The wave equation as a Port-Hamiltonian system, and a finite-dimensional approximation

V. Talasila, G. Golo, Arjan van der Schaft

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    Abstract

    The problem of approximating a distributed parameter system with free boundary conditions is solved for the 2-dimensional wave equation. To this end we first model the wave equation as a distributed-parameter port-Hamiltonian system. Then we employ the idea that it is natural to use different finite elements for the approximation of di?erent geometric variables (forms) describing a distributed-parameter system, to spatially discretize the system and we show that we obtain a ?nite-dimensional port-Hamiltonian system, which also preserves the conservation laws.
    Original languageUndefined
    Title of host publicationProceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems
    EditorsD.S. Gilliam, J. Rosenthal
    Place of PublicationSouth Bend, Indiana, USA
    PublisherUniversity of Notre Dame
    Pages-
    Number of pages15
    ISBN (Print)not assigned
    Publication statusPublished - 2002
    Event15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002 - University of Notre Dame, Notre Dame, United States
    Duration: 12 Aug 200216 Aug 2002
    Conference number: 15

    Publication series

    Name
    PublisherUniversity of Notre Dame

    Conference

    Conference15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002
    Abbreviated titleMTNS 2002
    CountryUnited States
    CityNotre Dame
    Period12/08/0216/08/02

    Keywords

    • EWI-16746
    • METIS-210940
    • IR-69144

    Cite this

    Talasila, V., Golo, G., & van der Schaft, A. (2002). The wave equation as a Port-Hamiltonian system, and a finite-dimensional approximation. In D. S. Gilliam, & J. Rosenthal (Eds.), Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems (pp. -). South Bend, Indiana, USA: University of Notre Dame.