Journal of Hydrodynamics

, Volume 18, Issue 1, pp 84–88 | Cite as

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

  • Hongmei Yan
  • Yuming Liu
  • Dick K. P. Yue
Session B1


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(N 2 ) 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.

Key words

boundary integral equation precorrected FFT nonlinear three-dimensional wave dynamics nonlinear wave-body interaction constant panel method quadratic boundary element method 


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  1. [1]
    Korsmeyer, F.T., Yue, D.K.P., Nabors, K. & White, J.K. 1993 Multipole-accelerated preconditioned iterative methods for three-dimensional potential problems. Presented at BEM 15 15 Worcester, Massachusetts, August.zbMATHGoogle Scholar
  2. [2]
    Mei, C.C., Stiassnie, M. & Yue, D.K.P. 2005 Theory and Applications of Ocean Surface Waves. World Scientific.Google Scholar
  3. [3]
    Nabors, K. & White, J.K. 1991 Fastcap: a multipole accelerated 3D capacitance extraction program. IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, Vol. 10.Google Scholar
  4. [4]
    Phillips, J. R. & White, J. K. 1997 A precorrected-FFT method for electrostatic analysis of complicated 3D structures. IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, Vol. 16.Google Scholar
  5. [5]
    Wu, G. 2004 Direct simulation and deterministic prediction of large-scale nonlinear ocean wavefield. Ph.D Thesis, Massachusetts Institute of Technology, USA.Google Scholar
  6. [6]
    Xue, M., Xu, H., Liu, Y. & Yue, D.K.P. 2001 Computations of fully nonlinear three-dimensional wave-wave and wave-body interactions. Part 1: Three-dimensional steep waves. J. Fluid Mech. 438.Google Scholar

Copyright information

© China Ship Scientific Research Center 2006

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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