Solving numerically the two-dimensional time harmonic Maxwell problem with sign-changing coefficients
Abstract
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.
Fields of Study & Subjects
Numerical methods in inverse problems
Electromagnetic Simulation and Numerical Methods
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- ESAIM Mathematical Modelling and Numerical Analysis
- Volume
- 60
- Issue
- 3
- Pages
- 1327–1362
- Publication date
- 3 April 2026
- Language
- EN