David B. King
Stanley A. Chin-Bing
Naval Res. Lab., Stennis Space Center, MS 39529
Michael D. Collins
Naval Res. Lab., Washington, DC 20375
The split-step Fourier algorithm [R. H. Hardin and F. D. Tappert, SIAM Rev. 15, 423 (1973); S. M. Flatte and F. D. Tappert, J. Acoust. Soc. Am. 58, 1151--1159 (1975)] has been an important technique for solving range-dependent ocean acoustics problems for more than two decades. Since this algorithm is restricted to leading-order asymptotics, parabolic equation solutions based on finite-difference algorithms have been developed for handling effects that require higher-order asymptotics, such as wide propagation angles, extensive bottom interaction, and elastic and poroelastic waves. The split-step Fourier algorithm has remained in widespread use despite the improved accuracy and capability of finite-difference solutions. The split-step Pade algorithm [M. D. Collins, J. Acoust. Soc. Am. 93, 1736--1742 (1993); M. D. Collins, J. Acoust. Soc. Am. 96, 382--385 (1994)], which includes higher-order asymptotics, is orders of magnitude faster than standard finite-difference solutions. Results will be presented for representative test problems to illustrate that the split-step Pade algorithm is also more efficient than the split-step Fourier solution for the coastal acoustics problems that are currently of interest.