Rath-Spivack O., Spivack M.

The calculation of acoustic scattering by large objects or extended rough surfaces is a challenging computational problem, especially in the presence of strong multiple scattering. This is particularly acute at low grazing angles. Boundary integral methods are flexible and often used for such problems but can be computationally intensive and scale badly with increasing frequency. Here we develop the left-right splitting method and apply this to several problems of acoustic scattering in 3d. In this approach the unknown surface field is expressed as the solution to the Helmholtz integral equation, where integration is taken over the surface. The integral can be split into two at each point of observation, corresponding to right- and left-going energy. This leads to a series solution, which, under the assumption that forward scattering is dominant, can often be truncated after one or two terms even in strong scattering regimes. The key advantages are (a) each term can be evaluated very quickly with low memory requirement; and (b) the term have a straightforward physical interpretation, which gives insight into scattering mechanisms. Results are validated by comparison with 'exact' numerical solution where possible and against analytical results for simple cases, and found to be robust and convergent. The method is then applied to derive scattering results for otherwise intractable cases. The approach is related to left-right splitting and related methods which have been recently developed for electromagnetic scattering by several researchers.