liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • 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
A Stable Domain Decomposition Technique for Advection–Diffusion Problems
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2018 (English)In: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 77, no 2, p. 755-774Article in journal (Refereed) Published
Abstract [en]

The use of implicit methods for numerical time integration typically generates very large systems of equations, often too large to fit in memory. To address this it is necessary to investigate ways to reduce the sizes of the involved linear systems. We describe a domain decomposition approach for the advection–diffusion equation, based on the Summation-by-Parts technique in both time and space. The domain is partitioned into non-overlapping subdomains. A linear system consisting only of interface components is isolated by solving independent subdomain-sized problems. The full solution is then computed in terms of the interface components. The Summation-by-Parts technique provides a solid theoretical framework in which we can mimic the continuous energy method, allowing us to prove both stability and invertibility of the scheme. In a numerical study we show that single-domain implementations of Summation-by-Parts based time integration can be improved upon significantly. Using our proposed method we are able to compute solutions for grid resolutions that cannot be handled efficiently using a single-domain formulation. An order of magnitude speed-up is observed, both compared to a single-domain formulation and to explicit Runge–Kutta time integration.

Place, publisher, year, edition, pages
2018. Vol. 77, no 2, p. 755-774
Keywords [en]
Domain decomposition, Partial differential equations, Summation-by-Parts, Finite difference methods, Stability
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-147768DOI: 10.1007/s10915-018-0722-xISI: 000446594600003OAI: oai:DiVA.org:liu-147768DiVA, id: diva2:1205445
Available from: 2018-05-14 Created: 2018-05-14 Last updated: 2018-10-17

Open Access in DiVA

fulltext(1231 kB)59 downloads
File information
File name FULLTEXT01.pdfFile size 1231 kBChecksum SHA-512
663910abee35363e5c501d958b5622a8bd944268497932b44d75ae57d213ee39f26f7ad1da6095f1c292c74ae1fa7a27a15f1abcc359476c38a5af4c5a5bc446
Type fulltextMimetype application/pdf

Other links

Publisher's full text

Authority records BETA

Nordström, Jan

Search in DiVA

By author/editor
Ålund, OskarNordström, Jan
By organisation
Computational MathematicsFaculty of Science & Engineering
In the same journal
Journal of Scientific Computing
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 59 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 155 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • 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