An adaptive finite element PML method for the elastic wave scattering problem in periodic structures

TL;DR

This paper introduces an adaptive finite element PML method for elastic wave scattering in periodic structures, combining PML truncation, error estimation, and adaptive refinement to improve accuracy and efficiency.

Contribution

The paper develops a new adaptive finite element PML approach with proven convergence and error control for elastic wave scattering in periodic media.

Findings

Proven exponential convergence of the PML method.

Effective a posteriori error estimates for adaptive refinement.

Numerical results demonstrate the method's efficiency and accuracy.

Abstract

An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the perfectly matched layer (PML) technique. The well-posedness and exponential convergence of the solution are established for the truncated PML problem by developing an equivalent transparent boundary condition. Second, an a posteriori error estimate is deduced for the discrete problem and is used to determine the finite elements for refinements and to determine the PML parameters. Numerical experiments are included to demonstrate the competitive behavior of the proposed adaptive method.