Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2026

Solving numerically the two-dimensional time harmonic Maxwell problem with sign-changing coefficients

Résumé

We are investigating the numerical solution to the 2D time-harmonic Maxwell equations in the presence of a classical medium and a metamaterial, that is with sign-changing coefficients. As soon as the problem has a (unique) solution, we are able to build a converging numerical approximation based on the finite element method, for which there is no constraint on the meshes related to the sign-changing behavior. To that aim, we use Lagrange finite elements to approximate the scalar potentials appearing in the Helmholtz decomposition of the vector-valued electromagnetic fields. Convergence in strong norm is proven for the fields. Numerical examples illustrate the theory.

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Dates et versions

hal-04909034 , version 1 (23-01-2025)
hal-04909034 , version 2 (02-04-2026)

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  • HAL Id : hal-04909034 , version 2

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Farah Chaaban, Patrick Ciarlet, Mahran Rihani. Solving numerically the two-dimensional time harmonic Maxwell problem with sign-changing coefficients. ESAIM: Mathematical Modelling and Numerical Analysis, In press. ⟨hal-04909034v2⟩
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