### Abstract

Original language | Undefined |
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Title of host publication | Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems |

Editors | D.S. Gilliam, J. Rosenthal |

Place of Publication | South Bend, Indiana, USA |

Publisher | University of Notre Dame |

Pages | - |

Number of pages | 15 |

ISBN (Print) | not assigned |

Publication status | Published - 2002 |

Event | 15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002 - University of Notre Dame, Notre Dame, United States Duration: 12 Aug 2002 → 16 Aug 2002 Conference number: 15 |

### Publication series

Name | |
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Publisher | University of Notre Dame |

### Conference

Conference | 15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002 |
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Abbreviated title | MTNS 2002 |

Country | United States |

City | Notre Dame |

Period | 12/08/02 → 16/08/02 |

### Keywords

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

### Cite this

*Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems*(pp. -). South Bend, Indiana, USA: University of Notre Dame.

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

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

PY - 2002

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

SN - not assigned

SP - -

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

A2 - Gilliam, D.S.

A2 - Rosenthal, J.

PB - University of Notre Dame

CY - South Bend, Indiana, USA

ER -