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On spurious solutions in finite element approximations of resonances in open systems

Araujo-Cabarcas, Juan Carlos and Engström, Christian LU (2017) In Computers and Mathematics with Applications 74(10). p.2385-2402
Abstract

In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when the computational domain is truncated with a perfectly matched layer (PML) as well as with a Dirichlet-to-Neumann map (DtN). The new test is based on the Lippmann–Schwinger equation and we use computations of the pseudospectrum to show that this is a suitable choice. Numerical simulations indicate that the presented test can distinguish between spurious eigenvalues and true eigenvalues also in difficult cases.

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author
and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Acoustic resonator, Bragg resonator, Dielectric resonator, Lippmann–Schwinger equation, Nonlinear eigenvalue problems, Scattering resonances
in
Computers and Mathematics with Applications
volume
74
issue
10
pages
18 pages
publisher
Elsevier
external identifiers
  • scopus:85026531962
ISSN
0898-1221
DOI
10.1016/j.camwa.2017.07.020
language
English
LU publication?
no
additional info
Funding Information: This work is fundedby the Swedish Research Council under Grant No. 621-2012-3863 . The authors are grateful to both referees for their highly valuable comments. Publisher Copyright: © 2017 Elsevier Ltd
id
ba399870-e7e3-4e5d-bddc-480c21c124db
date added to LUP
2023-03-24 11:07:56
date last changed
2023-03-24 13:53:29
@article{ba399870-e7e3-4e5d-bddc-480c21c124db,
  abstract     = {{<p>In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when the computational domain is truncated with a perfectly matched layer (PML) as well as with a Dirichlet-to-Neumann map (DtN). The new test is based on the Lippmann–Schwinger equation and we use computations of the pseudospectrum to show that this is a suitable choice. Numerical simulations indicate that the presented test can distinguish between spurious eigenvalues and true eigenvalues also in difficult cases.</p>}},
  author       = {{Araujo-Cabarcas, Juan Carlos and Engström, Christian}},
  issn         = {{0898-1221}},
  keywords     = {{Acoustic resonator; Bragg resonator; Dielectric resonator; Lippmann–Schwinger equation; Nonlinear eigenvalue problems; Scattering resonances}},
  language     = {{eng}},
  month        = {{11}},
  number       = {{10}},
  pages        = {{2385--2402}},
  publisher    = {{Elsevier}},
  series       = {{Computers and Mathematics with Applications}},
  title        = {{On spurious solutions in finite element approximations of resonances in open systems}},
  url          = {{http://dx.doi.org/10.1016/j.camwa.2017.07.020}},
  doi          = {{10.1016/j.camwa.2017.07.020}},
  volume       = {{74}},
  year         = {{2017}},
}