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

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

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 proceeding › Conference contribution › Academic › peer-review

161 Downloads (Pure)

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 language	Undefined
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
Publisher	University of Notre Dame

Conference

Conference	15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002
Abbreviated title	MTNS 2002
Country/Territory	United States
City	Notre Dame
Period	12/08/02 → 16/08/02
Other	12-16 Aug 2002

Keywords

EWI-16746
METIS-210940
IR-69144

Access to Document

http://www.nd.edu/~mtns/papers/1182.pdf

Cite this

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

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.",

keywords = "EWI-16746, METIS-210940, IR-69144",

author = "V. Talasila and G. Golo and {van der Schaft}, Arjan",

year = "2002",

language = "Undefined",

isbn = "not assigned",

publisher = "University of Notre Dame",

pages = "--",

editor = "D.S. Gilliam and J. Rosenthal",

booktitle = "Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems",

address = "United States",

note = "15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002 ; Conference date: 12-08-2002 Through 16-08-2002",

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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, Indiana, United States, 12/08/02. <http://www.nd.edu/~mtns/papers/1182.pdf>

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 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

N1 - Conference code: 15

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

T2 - 15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002

Y2 - 12 August 2002 through 16 August 2002

ER -