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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on July 24, 2009
The Quarterly Journal of Mechanics and Applied Mathematics 2009 62(4):431-450; doi:10.1093/qjmam/hbp018
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© The author 2009. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

On The Choice of Coupling Parameter in The Time Domain Burton–Miller Formulation

D. J. Chappell{dagger}

( Division of Applied Mathematics, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD )

P. J. Harris{ddagger}

( Division of Mathematical Sciences, School of Computing and Mathematical Sciences, University of Brighton, Brighton BN2 4GJ )

{dagger} Corresponding author. <david.chappell{at}nottingham.ac.uk>

{ddagger} <p.j.harris{at}brighton.ac.uk>

Received 30 October 2008. Revise 8 June 2009. Accepted 26 June 2009.


  Abstract

A Burton–Miller-type integral equation for time domain exterior acoustic radiation and scattering problems is considered as a way of overcoming the well-known stability problems associated with collocation-based time domain boundary element methods. The stability of the method is considered and justified using an argument based on the associated frequency domain integral equation. This allows for the justification of a choice of coupling coefficient that is in some sense optimal for the time domain formulation for acoustic radiation and scattering by spheres. Finally, computational results are given in support of these observations and the impact of choosing the optimal parameter in the computations is discussed. Results for non-spherical bodies are also considered to see whether the results may be more widely applicable.


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