Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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
Parareal multiscale methods for highly oscillatory dynamical systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.ORCID iD: 0000-0001-8441-3678
2016 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 38, no 6, p. A3540-A3564Article in journal (Refereed) Published
Abstract [en]

We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the system using an appropriate multiscale integrator, which is refined using parallel fine scale integrations. Convergence is obtained using an alignment algorithm for fast phase-like variables. The method may be used either to enhance the accuracy and range of applicability of the multiscale method in approximating only the slow variables, or to resolve all the state variables. The numerical scheme does not require that the system is split into slow and fast coordinates. Moreover, the dynamics may involve hidden slow variables, for example, due to resonances. We propose an alignment algorithm for almost-periodic solutions, in which case convergence of the parareal iterations is proved. The applicability of the method is demonstrated in numerical examples.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics Publications , 2016. Vol. 38, no 6, p. A3540-A3564
Keywords [en]
Highly oscillatory problems, Multiscale computation, Parallel algorithms
National Category
Mathematics Computer and Information Sciences
Identifiers
URN: urn:nbn:se:kth:diva-201582DOI: 10.1137/15M1011044ISI: 000391853100019Scopus ID: 2-s2.0-85007115644OAI: oai:DiVA.org:kth-201582DiVA, id: diva2:1073294
Note

QC 20170210

Available from: 2017-02-10 Created: 2017-02-10 Last updated: 2018-01-13Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Tsai, Richard
By organisation
Numerical Analysis, NA
In the same journal
SIAM Journal on Scientific Computing
MathematicsComputer and Information Sciences

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 122 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • 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