### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 5aUW8. Convergence properties of wide-angle techniques.

**David Yevick
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*Dept. of Electrical Eng., Queen's Univ., Kingston, ON K7L 3N6, Canada
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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.