Nonlocal models for interface problems between dielectrics and metamaterials

Juan Pablo Borthagaray (1) , Patrick Ciarlet (2)

1 CONICET - Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires]
2 POEMS - Propagation des Ondes : Étude Mathématique et Simulation

Consider two materials with permittivities/diffusivities of opposite sign, and separated by an interface with a corner. Then, when solving the classic (local) models derived from electromagnetics theory, strong singularities may appear. For instance the scalar problem may be ill-posed in H1. To address this difficulty, we study here a nonlocal model for scalar problems with sign-changing coefficients. Numerical results indicate that the proposed nonlocal model has some key advantages over the local one.

Domaines: Analyse numérique [math.NA]

Juan Pablo Borthagaray, Patrick Ciarlet. Nonlocal models for interface problems between dielectrics and metamaterials. 11th International Congress on Engineered Material Platforms for Novel Wave Phenomena - Metamaterials 2017, Aug 2017, Marseille, France. pp.3. ⟨hal-01547364⟩