Scattering problems from slightly perturbed periodic surfaces: Part II. High order numerical method
For researchers in computational electromagnetics or wave scattering, this provides an incremental improvement in numerical methods for perturbed periodic surfaces.
This paper develops a high-order numerical method for scattering problems from slightly perturbed periodic surfaces in 2D, achieving high accuracy by leveraging regularity properties to transfer incident field decay to the total field. Numerical examples demonstrate efficiency, though no specific accuracy or speed numbers are provided.
In this paper, we develop a high order numerical method for the numerical solutions of scattering problems with slightly perturbed periodic surfaces in two dimensional spaces. Based on the regularity property introduced in Part I, the decaying rate of the incident field could be transferred directly to the total field for small perturbations. Thus the finite section method could reach a high accuracy rate. With the help of a modification of the truncated problem, the problem is solved by a finite element method. The convergence of the finite element method is proved and numerical examples have been carried out to show the efficiency of the numerical scheme.