This paper studies time-dependent electromagnetic scattering from metamaterials that are described by dispersive material laws. We consider the numerical treatment of a scattering problem in which a dispersive material law, for a causal and passive homogeneous material, determines the wave-material interaction in the scatterer. The resulting problem is nonlocal in time inside the scatterer and is posed on an unbounded domain. Well-posedness of the scattering problem is shown using a formulation that is fully given on the surface of the scatterer via a time-dependent boundary integral equation. Discretizing this equation by convolution quadrature in time and boundary elements in space yields a provably stable and convergent method that is fully parallel in time and space. Under regularity assumptions on the exact solution we derive error bounds with explicit convergence rates in time and space. Numerical experiments illustrate the theoretical results and show the effectiveness of the method.

翻译：本文研究由色散材料定律描述的电磁超材料中的时间依赖电磁散射问题。我们考虑一种散射问题的数值处理，其中因果且被动的均匀材料的色散材料定律决定了散射体中波与材料的相互作用。由此产生的问题在散射体内部具有时间非局部性，且定义在无界区域上。通过基于时间依赖边界积分方程完全在散射体表面给出的公式，证明了散射问题的适定性。采用时间域卷积求积法与空间域边界元法对该方程进行离散，得到一种可在时间和空间上完全并行化的、具有可证明稳定性和收敛性的方法。在精确解的正则性假设下，我们推导了具有显式时间和空间收敛率的误差界。数值实验验证了理论结果，并展示了该方法的有效性。