On the Well-Posedness of UPML Method for Wave Scattering in Layered Media

On the Well-Posedness of UPML Method for Wave Scattering in Layered Media

Year:    2024

Author:    Wangtao Lu, Jun Lai, Haijun Wu

CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 2 : pp. 264–294

Abstract

This paper proposes a novel method to establish the well-posedness of uniaxial perfectly matched layer (UPML) method for a two-dimensional acoustic scattering from a compactly supported source in a two-layered medium. We solve a long standing problem by showing that the truncated layered medium scattering problem is always resonance free regardless of the thickness and absorbing strength of UPML. The main idea is based on analyzing an auxiliary waveguide problem obtained by truncating the layered medium scattering problem through PML in the vertical direction only. The Green function for this waveguide problem can be constructed explicitly based on the separation of variables and Fourier transform. We prove that such a construction is always well-defined regardless of the absorbing strength. The well-posedness of the fully UPML truncated scattering problem follows by assembling the waveguide Green function through periodic extension.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/csiam-am.SO-2023-0023

CSIAM Transactions on Applied Mathematics, Vol. 5 (2024), Iss. 2 : pp. 264–294

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    31

Keywords:    Helmholtz equation perfectly matched layer layered medium scattering source scattering problem.

Author Details

Wangtao Lu

Jun Lai

Haijun Wu