  The left-right operator splitting method is studied for the efficient
calculation of acoustic fields scattered by arbitrary rough surfaces. Here the
governing boundary integral is written as a sum of left- and right-going
components, and the solution expressed as an iterative series, expanding about
the predominant direction of propagation. Calculation of each term is
computationally inexpensive both in time and memory, and the field is often
accurately captured using one or two terms. The convergence and accuracy are
examined by comparison with exact solution for smaller problems, and a series
of much larger problems are tackled. The method is also immediately applicable
to other scatterers such as waveguides, of which examples are given.
