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Geometric Integration of Weakly Dissipative Systems

In English

Författare

Summary, in English

Some problems in mechanics, e.g. in bearing simulation, contain subsystems that are conservative as well as weakly dissipative subsystems. Our experience is that geometric integration methods are often superior for such systems, as long as the dissipation is weak. Here we develop adaptive methods for dissipative perturbations of Hamiltonian systems. The methods are "geometric" in the sense that the form of the dissipative perturbation is preserved. The methods are linearly explicit, i.e., they require the solution of a linear subsystem. We sketch an analysis in terms of backward error analysis and numerical comparisons with a conventional RK method of the same order is given.

Avdelning/ar

Publiceringsår

2009

Språk

Engelska

Sidor

877-877

Publikation/Tidskrift/Serie

Numerical Analysis and Applied Mathematics, Vols 1 and 2

Volym

1168

Dokumenttyp

Konferensbidrag

Förlag

American Institute of Physics (AIP)

Ämne

  • Mathematics

Nyckelord

  • weakly dissipative systems
  • Geometric integration
  • splitting methods
  • adaptive geometric integration

Conference name

International Conference on Numerical Analysis and Applied Mathematics, 2009

Conference date

2009-09-18 - 2009-09-22

Conference place

Rethymno, Greece

Status

Published

Forskningsgrupp

  • Numerical Analysis

ISBN/ISSN/Övrigt

  • ISSN: 0094-243X
  • ISSN: 1551-7616