Convergence of the PML method for thermoelastic wave scattering problems

TL;DR

This paper introduces a PML method for 3D thermoelastic obstacle scattering problems, proving its well-posedness and exponential convergence, marking the first such convergence result for this class of problems.

Contribution

It presents the first convergence analysis of the PML method applied to time-harmonic thermoelastic scattering problems, including well-posedness and exponential convergence.

Findings

Proved well-posedness of the truncated PML problem under certain conditions.

Established exponential convergence of the PML method with respect to layer thickness and parameters.

First convergence result for PML in thermoelastic wave scattering.

Abstract

This paper is concerned with the thermoelastic obstacle scattering problem in three dimensions. A uniaxial perfectly matched layer (PML) method is firstly introduced to truncate the unbounded scattering problem, leading to a truncated PML problem in a bounded domain. Under certain constraints on model parameters, the well-posedness for the truncated PML problem is then proved except possibly for a discrete set of frequencies, based on the analytic Fredholm theory. Moreover, the exponential convergence of the uniaxial PML method is established in terms of the thickness and absorbing parameters of PML layer. The proof is based on the PML extension technique and the exponential decay properties of the modified fundamental solution. As far as we know, this is the first convergence result of the PML method for the time-harmonic thermoelastic scattering problem.