On spurious solutions in finite element approximations of resonances in open systems
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/ba399870-e7e3-4e5d-bddc-480c21c124db
- author
- Araujo-Cabarcas, Juan Carlos and Engström, Christian LU
- publishing date
- 2017-11-15
- 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}}, }