Parallel Numerical Simulation of Meta-surfaces: Finite Elements Full simulation, Comparison with Asymptotic Models and Application to the Faraday Cage

This paper deals with the simulation of electromagnetic waves in presence of meta-surfaces, namely thin and periodic structures made of small scatterers that are used to control the propagation of waves. Because of the different scales, the numerical solution of the underlying time-harmonic Maxwell's equations on such structures is a challenging task, highly non-uniform meshes leading to a high number of degrees of freedom to reach admissible output errors. Besides, for simple configurations, assuming for instance that the meta-surface is infinite, periodic homogenisation theory permits to derive approximate effective models that capture the macroscopic effect of the meta-surface, and are then much easier to simulate. In this article, we verify through parallel simulations the accuracy of the effective models and we show that the phenomena predicted by periodic homogenisation theory can be recovered on finite devices. We detail how these simulations can be performed in parallel through domain decomposition methods and multiple preconditioning strategies. The numerical experiments are supplemented by discussions on observed convergence speed both in terms of measured timings and in terms of number of Krylov solver iterations in a parallel setting.