| Popis: |
The operator expansion method for quickly solving the Helmholtz boundary value equation was outlined by Milder [J. Acoust. Soc. Am. 89, 529–541 (1991)]. This method was verified by Kaczkowski and Thorsos for impenetrable surface scattering where Kirchhoff and small perturbation theory hold [J. Acoust. Soc. Am. 90, 2258 (A) (1991)]. In this presentation the third‐order and higher terms of the symmetric operator expansion will be derived in order to place error bounds on the integral approximation for second‐order and higher terms of the expansion. These error bounds can then be used to determine the regions of validity for the next lower‐order expansion approximations. Some examples and comparisons to other scattering methods will be shown. |
