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EIGENVALUE PROBLEM IN A SOLID WITH MANY INCLUSIONS: ASYMPTOTIC ANALYSIS
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
University of Liverpool, England.
Liverpool John Moores University, England.
2017 (English)In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 15, no 2, p. 1003-1047Article in journal (Refereed) Published
Abstract [en]

We construct the asymptotic approximation to the first eigenvalue and corresponding eigensolution of Laplaces operator inside a domain containing a cloud of small rigid inclusions. The separation of the small inclusions is characterized by a small parameter which is much larger when compared with the nominal size of inclusions. Remainder estimates for the approximations to the first eigenvalue and associated eigenfield are presented. Numerical illustrations are given to demonstrate the efficiency of the asymptotic approach compared to conventional numerical techniques, such as the finite element method, for three-dimensional solids containing clusters of small inclusions.

Place, publisher, year, edition, pages
SIAM PUBLICATIONS , 2017. Vol. 15, no 2, p. 1003-1047
Keywords [en]
singular perturbations; clouds of inclusions; asymptotic approximations; eigenvalue problem; Helmholtz equation
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-139666DOI: 10.1137/16M1079348ISI: 000404779900013OAI: oai:DiVA.org:liu-139666DiVA, id: diva2:1133532
Available from: 2017-08-16 Created: 2017-08-16 Last updated: 2017-09-05

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Mazya, Vladimir
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CiteExportLink to record
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Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
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  • Other locale
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Output format
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