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

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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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.
Talasila, V. ; Golo, G. ; van der Schaft, Arjan. / The wave equation as a Port-Hamiltonian system, and a finite-dimensional approximation. Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems. editor / D.S. Gilliam ; J. Rosenthal. South Bend, Indiana, USA : University of Notre Dame, 2002. pp. -
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Talasila, V, Golo, G & van der Schaft, A 2002, The wave equation as a Port-Hamiltonian system, and a finite-dimensional approximation. in DS Gilliam & J Rosenthal (eds), Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems. University of Notre Dame, South Bend, Indiana, USA, pp. -, 15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002, Notre Dame, United States, 12/08/02.

The wave equation as a Port-Hamiltonian system, and a finite-dimensional approximation. / Talasila, V.; Golo, G.; van der Schaft, Arjan.

Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems. ed. / D.S. Gilliam; J. Rosenthal. South Bend, Indiana, USA : University of Notre Dame, 2002. p. -.

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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T1 - The wave equation as a Port-Hamiltonian system, and a finite-dimensional approximation

AU - Talasila, V.

AU - Golo, G.

AU - van der Schaft, Arjan

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Y1 - 2002

N2 - 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.

AB - 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.

KW - EWI-16746

KW - METIS-210940

KW - IR-69144

M3 - Conference contribution

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BT - Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems

A2 - Gilliam, D.S.

A2 - Rosenthal, J.

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CY - South Bend, Indiana, USA

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