Georg, Niklas; Ackermann, Wolfgang; Corno, Jacopo; Schöps, Sebastian Uncertainty quantification for Maxwell’s eigenproblem based on isogeometric analysis and mode tracking. (English) Zbl 1441.78003 Comput. Methods Appl. Mech. Eng. 350, 228-244 (2019). Summary: 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-Loève 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. Cited in 4 Documents MSC: 78A25 Electromagnetic theory (general) 78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory 65D07 Numerical computation using splines 65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs Keywords:cavity resonators; eigenvalues and eigenfunctions; isogeometric analysis; radio frequency; sensitivity analysis Software:ARPACK; GeoPDEs; JDQR; FEniCS; JDQZ; Poisson SUPERFISH; NewtonLib PDFBibTeX XMLCite \textit{N. Georg} et al., Comput. Methods Appl. Mech. Eng. 350, 228--244 (2019; Zbl 1441.78003) Full Text: DOI arXiv References: [1] Halbach, K.; Holsinger, R. F., Superfish – a computer program for evaluation of RF cavities with cylindrical symmetry, Part. 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