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Journal Articles SIAM Journal on Numerical Analysis Year : 2023

An optimal control-based numerical method for scalar transmission problems with sign-changing coefficients

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.
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hal-03666913 , version 1 (12-05-2022)
hal-03666913 , version 2 (13-10-2022)

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Patrick Ciarlet, David Lassounon, Mahran Rihani. An optimal control-based numerical method for scalar transmission problems with sign-changing coefficients. SIAM Journal on Numerical Analysis, 2023, 61 (3), pp.1316-1339. ⟨10.1137/22M1495998⟩. ⟨hal-03666913v2⟩
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