fixed amplitude domain perturbations in a vicinity of the nominal domain, thereby extending the widely used asymptotic linearizations employed in first-order, second moment domain uncertainty quantification.