| Title | Geometric Integration of Weakly Dissipative Systems |
| Authors | Klas Modin, Claus Führer, Gustaf Söderlind |
| Publication | Numerical Analysis and Applied Mathematics, Vols 1 and 2 |
| Year | 2009 |
| Volume | 1168 |
| Pages | 877 - 877 |
| Document type | Conference paper |
| Conference name | International Conference on Numerical Analysis and Applied Mathematics |
| Conference Date | Sep 18-22, 2009 |
| Conference Location | Rethymno, Greece |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | American Institute of Physics |
| Abstract 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. |
| Keywords | weakly dissipative systems, Geometric integration, splitting methods, adaptive geometric integration, |
| ISBN/ISSN/Other | ISSN: 0094-243X |
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