Scattering problems from slightly perturbed periodic surfaces: Part II. High order numerical method

TL;DR

This paper presents a high order finite element method for solving scattering problems involving slightly perturbed periodic surfaces, achieving high accuracy and proven convergence.

Contribution

It introduces a novel high order numerical scheme leveraging regularity properties for improved accuracy in perturbed periodic surface scattering.

Findings

Finite element method converges with proven accuracy.

Numerical examples demonstrate the scheme's efficiency.

High order method outperforms lower order approaches.

Abstract

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.