Computing scattering resonances using perfectly matched layers with frequency dependent scaling functions
type: Item
instance of: scholarly article
title: Computing scattering resonances using perfectly matched layers with frequency dependent scaling functions
zbMATH Open document ID: 1394.65138
author: Lothar Nannen
author: Markus Wess
published in: BIT
publication date: 2018-06-26T00:00:00Z
review text: The authors are concerned with an eigenvalue problem for the Laplace operator on some real 1D and 2D unbounded domains. The problem involves a Dirichlet or Neumann condition on the finite part of boundary along with a radiation condition at large distances. In solving such problems they proceed in three steps, namely: formulation of a complex scaled eigenvalue problem, truncation of the original unbounded domain to a bounded one and finally finite element solution to the eigenvalue problem on this bounded domain. They compare the numerical outcomes obtained by frequency dependent scaling with those provided by standard scaling. Then they observe that, in spite of the fact that the former scaling method leads to polynomial eigenproblems, eigenvalues (resonances) produced by such scaling are less sensitive to the discretization parameters. Actually, they suggest that this fact could lead to the construction of a reliable filter for spurious resonances. Some numerical experiments focused on the location of spurious eigenvalues are carried out.
Mathematics Subject Classification ID: 65N25
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 6894729
zbMATH Keywords: Laplace operator
zbMATH Keywords: open system
zbMATH Keywords: domain truncation
zbMATH Keywords: finite element method
zbMATH Keywords: Helmholtz resonance
zbMATH Keywords: frequency
zbMATH Keywords: perfectly matched layer
zbMATH Keywords: complex scaling
zbMATH Keywords: spurious resonance
Wikidata QID: Q92583396
reviewed by: Calin Ioan Gheorghiu
describes a project that uses: NGSolve
describes a project that uses: Netgen
MaRDI profile type: Publication
full work available at URL: s10543-018-0694-0
OpenAlex ID: W2787265830
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DOI: 10.1007/S10543-018-0694-0
description: scientific article; zbMATH DE number 6894729