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λ-scale convergence applied to the stationary heat conduction equation with non-periodic thermal conductivity matrix
Mid Sweden University, Faculty of Science, Technology and Media, Department of Engineering and Sustainable Development.ORCID iD: 0000-0001-9984-2424
2009 (English)In: MATHMOD 2009 - 6th Vienna International Conference on Mathematical Modelling, Wien: Vienna University Press (WUV), 2009, p. 2720-2723Conference paper, Published paper (Refereed)
Abstract [en]

In this contribution we study the homogenization of non-periodic stationary heat conduction problems with homogeneous Dirichlet boundary data by applying the recently developed λ-scale convergence technique developed by Holmbom and Silfver. λ-scale convergence can be seen as either being a special case of scale convergence (developed by Mascarenhas and Toader) or of “generalized” two-scale convergence (developed by Holmbom, Silfver, Svanstedt and Wellander). From either viewpoint, it is a possibly powerful generalization of Nguetseng’s classical, periodic two-scale convergence method. We give a definition of the concept of λ-scale convergence, which is then used to claim a main theorem on homogenization of certain non-periodic stationary heat conduction problems. The original part of the contribution starts by defining a two-dimensional “toy model”. We show that the “toy model” satisfies the right conditions such that the aforementioned main theorem on the homogenization can be employed. In this way we derive the homogenized problem, i.e. the homogenized thermal conductivity matrix, and the local problem. The contribution is concluded by giving a numerical example where we explicitly compute the homogenized thermal conductivity matrix.

Place, publisher, year, edition, pages
Wien: Vienna University Press (WUV), 2009. p. 2720-2723
Series
Argesim Report ; 35
Keywords [en]
homogenization, elliptic, heat conduction equation, λ-scale convergence, non-periodic
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:miun:diva-8747ISBN: 978-3-901608-35-3 (print)OAI: oai:DiVA.org:miun-8747DiVA, id: diva2:209550
Available from: 2009-03-25 Created: 2009-03-25 Last updated: 2013-11-01Bibliographically approved

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Persson, Jens

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf