Analysis of a Cartesian PML approximation to acoustic scattering problems in \(\mathbb R^2\) and \(\mathbb R^3\)
type: Item
instance of: scholarly article
title: Analysis of a Cartesian PML approximation to acoustic scattering problems in \(\mathbb R^2\) and \(\mathbb R^3\)
zbMATH Open document ID: 1268.65150
author: James H. Bramble
author: Joseph E. Pasciak
published in: Journal of Computational and Applied Mathematics
publication date: 2013-04-18T00:00:00Z
review text: This paper deals with the exterior Helmholtz scattering problem \[ \Delta u+ k^2u= 0\quad\text{in }\Omega^c,\;u= g\quad\text{on }\Gamma=\partial\Omega^c, \] \[ \lim_{r\to\infty} r^{(n-1)/2} \Biggl({\partial u\over\partial r}- iku\Biggr)= 0. \] Here \(\Omega\) is a bounded domain in \(\mathbb{R}^n\), \(n= 2,3\), and \(\Omega^c\) denotes the complement of its closure. The limit is taken to mean uniformly on the sphere of radius \(r\). The authors use a perfectly matched layer (PML) technique based on Cartesian geometry where each variable is transformed independently to approximate solutions. Some results of numerical calculations which illustrate the convergence behavior of the PML approximations are presented.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 76M10
Mathematics Subject Classification ID: 76Q05
zbMATH DE Number: 6155449
zbMATH Keywords: acoustic scattering
zbMATH Keywords: Helmholtz equation
zbMATH Keywords: perfectly matched layer
zbMATH Keywords: variational stability
zbMATH Keywords: numerical examples
zbMATH Keywords: scattering problem
zbMATH Keywords: Cartesian geometry
zbMATH Keywords: convergence
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
full work available at URL: j.cam.2012.12.022
OpenAlex ID: W2083246567
DOI: 10.1016/J.CAM.2012.12.022
description: scientific article; zbMATH DE number 6155449