Abstract
Numerical integration methods for Hamiltonian systems are of importance across many disciplines, including musical acoustics, where many systems of interest are very nearly lossless. Of particular interest are methods possessing a conserved pseudoenergy. Though most such methods have an implicit character, an explicit method was proposed recently by Marazzato et al. The proposed method relies on a continuous integration which must be performed exactly in order for the conservation property to hold—as a result, it holds only approximately under numerical quadrature. Here, we show an explicit scheme for Hamiltonian integration, with a different choice of pseudoenergy, which is exactly conserved. A fast implementation is possible through the use of structured matrix inversion. The application to the case of fully nonlinear string vibration is illustrated.
Original language | English |
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Title of host publication | Proceedings of the 2020 European Nonlinear Dynamics Conference |
Place of Publication | Lyon, France |
Number of pages | 7 |
Publication status | Published - 22 Jul 2022 |
Event | 10th European Nonlinear Dynamics Conference - Lyon Convention Centre, Lyon, France Duration: 5 Jul 2020 → 10 Jul 2020 https://web.archive.org/web/20200205144800/https://enoc2020.sciencesconf.org/ |
Conference
Conference | 10th European Nonlinear Dynamics Conference |
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Abbreviated title | ENOC2020 |
Country/Territory | France |
City | Lyon |
Period | 5/07/20 → 10/07/20 |
Internet address |