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The infinite depth free surface Green function (GF) and its high order derivatives for diffraction and radiation of water waves are considered. Especially second order derivatives are essential requirements in high-order panel method. In this paper, concerning the classical representation, composed of a semi-infinite integral involving a Bessel function and a Cauchy singularity, not only the GF and its first order derivatives but also second order derivatives are derived from four kinds of analytical series expansion and refined division of whole calculation domain. The approximations of special functions, particularly the hypergeometric function and the algorithmic applicability with different subdomains are implemented. As a result, the computation accuracy can reach 10 in whole domain compared with conventional methods based on direct numerical integration. Furthermore, numerical efficiency is almost equivalent to that with the classical method.

HIGHLY PRECISE APPROXIMATION OF FREE SURFACE GREEN FUNCTION AND ITS HIGH ORDER DERIVATIVES BASED ON REFINED SUBDOMAINS