Summary
Numerical methods are outlined for computing the velocity potential, and its derivatives, for linearized three-dimensional wave motions due to a unit source with harmonic time dependence beneath a free surface. Two distinct cases are considered where the fluid depth is either infinite, or of constant finite depth. Efficient algorithms are developed in both cases, to replace the numerical evaluation of the relevant integrals by multi-dimensional approximations in economized polynomials. This technique is substantially faster than conventional direct methods based on numerical integration.
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Newman, J.N. Algorithms for the free-surface Green function. J Eng Math 19, 57–67 (1985). https://doi.org/10.1007/BF00055041
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DOI: https://doi.org/10.1007/BF00055041