Efficient approximation of free-surface Green function and OpenMP parallelization in frequency-domain wave–body interactions

The evaluation of Green function without translation has always been the most time-consuming part of the hydrodynamic analysis based on potential flow theory. This research investigates the new implementations of efficient approximations of Green function and the code parallelization with OpenMP library. First, algorithms of infinite-depth case are developed with economized Chebyshev polynomials based on modified region and subdomain partitions. Second, an improved Gauss–Laguerre method for the Cauchy integral is presented to evaluate the finite-depth case with the convergence acceleration by the reduction of fraction and singularity elimination by the infinite-depth case together with the exponential integral. For the analyzed container vessel, on the premise of good numerical accuracy, we conclude that the present method has nearly obtain the same efficiency as Chen (Hydrodynamics in offshore and naval applications—Part I, Bureau Veritas, Paris, 2004) for the infinite-depth case and almost 30% higher efficiency for the finite-depth case. Moreover, we also point out that the numerical efficiency is significantly enhanced again due to the OpenMP parallelization of the serial code.