In the final test problem the important acoustic property of the radiation ratio is considered. In Figures 5.1 and 5.2 the computed versus exact radiation ratios for pulsating and oscillating spheres across a wide wavenumber range are given where the acoustic field is taken to be axisymmetric. The results show some numerical drift from the exact solution with increasing wavenumber. As a general rule, the accuracy of the BEM solution of acoustic problems slowly deteriorates with frequency if the same boundary element mesh is used throughout. It may often be necessary to use finer meshes at higher wavenumbers.
In the introduction to the Chapter, a history of the difficulties in employing the boundary element method successfully to exterior problems was outlined. However, the test problems in Section 5.6 and the application in Section 5.7 show that the improved formulations provide the foundation for methods that are robust throughout the frequency range; the methods do not show the wild errors that have been reported in the solution by the elementary methods of Section 5.1.
The Schenck or CHIEF method of Section 5.2
is currently the most popular in the solution of exterior acoustic problems.
However it is the author's view that the method, however implemented,
will tend to degrade at higher wavenumbers, although the point
at which this happens is often beyond the range of wavenumbers of interest
in practice. Basing the boundary element method
on the improved formulations of Burton and Miller [15]
(direct) and Brackage and Werner [12],
Leis [57], Panich [66] and Kussmaul [54]
(indirect) is the most suitable for the numerical solution
of exterior acoustic problems.