Mode Recognition by Shape Morphing for Maxwell's Eigenvalue Problem

Abstract

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.

Tensor train based isogeometric analysis for PDE approximation on parameter dependent geometries

“…where the parameter-dependent waveguide geometry Ω(θ) is shown in Figure 8a In Figure 8b, the solution is plotted for the nominal geometry and ρ = 49. For this computation, the B-spline basis consists of quadratic B-splines with dimensions n = (64,64,128). When resolving the parametric dependency, the parameter grid has size = (8,8,8).…”

“…Moreover, the complexity of explicitly computing the matrix entries is bounded from below by the storage complexity. This bottleneck is greatly exacerbated in cases where IGA-based models are utilized within parametric studies, such as shape optimization [22,42,52,62], uncertainty quantification (UQ) for stochastic geometry deformations [24,63], or studies utilizing shape morphing techniques [64]. These parametric studies demand that multiple, often numerous, geometry configurations must be explored until an optimal shape or a statistical quantity of interest (QoI) can be estimated to sufficient accuracy.…”