Unified formulation of radiation conditions for the wave equation

A family of radiation boundary conditions for the wave equation is derived by truncating a rational function approximation 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 seco...

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2002-01, Vol.53 (2), p.275-295
Main Author: Krenk, Steen
Format: Article
Language:English
Subjects:
absorbing boundary conditions
non-reflecting boundary conditions
radiation boundary conditions
wave equation
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Summary:A family of radiation boundary conditions for the wave equation is derived by truncating a rational function approximation 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 choices 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 presented. 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. Copyright © 2001 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.268