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  Optimal Galerkin approximations of partial differential equations using principal interaction patterns.

Kwasniok, F. (1997). Optimal Galerkin approximations of partial differential equations using principal interaction patterns. Physical Review E, 55, 5365-5375. doi:10.1103/PhysRevE.55.5365.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0009-ECEA-6 Version Permalink: https://hdl.handle.net/21.11116/0000-0009-ED20-8
Genre: Journal Article

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PhysRevE.55.5365.pdf (Publisher version), 310KB
 
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1997
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233-Report-txt.pdf (Preprint), 2MB
 
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 Creators:
Kwasniok, Frank1, Author
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1MPI for Meteorology, Max Planck Society, Bundesstraße 53, 20146 Hamburg, DE, ou_913545              

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 Abstract: A method of constructing minimal systems of ordinary differential equations modeling the dynamics of nonlinear partial differential equations is presented. Characteristic spatial structures called principal interaction patterns are extracted from the system according to a nonlinear variational principle based on a dynamical optimality criterion and used as basis functions in a Galerkin approximation. The potential of the method is illustrated using the Kuramoto-Sivashinsky equation as an example. As to the number of modes required to capture the dynamics of the complete system a reduced model based on principal interaction patterns yields a considerable improvement on more conventional approaches using Sobolev eigenfunctions or Karhunen-Lo`eve modes as basis functions and is far more efficient than a dynamical description based on Fourier modes

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Language(s): eng - English
 Dates: 1997
 Publication Status: Issued
 Pages: -
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 Rev. Type: Peer
 Identifiers: DOI: 10.1103/PhysRevE.55.5365
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Title: Physical Review E
  Other : Phys. Rev. E
Source Genre: Journal
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Publ. Info: Melville, NY : American Physical Society
Pages: - Volume / Issue: 55 Sequence Number: - Start / End Page: 5365 - 5375 Identifier: ISSN: 1539-3755
CoNE: https://pure.mpg.de/cone/journals/resource/954925225012

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Title: Report / Max-Planck-Institut für Meteorologie
  Other : MPI Report
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Publ. Info: Hamburg : Max-Planck-Institut für Meteorologie
Pages: - Volume / Issue: 233 Sequence Number: - Start / End Page: - Identifier: ISSN: 0937-1060
CoNE: https://pure.mpg.de/cone/journals/resource/0937-1060