Short wave modelling using special finite elements

Omar Laghrouche, Peter Bettess

    Research output: Contribution to journalArticlepeer-review

    110 Citations (Scopus)


    The solutions to the Helmholtz equation in the plane are approximated by systems of plane waves. The aim is to develop finite elements capable of containing many wavelengths and therefore simulating problems with large wave numbers without refining the mesh to satisfy the traditional requirement of about ten nodal points per wavelength. At each node of the meshed domain, the wave potential is written as a combination of plane waves propagating in many possible directions. The resulting element matrices contain oscillatory functions and are evaluated using high order Gauss-Legendre integration. These finite elements are used to solve wave problems such as a diffracted potential from a cylinder. Many wavelengths are contained in a single finite element and the number of parameters in the problem is greatly reduced.

    Original languageEnglish
    Pages (from-to)189-210
    Number of pages22
    JournalJournal of Computational Acoustics
    Issue number1
    Publication statusPublished - Mar 2000


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