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Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2015 (English)Report (Other academic)
Abstract [en]

We construct accurate central difference stencils for problems involving high frequency waves or multi-frequency solutions over long time intervals with a relatively coarse spatial mesh, and with an easily obtained bound on the dispersion error. This is done by demonstrating that the problem of constructing central difference stencils that have minimal dispersion error in the infinity norm can be recast into a problem of approximating a continuous function from a finite dimensional subspace with a basis forming a Chebyshev set. In this new formulation, characterising and numerically obtaining optimised schemes can be done using established theory.

Place, publisher, year, edition, pages
Linköping University Electronic Press, 2015. , 29 p.
Series
LiTH-MAT-R, ISSN 0348-2960 ; 2014:17
Keyword [en]
Dispersion relation; Wave propagation; Wavenumber approximation; Finite differences; Approximation theory
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-114132ISRN: LiTH-MAT-R--2014/17--SEOAI: oai:DiVA.org:liu-114132DiVA: diva2:787531
Available from: 2015-02-10 Created: 2015-02-10 Last updated: 2015-02-10Bibliographically approved

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Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators(1527 kB)242 downloads
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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • vancouver
  • Other style
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Language
  • de-DE
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  • en-US
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  • nn-NB
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Output format
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