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Uncertainty quantification for Maxwell's eigenproblem based on isogeometric analysis and mode tracking

机译：基于ISOGeometric分析和模式跟踪的Maxwell eIgenProbrom的不确定性量化

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The electromagnetic field distribution as well as the resonating frequency of various modes in superconducting cavities used in particle accelerators for example is sensitive to small geometry deformations. The occurring variations are motivated by measurements of an available set of resonators from which we propose to extract a small number of relevant and independent deformations by using a truncated Karhunen-Loeve expansion. The random deformations are used in an expressive uncertainty quantification workflow to determine the sensitivity of the eigenmodes. For the propagation of uncertainty, a stochastic collocation method based on sparse grids is employed. It requires the repeated solution of Maxwell's eigenvalue problem at predefined collocation points, i.e., for cavities with perturbed geometry. The main contribution of the paper is ensuring the consistency of the solution, i.e., matching the eigenpairs, among the various eigenvalue problems at the stochastic collocation points. To this end, a classical eigenvalue tracking technique is proposed that is based on homotopies between collocation points and a Newton-based eigenvalue solver. The approach can be efficiently parallelized while tracking the eigenpairs. In this paper, we propose the application of isogeometric analysis since it allows for the exact description of the geometrical domains with respect to common computer-aided design kernels, for a straightforward and convenient way of handling geometrical variations and smooth solutions. (C) 2019 Elsevier B.V. All rights reserved.
机译：电磁场分布以及颗粒促进剂中使用的超导腔中各种模式的谐振频率对小几何变形敏感。发生的变化是通过测量可用的谐振器的测量来激励，从中提出通过使用截短的Karhunen-Loeve扩展来提取少量相关和独立变形。随机变形用于表现力的不确定量化工作流程以确定特征幅度的灵敏度。为了不确定性的传播，采用基于稀疏网格的随机搭配方法。它需要Maxwell的特征值问题在预定义的搭配点，即具有扰动几何形状的空腔中的重复解决。本文的主要贡献是确保解决方案的稳定性，即匹配特征环，在随机搭配点的各种特征值问题中。为此，提出了一种基于配偶与基于牛顿的特征值求解器之间的同象的经典特征值跟踪技术。在跟踪特征方的同时，该方法可以有效地平行化。在本文中，我们提出了ISOGeometric分析的应用，因为它允许几何域对公共计算机辅助设计内核的精确描述，用于处理几何变化和平滑解决方案的直接和方便的方式。 （c）2019 Elsevier B.v.保留所有权利。

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