An efficient computational method for nonlinear three-dimensional wave-wave and wave-body interactions

We develop and apply a highly efficient computational method for the study of three-dimensional nonlinear wave dynamics and interactions with floating bodies and bottom topography. Similarly to the classical boundary element methods, this method is based on the boundary integral equation formulation in the context of potential flow assumptions. In solving the integral equation, however, it employs a highly efficient fast Fourier transform technique for the calculation of far-field influences of boundary source/dipole distributions without an explicit realization of the influence coefficient matrix. As a result, the computational cost associated with the boundary-value solution at each time in the simulation of nonlinear wave-wave and wave-body interactions is reduced to O(NlnN) in comparison to the requisite O(N2) effort of the classical methods, where N is the total number of boundary unknowns. The focus of this paper is on the development of the method and investigation of the features and dependence of its efficiency and accuracy on physical and computational parameters.