Three dimensional plane wave basis finite elements for short wave modelling

Omar Laghrouche; Peter Bettess; Jon Trevelyan

doi:10.1007/978-3-642-55856-6_121

Three dimensional plane wave basis finite elements for short wave modelling

Omar Laghrouche, Peter Bettess, Jon Trevelyan

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This work deals with the solution of the Helmholtz equation in three dimensions using finite elements capable of capturing many wavelengths per nodal spacing. This is done by constructing oscillatory shape functions as the product of the usual polynomial shape functions and planar waves. This technique leads to larger elementary matrices but since the mesh contains fewer finite elements, the final system to solve is greatly reduced. The current model is used to solve a problem of a plane wave with a local wavenumber or the so-called evanescent mode problem. The results show the validity of the technique and a significant reduction in the total number of degrees of freedom compared to the classical finite element model.

Original language	English
Title of host publication	Mathematical and Numerical Aspects of Wave Propagation WAVES 2003
Subtitle of host publication	Proceedings of The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyväskylä, Finland, 30 June – 4 July 2003
Editors	Gary C Cohen, Patrick Joly, Erkki Heikkola, Pekka Neittaanmäki
Publisher	Springer
Pages	749-753
Number of pages	5
Volume	Part XVII
ISBN (Electronic)	978-3-642-55856-6
ISBN (Print)	978-3-642-62480-3
DOIs	https://doi.org/10.1007/978-3-642-55856-6_121
Publication status	Published - 2003
Event	6th International Conference on Mathematical and Numerical Aspects of Wave Propagation - Jyväskylä, Finland Duration: 30 Jun 2003 → 4 Jul 2003

Conference

Conference	6th International Conference on Mathematical and Numerical Aspects of Wave Propagation
Abbreviated title	WAVES 2003
Country/Territory	Finland
City	Jyväskylä
Period	30/06/03 → 4/07/03

Access to Document

10.1007/978-3-642-55856-6_121

Cite this

Laghrouche, O., Bettess, P., & Trevelyan, J. (2003). Three dimensional plane wave basis finite elements for short wave modelling. In G. C. Cohen, P. Joly, E. Heikkola, & P. Neittaanmäki (Eds.), Mathematical and Numerical Aspects of Wave Propagation WAVES 2003: Proceedings of The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyväskylä, Finland, 30 June – 4 July 2003 (Vol. Part XVII, pp. 749-753). Springer. https://doi.org/10.1007/978-3-642-55856-6_121

Laghrouche, Omar ; Bettess, Peter ; Trevelyan, Jon. / Three dimensional plane wave basis finite elements for short wave modelling. Mathematical and Numerical Aspects of Wave Propagation WAVES 2003: Proceedings of The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyväskylä, Finland, 30 June – 4 July 2003. editor / Gary C Cohen ; Patrick Joly ; Erkki Heikkola ; Pekka Neittaanmäki. Vol. Part XVII Springer, 2003. pp. 749-753

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title = "Three dimensional plane wave basis finite elements for short wave modelling",

abstract = "This work deals with the solution of the Helmholtz equation in three dimensions using finite elements capable of capturing many wavelengths per nodal spacing. This is done by constructing oscillatory shape functions as the product of the usual polynomial shape functions and planar waves. This technique leads to larger elementary matrices but since the mesh contains fewer finite elements, the final system to solve is greatly reduced. The current model is used to solve a problem of a plane wave with a local wavenumber or the so-called evanescent mode problem. The results show the validity of the technique and a significant reduction in the total number of degrees of freedom compared to the classical finite element model.",

author = "Omar Laghrouche and Peter Bettess and Jon Trevelyan",

year = "2003",

doi = "10.1007/978-3-642-55856-6_121",

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editor = "Cohen, {Gary C} and Patrick Joly and Erkki Heikkola and Pekka Neittaanm{\"a}ki",

booktitle = "Mathematical and Numerical Aspects of Wave Propagation WAVES 2003",

publisher = "Springer",

note = "6th International Conference on Mathematical and Numerical Aspects of Wave Propagation, WAVES 2003 ; Conference date: 30-06-2003 Through 04-07-2003",

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Laghrouche, O, Bettess, P & Trevelyan, J 2003, Three dimensional plane wave basis finite elements for short wave modelling. in GC Cohen, P Joly, E Heikkola & P Neittaanmäki (eds), Mathematical and Numerical Aspects of Wave Propagation WAVES 2003: Proceedings of The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyväskylä, Finland, 30 June – 4 July 2003. vol. Part XVII, Springer, pp. 749-753, 6th International Conference on Mathematical and Numerical Aspects of Wave Propagation, Jyväskylä, Finland, 30/06/03. https://doi.org/10.1007/978-3-642-55856-6_121

Three dimensional plane wave basis finite elements for short wave modelling. / Laghrouche, Omar; Bettess, Peter; Trevelyan, Jon.
Mathematical and Numerical Aspects of Wave Propagation WAVES 2003: Proceedings of The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyväskylä, Finland, 30 June – 4 July 2003. ed. / Gary C Cohen; Patrick Joly; Erkki Heikkola; Pekka Neittaanmäki. Vol. Part XVII Springer, 2003. p. 749-753.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Y1 - 2003

N2 - This work deals with the solution of the Helmholtz equation in three dimensions using finite elements capable of capturing many wavelengths per nodal spacing. This is done by constructing oscillatory shape functions as the product of the usual polynomial shape functions and planar waves. This technique leads to larger elementary matrices but since the mesh contains fewer finite elements, the final system to solve is greatly reduced. The current model is used to solve a problem of a plane wave with a local wavenumber or the so-called evanescent mode problem. The results show the validity of the technique and a significant reduction in the total number of degrees of freedom compared to the classical finite element model.

AB - This work deals with the solution of the Helmholtz equation in three dimensions using finite elements capable of capturing many wavelengths per nodal spacing. This is done by constructing oscillatory shape functions as the product of the usual polynomial shape functions and planar waves. This technique leads to larger elementary matrices but since the mesh contains fewer finite elements, the final system to solve is greatly reduced. The current model is used to solve a problem of a plane wave with a local wavenumber or the so-called evanescent mode problem. The results show the validity of the technique and a significant reduction in the total number of degrees of freedom compared to the classical finite element model.

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DO - 10.1007/978-3-642-55856-6_121

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BT - Mathematical and Numerical Aspects of Wave Propagation WAVES 2003

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Laghrouche O, Bettess P, Trevelyan J. Three dimensional plane wave basis finite elements for short wave modelling. In Cohen GC, Joly P, Heikkola E, Neittaanmäki P, editors, Mathematical and Numerical Aspects of Wave Propagation WAVES 2003: Proceedings of The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyväskylä, Finland, 30 June – 4 July 2003. Vol. Part XVII. Springer. 2003. p. 749-753 doi: 10.1007/978-3-642-55856-6_121

Three dimensional plane wave basis finite elements for short wave modelling

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