David Yevick
Dept. of Electrical Eng., Queen's Univ., Kingston, ON K7L 3N6, Canada
The relative accuracy of various high-angle propagation methods were examined for the case of a rapidly expanding point source. It was established that the removal of evanescent modes in wide-angle calculations through, e.g., hybrid Fourier/Lanczos or Fourier/Pade algorithms [J. Acoust. Soc. Am. 96, 396 (1994)], greatly improves the numerical predictions of such techniques. Alternatively, procedures in which the imaginary part of the Thomson--Chapman propagation operator is applied after each propagation step may also be employed to increase the rate of convergence of standard unitary methods. Further, it was found that for moderate step lengths and highly divergent fields the errors implicit in rational approximations to the square-root operator are comparable to those associated with analogous approximations to the full propagator as well as with Chebyszev expansions of the exponent of the propagation operator with degree about twice that of the equivalent Pade method. Finally, a heuristic but useful relationship between the rate of convergence of a given Lanczos technique and the Taylor series expansion of the underlying propagation operator is outlined.