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Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains
Division of Scientific Computing, Department of Information Technology, Uppsala University, Sweden.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2012 (English)In: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 62, no 11, 1620-1638 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we study the heat and advectionequation in single and multipledomains. The equations are discretized using a second order accurate finite difference method on Summation-By-Parts form with weak boundary and interface conditions. We derive analytic expressions for the spectrum of the continuous problem and for their corresponding discretization matrices.

It is shown how the spectrum of the singledomain operator is contained in the multi domain operator spectrum when artificial interfaces are introduced. The interface treatments are posed as a function of one parameter, and the impact on the spectrum and discretization error is investigated as a function of this parameter. Finally we briefly discuss the generalization to higher order accurate schemes.

Place, publisher, year, edition, pages
2012. Vol. 62, no 11, 1620-1638 p.
Keyword [en]
Spectralanalysis; Eigenvalues; Diffusion; Advection; Summation-By-Parts; Weak boundary conditions; Weak interface conditions
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-80947DOI: 10.1016/j.apnum.2012.05.002ISI: 000309027700002OAI: diva2:549609
Available from: 2012-09-05 Created: 2012-09-04 Last updated: 2013-08-30

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