Unified formulation of radiation conditions for the wave equation

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    Abstract

    A family of radiation conditions for the wave equation is derived by truncating a rational function approxiamtion of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to different choice of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms of selected directions with ideal transmission is established. A mechanical interpretation of the fictitious surface densities enables identification of suitable conditions at corners and boundaries of the radiating surface. Numerical examples illustrate excellent results with one or two fictitious layers with suitable corner and boundary conditions.
    Original languageEnglish
    JournalInternational Journal for Numerical Methods in Engineering
    VolumeVol. 53
    Pages (from-to)pp. 275-295
    ISSN0029-5981
    Publication statusPublished - 2002

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