On the choice of coupling parameter in the time domain Burton and Miller formulation

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.