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On spurious solutions in finite element approximations of resonances in open systems
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics. (UMIT)
2017 (English)In: Computers and Mathematics with Applications, ISSN 0898-1221, E-ISSN 1873-7668Article in journal (Refereed) In press
Abstract [en]

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.

Place, publisher, year, edition, pages
2017.
Keyword [en]
Lippmann–Schwinger equation, Nonlinear eigenvalue problems
National Category
Computational Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-138096DOI: 10.1016/j.camwa.2017.07.020OAI: oai:DiVA.org:umu-138096DiVA: diva2:1130348
Funder
Swedish Research Council, 621-2012-3863
Available from: 2017-08-09 Created: 2017-08-09 Last updated: 2017-08-18

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Araujo-Cabarcas, Juan CarlosEngström, Christian
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CiteExportLink to record
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