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Spectral analysis of the continuous and discretized heat and advection equation on single and multiple domains
(Teknisk-naturvetenskapliga vetenskapsområdet, Matematisk-datavetenskapliga sektionen, Institutionen för informationsteknologi, Avdelningen för teknisk databehandling, Uppsala University)
Linköping University, Department of Mathematics, Scientific Computing. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
2010 (English)Report (Other academic)
Abstract [en]

In this paper we study the heat and advection equation in single and multiple domains. We discretize 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. We show how the spectrum of the single domain operator is contained in the multi domain operator spectrum when artificial interfaces are introduced. We study the impact on the spectrum and discretization errors depending on the interface treatment and verify that the results are carried over to higher order accurate schemes.

Place, publisher, year, edition, pages
2010. , 31 p.
Series
, Technical report / Department of Information Technology, Uppsala University, ISSN 1404-3203 ; 2010:030
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-68277OAI: oai:DiVA.org:liu-68277DiVA: diva2:417266
Available from: 2011-05-16 Created: 2011-05-16 Last updated: 2013-08-30Bibliographically approved

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fulltext(241 kB)171 downloads
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Nordström, Jan
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Scientific ComputingThe Institute of Technology
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