Skip to Main content Skip to Navigation
Journal articles

Analysis of variational formulations and low-regularity solutions for time-harmonic electromagnetic problems in complex anisotropic media

Damien Chicaud 1 Patrick Ciarlet 1 Axel Modave 1
1 POEMS - Propagation des Ondes : Étude Mathématique et Simulation
Inria Saclay - Ile de France, UMA - Unité de Mathématiques Appliquées, CNRS - Centre National de la Recherche Scientifique : UMR7231
Abstract : We consider the time-harmonic Maxwell's equations with physical parameters, namely the electric permittivity and the magnetic permeability, that are complex, possibly non-Hermitian, tensor fields. Both tensor fields verify a general ellipticity condition. In this work, the well-posedness of formulations for the Dirichlet and Neumann problems (i.e. with a boundary condition on the electric field or its curl, respectively) is proven using well-suited functional spaces and Helmholtz decompositions. For both problems, the a priori regularity of the solution and the solution's curl is analysed. The regularity results are obtained by splitting the fields and using shift theorems for second-order divergence elliptic operators. Finally, the discretization of the formulations with a H(curl)-conforming approximation based on edge finite elements is considered. An a priori error estimate is derived and verified thanks to numerical results with an elementary benchmark.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-02651682
Contributor : Axel Modave <>
Submitted on : Tuesday, June 29, 2021 - 9:48:14 AM
Last modification on : Thursday, July 29, 2021 - 9:03:40 AM

File

ChCM20_Postprint.pdf
Files produced by the author(s)

Identifiers

Citation

Damien Chicaud, Patrick Ciarlet, Axel Modave. Analysis of variational formulations and low-regularity solutions for time-harmonic electromagnetic problems in complex anisotropic media. SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2021, 53 (3), pp.2691-2717. ⟨10.1137/20M1344111⟩. ⟨hal-02651682v2⟩

Share

Metrics

Record views

29

Files downloads

53