3 citations · 4 across the 6 of their papers we have counts for
8 papers
Geometric spectral properties of electromagnetic waveguides
Philippe Briet, Maxence Cassier, Thomas Ourmières-Bonafos +1
Consider a reference homogeneous and isotropic electromagnetic waveguide with a simply connected cross-section embedded in a perfect conductor. In this setting, when the waveguide…
Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part II
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron
In this second part of our series of papers, we develop an abstract framework suitable for de Rham complexes that depend on a parameter belonging to an arbitrary Banach space. Our…
Shape Derivatives of the Eigenvalues of the De Rham Complex for Lipschitz Deformations and Variable Coefficients: Part I
Pier Domenico Lamberti, Dirk Pauly, Michele Zaccaron
We study eigenvalue problems for the de Rham complex on varying three dimensional domains. Our analysis includes the Helmholtz equation as well as the Maxwell system with mixed bou…
A note on the failure of the Faber-Krahn inequality for the vector Laplacian
David Krejcirik, Pier Domenico Lamberti, Michele Zaccaron
We consider a natural eigenvalue problem for the vector Laplacian related to stationary Maxwell's equations in a cavity and we prove that an analog of the celebrated Faber-Krahn in…
Permittivity optimization for Maxwell's eigenvalues
Pier Domenico Lamberti, Paolo Luzzini, Michele Zaccaron
We formulate an optimization problem for the dependence of the eigenvalues of Maxwell's equations in a cavity upon variation of the electric permittivity and we prove a correspondi…
A few results on permittivity variations in electromagnetic cavities
Paolo Luzzini, Michele Zaccaron
We study the eigenvalues of time-harmonic Maxwell's equations in a cavity upon changes in the electric permittivity of the medium. We prove that all the eigenvalues,…
Spectral stability of the operator via uniform Gaffney inequalities on perturbed electromagnetic cavities
Pier Domenico Lamberti, Michele Zaccaron
We prove spectral stability results for the operator subject to electric boundary conditions on a cavity upon boundary perturbations. The cavities are assumed to be suf…
Shape sensitivity analysis for electromagnetic cavities
Pier Domenico Lamberti, Michele Zaccaron
We study the dependence of the eigenvalues of time-harmonic Maxwell's equations in a cavity upon variation of its shape. The analysis concerns all eigenvalues both simple and multi…