## 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 |
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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 | |

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 |
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Abbreviated title | WAVES 2003 |

Country/Territory | Finland |

City | Jyväskylä |

Period | 30/06/03 → 4/07/03 |