Generalization of the split‐step Padé solution

The split‐step Pade solution [J. Acoust. Soc. Am. 93, 1736–1742 (1993)] is generalized to simultaneously permit arbitrarily large range steps (in range‐independent regions) and dense sampling in range. Although the range step size is limited by the rate of range dependence, range steps of many wavelengths are possible for many range‐dependent ocean acoustics problems. At each range point in a dense grid, the acoustic pressure is defined over depth in terms of a linear combination of solutions of tridiagonal systems. On a multiprocessor computer, each of the tridiagonal systems is solved on a different processor, and the acoustic field can be generated throughout a large range‐independent region in the time required by standard finite‐difference solutions to take one range step. The generalized split‐step Pade solution is also applicable to elastic media.