Eigenvalue Optimization with respect to Shape‐Variations in Electromagnetic Cavities
Abstract: The article considers the optimization of eigenvalues in electromagnetic cavities by means of shape variations. The field distribution and its frequency in a radio‐frequency cavity are governed by Maxwell's eigenvalue problem. To this end, we utilize a mixed formulation by Kikuchi (1987) and a mixed finite element discretization by means of Nédélec and Lagrange elements. The shape optimization is based on the method of mappings, where a Piola transformation is utilized to assert conformity of the mapped spaces. We derive the derivatives by the use of adjoint calculus for the constraining Maxwell eigenvalue problem. In two numerical examples, we demonstrate the functionality of this method.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Eigenvalue Optimization with respect to Shape‐Variations in Electromagnetic Cavities ; volume:22 ; number:1 ; year:2023 ; extent:0
Proceedings in applied mathematics and mechanics ; 22, Heft 1 (2023) (gesamt 0)
- DOI
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10.1002/pamm.202200122
- URN
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urn:nbn:de:101:1-2023032514193227674435
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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14.08.2025, 11:02 AM CEST
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Eigenvalue Optimization with respect to Shape‐Variations in Electromagnetic Cavities
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Hamiltonian eigenvalue symmetry for quadratic operator eigenvalue problems
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Pareto Z-eigenvalue inclusion theorems for tensor eigenvalue complementarity problems
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Eigenvalue Optimization with respect to Shape‐Variations in Electromagnetic Cavities
Eigenvalue Optimization with respect to Shape-Variations in Electromagnetic Systems
Gradient‐based eigenvalue optimization for electromagnetic cavities with built‐in mode matching
Optimal shape of a domain which minimizes the first buckling eigenvalue
Optimal shape of a domain which minimizes the first buckling Eigenvalue
Hamiltonian eigenvalue symmetry for quadratic operator eigenvalue problems
Eigenvalue inclusion sets for linear response eigenvalue problems
Nonlinear Eigenvalue Problems: A Challenge for Modern Eigenvalue Methods
Rectangular eigenvalue problems
Pareto Z-eigenvalue inclusion theorems for tensor eigenvalue complementarity problems
Stability of the Wulff shape with respect to anisotropic curvature functionals
Stability of the Wulff shape with respect to anisotropic curvature functionals
Eigenvalue Optimization with respect to Shape‐Variations in Electromagnetic Cavities
Eigenvalue Optimization with respect to Shape-Variations in Electromagnetic Systems
Gradient‐based eigenvalue optimization for electromagnetic cavities with built‐in mode matching
Optimal shape of a domain which minimizes the first buckling eigenvalue
Optimal shape of a domain which minimizes the first buckling Eigenvalue
Hamiltonian eigenvalue symmetry for quadratic operator eigenvalue problems
Eigenvalue inclusion sets for linear response eigenvalue problems
Nonlinear Eigenvalue Problems: A Challenge for Modern Eigenvalue Methods
Rectangular eigenvalue problems
Pareto Z-eigenvalue inclusion theorems for tensor eigenvalue complementarity problems
Stability of the Wulff shape with respect to anisotropic curvature functionals