On the computation of analytic sensitivities of eigenpairs in isogeometric analysis

Abstract

The eigenmodes of resonating structures, e.g., electromagnetic cavities, are sensitive to deformations of their shape. In order to compute the sensitivities of the eigenpair with respect to a scalar parameter, we state the Laplacian and Maxwellian eigenvalue problems and discretize the models using isogeometric analysis. Since we require the derivatives of the system matrices, we differentiate the system matrices for each setting considering the appropriate function spaces for geometry and solution. This approach allows for a straightforward computation of arbitrary higher order sensitivities in a closed-form. In our work, we demonstrate the application in a setting of small geometric deformations, e.g., for the investigation of manufacturing uncertainties of electromagnetic cavities, as well as in an eigenvalue tracking along a shape morphing.

References in corpus (5)

• The Superconducting TESLA Cavities
• Automated shape differentiation in the Unified Form Language
• Shape Optimization of Rotating Electric Machines using Isogeometric Analysis and Harmonic Stator-Rotor Coupling
• Uncertainty Quantification for Maxwell's Eigenproblem based on Isogeometric Analysis and Mode Tracking
• Mode Recognition by Shape Morphing for Maxwell's Eigenvalue Problem

Cited by in corpus (2)

• Shape uncertainty quantification of Maxwell eigenvalues and -modes with application to TESLA cavities
• Isogeometric Shape Optimization of Multi-Tapered Coaxial Baluns Simulated by an Integral Equation Method