Nonlocal models for interface problems between dielectrics and metamaterials

Abstract

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 H 1. 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.

Numerical methods for fractional diffusion

“…In fact, the problem under consideration is of Fredholm type if and only if the quotient between the value of permittivities/diffusivities taken from both sides of the interface lies outside a so-called critical interval, which always contains the value −1. In [26] a non-local interaction model for the materials is proposed. Numerical evidence indicates that the non-local model may reduce the critical interval and that solutions are more stable than for the local problem.…”