A precorrected-FFT higher-order boundary element method for wave–body problems

The boundary element method (BEM) has been widely applied in the field of wave interaction with offshore structures, but it is still not easy to use in resolving large-scale problems because of computing costs and computer storage being increased by O(N2) for the traditional BEM. In this paper a precorrected Fast Fourier Transform (pFFT) higher-order boundary element method (HOBEM) is proposed for reducing the computational time and computer memory by O(N). By using a free-surface Green function for infinite water-depth, the disadvantage of the Fast Multipole Boundary Element Method (FMBEM)—i.e. unable to solve infinite deep-water wave problems—can be overcome. Numerical results from the problems of wave interaction with single- and multi-bodies show that the present method evidently has more advantages in saving memory and computing time, especially for large-scale problems, than the traditional HOBEM. In addition, the optimal variable of pFFT mesh is recommended to minimize time cost.

▶ A precorrected Fast Fourier Transform (pFFT) higher-order boundary element method (HOBEM) is proposed for reducing the computational time and computer memory by O(N). ▶ The disadvantage of the Fast Multipole Boundary Element Method (FMBEM)—i.e. unable to solve infinite deep-water wave problems—can be overcome. ▶ Optimal variable of pFFT mesh is recommended to minimize time cost.