Generalization of the split-step Padé solution

The split-step Padé 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 Padé solution is also applicable to elastic media.