Mode tracking for parametrized eigenvalue problems in computational electromagnetics

Jorkowski, Philipp; Schuhmann, Rolf

doi:10.23919/ropaces.2018.8364147

Cited by 6 publications

(4 citation statements)

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“…[14]. The numerical efficiency of our tracking method could be further improved by enhancing the prediction step ( 14) with higher order Taylor expansion [25] or by reducing our system matrices to a subspace of eigenpairs [32]. Furthermore, the accuracy of the derivatives of the system matrices can be improved by formulating them as shape derivatives along the geometry deformation [33].…”

Section: Discussionmentioning

confidence: 99%

“…pillbox. This allows to use the established nomenclature from field theory [15, Section 8.7] and is less error-prone than methods based on counting zero-crossing or maxima [14] as we will demonstrate in Section V. However, our classification method requires a numerical tracking procedure of the eigenpairs [24], [25], [26], [3]. This is necessary since eigenvalues may cross on T , see Fig.…”

Section: Shape Morphingmentioning

confidence: 99%

“…and added a normalization constraint based on e i−1,j . Finally, we use the correlation factor proposed by [25]…”

Section: A Eigenvalue Trackingmentioning

confidence: 99%

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Mode Recognition by Shape Morphing for Maxwell's Eigenvalue Problem

Ziegler¹,

Georg²,

Ackermann³

et al. 2022

Preprint

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In electrical engineering, for example during the design of superconducting radio-frequency cavities, eigenmodes must be identified based on their field patterns. This allows to understand the working principle, optimize the performance of a device and distinguish desired from parasitic modes. For cavities with simple shapes, the eigenmodes are easily classified according to the number of nodes and antinodes in each direction as is obvious from analytical formulae. For cavities with complicated shapes, the eigenmodes are determined numerically. Thereby, the classification is cumbersome, if not impossible. In this paper, we propose a new recognition method by morphing the cavity geometry to a pillbox and tracking its eigenmodes during the deformation.

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Section: Discussionmentioning

confidence: 99%

Section: Shape Morphingmentioning

confidence: 99%

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Mode Recognition by Shape Morphing for Maxwell's Eigenvalue Problem

Ziegler¹,

Georg²,

Ackermann³

et al. 2022

Preprint

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“…The numerical efficiency of the presented tracking method could also be further improved, e.g. by using a simplified Newton method [36], by employing a higher order Taylor approximation in the prediction step (37) or by tracking a subspace of eigenpairs and matching the eigenpairs based on a correlation coefficient [37,38].…”

Section: Eigenvalue Trackingmentioning

confidence: 99%

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

Georg

Ackermann

Corno

et al. 2019

Computer Methods in Applied Mechanics and Engineering

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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 are 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.

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