Three dimensional plane wave basis finite elements for short wave modelling

Omar Laghrouche, Peter Bettess, Jon Trevelyan

    Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
    Title of host publicationMathematical and Numerical Aspects of Wave Propagation WAVES 2003
    Subtitle of host publicationProceedings of The Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation Held at Jyväskylä, Finland, 30 June – 4 July 2003
    EditorsGary C Cohen, Patrick Joly, Erkki Heikkola, Pekka Neittaanmäki
    PublisherSpringer
    Pages749-753
    Number of pages5
    VolumePart XVII
    ISBN (Electronic)978-3-642-55856-6
    ISBN (Print)978-3-642-62480-3
    DOIs
    Publication statusPublished - 2003
    Event6th International Conference on Mathematical and Numerical Aspects of Wave Propagation - Jyväskylä, Finland
    Duration: 30 Jun 20034 Jul 2003

    Conference

    Conference6th International Conference on Mathematical and Numerical Aspects of Wave Propagation
    Abbreviated titleWAVES 2003
    CountryFinland
    CityJyväskylä
    Period30/06/034/07/03

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