Fast explicit algorithms for Hamiltonian numerical integration

Stefan Bilbao, Michele Ducceschi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish
Title of host publicationProceedings of the 2020 European Nonlinear Dynamics Conference
Place of PublicationLyon, France
Number of pages2
Publication statusAccepted/In press - 31 Jan 2020
Event10th European Nonlinear Dynamics Conference - Lyon Convention Centre, Lyon, France
Duration: 5 Jul 202010 Jul 2020
https://web.archive.org/web/20200205144800/https://enoc2020.sciencesconf.org/

Conference

Conference10th European Nonlinear Dynamics Conference
Abbreviated titleENOC2020
Country/TerritoryFrance
CityLyon
Period5/07/2010/07/20
Internet address

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