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Erschienen in:
2003 | OriginalPaper | Buchkapitel
Three Dimensional Plane Wave Basis Finite Elements for Short Wave Modelling
verfasst von : Omar Laghrouche, Peter Bettess, Jon Trevelyan
Erschienen in: Mathematical and Numerical Aspects of Wave Propagation WAVES 2003
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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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.