Abstract
In this study, the three-dimensional Cartesian acoustic parabolic equation is fully solved in the stair-step representation of an ocean environment based on the split-step Padé algorithm. The sum representation of the Padé approximation of a full exponential operator in the split-step marching solution is used for parallel computing. A stabilized self-starter solution is derived in the same way. This solver is benchmarked against reference solutions for a rectangular duct propagation, an ideal wedge problem, and an axisymmetric ocean. Additionally, a solution for the Gaussian canyon problem is provided and compared with that obtained from the approximate parabolic equation solver, considering a leading-order cross-term.
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