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.

翻译：在这项工作中,我们提出了一个用符号变化系数解决卡路里传输问题的新的数字方法。在电磁学中,如果兴趣领域由古典的电磁材料和金属或元物质组成,例如,在金属或元物质上,电动允许度严格为负值,那么这种传输问题就可能发生。这种方法的基础是对问题进行最佳控制,与其他现有办法相反,这种方法的趋同证明没有任何限制性条件。特别是,对于问题的优先解决没有附加任何条件,除了与两种媒介之间的界面相适应外,对模具没有附加任何条件。我们的结果通过一些(2D)数字实验来说明。