论文标题
基于最佳控制的数值方法，用于标量传输问题，并改变签名系数
An optimal control-based numerical method for scalar transmission problems with sign-changing coefficients
论文作者
论文摘要
在这项工作中，我们提出了一种新的数值方法，用于通过改变标志的系数解决标量传输问题。在电磁主义中，如果感兴趣的域是由经典的介电材料和金属或超材料制成的，例如，在金属或超材料中严格呈负阴性，则可能会出现这种传播问题。该方法基于对问题的最佳控制重新重新制定。与其他现有方法相反，该方法的融合被证明没有任何限制性条件。特别是，除了与两个介质之间的接口外，没有任何条件对问题的先验规律性施加，并且在网格上没有任何条件。我们的结果通过一些（2D）的数值实验来说明。
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.
