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A time-spectral method for initial-value problems using a novel spatial subdomain scheme
KTH, School of Electrical Engineering and Computer Science (EECS), Fusion Plasma Physics.
KTH, School of Electrical Engineering and Computer Science (EECS), Fusion Plasma Physics.ORCID iD: 0000-0001-6379-1880
2018 (English)In: COGENT MATHEMATICS, ISSN 2331-1835, Vol. 5, no 1, article id 1529280Article in journal (Refereed) Published
Abstract [en]

We analyse a novel subdomain scheme for time-spectral solution of initial-value partial differential equations. In numerical modelling spectral methods are commonplace for spatially dependent systems, whereas finite difference schemes are typically applied for the temporal domain. The Generalized Weighted Residual Method (GWRM) is a fully spectral method that spectrally decomposes all specified domains, including the temporal domain, using multivariate Chebyshev polynomials. The Common Boundary-Condition method (CBC) here proposed is a spatial subdomain scheme for the GWRM. It solves the physical equations independently from the global connection of subdomains in order to reduce the total number of modes. Thus, it is a condensation procedure in the spatial domain that allows for a simultaneous global temporal solution. It is here evaluated against the finite difference methods of Crank-Nicolson and Lax-Wendroff for two example linear PDEs. The CBC-GWRM is also applied to the linearised ideal magnetohydrodynamic (MHD) equations for a screw pinch equilibrium. The growth rate of the most unstable mode was efficiently computed with an error <0.1%.

Place, publisher, year, edition, pages
TAYLOR & FRANCIS AS , 2018. Vol. 5, no 1, article id 1529280
Keywords [en]
time, spectral, weighted residual methods, MHD, Chebyshev, subdomain, PDE, initial, boundary
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-240022DOI: 10.1080/25742558.2018.1529280ISI: 000451205400001OAI: oai:DiVA.org:kth-240022DiVA, id: diva2:1269270
Note

QC 20181210

Available from: 2018-12-10 Created: 2018-12-10 Last updated: 2018-12-10Bibliographically approved

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Scheffel, Jan

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CiteExportLink to record
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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
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  • asciidoc
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