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Computational Science, Engineering & Technology Series
ISSN 1759-3158
Edited by: F. Magoulès
Chapter 8

Advances in the On-Surface Radiation Condition Method: Theory, Numerics and Applications

X. Antoine

Institut Elie Cartan Nancy, University Henri Poincaré Nancy I, France

Full Bibliographic Reference for this chapter
X. Antoine, "Advances in the On-Surface Radiation Condition Method: Theory, Numerics and Applications", in F. Magoulès, (Editor), "Computational Methods for Acoustics Problems", Saxe-Coburg Publications, Stirlingshire, UK, Chapter 8, pp 207-232, 2008. doi:10.4203/csets.18.8
Keywords: on-surface radiation condition, computational acoustics, high frequency, fast algorithms, surface scattering, non-reflecting boundary condition, generalised impedance boundary condition, integral equations, preconditioner.

The aim of this chapter is to give a comprehensive introduction to the recent advances in the on-surface radiation condition (OSRC) method for the numerical representation of acoustic scattering problems in the frequency domain. After a presentation of the main theoretical developments in this area, the finite element formulation of the resulting problem is introduced. A few numerical tests show the efficiency and accuracy of the OSRC formulations for various model problems but also point out some remaining difficulties. Next, the discussion is directed towards some applications of the OSRC method to various current problems in computational acoustic scattering: modelling of exterior domains and penetrable scatterers, improvement of existing integral equation formulations in view of a fast iterative Krylov subspace solution and other potentially interesting applications for prospecting large scale scattering problems at high frequency.

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