An optimal control-based numerical method for scalar transmission problems with sign-changing coefficients
Year: 2022
Type: preprint
Abstract: In this work, we present a new numerical method for solving the scalar transmission problem with sign-changing coefficients. In electromagnetism, such a transmission problem can occur if the domain of interest is made of a classical dielectric material and a metal or a metamaterial, with for instance an electric permittivity that is strictly negative in the metal or metamaterial. The method is based on an optimal control reformulation of the problem. Contrary to other existing approaches, the convergence of this method is proved without any restrictive condition. In particular, no condition is imposed on the a priori regularity of the solution to the problem, and no condition is imposed on the meshes, other than that they fit with the interface between the two media. Our results are illustrated by some (2D) numerical experiments.
Source: arXiv (Cornell University)
Institutions: Institut Polytechnique de Paris, POEMS: Propagation des Ondes : Etude Mathématique et Simulationan, École Nationale Supérieure de Techniques Avancées Paris, Université Européenne de Bretagne, Institut de recherche mathématique de Rennes, École Polytechnique, Centre de Mathématiques Appliquées de l'École polytechnique
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4281388700