预修正快速傅里叶变换高阶边界元方法在波浪对物体作用问题中的应用

Applications of precorrected-FFT method to higher-order boundary element method for wave-body problem

边界元方法被广泛应用于波浪对海上建筑物作用领域,但由于传统边界元方法的存储量和计算量均为未知量的平方量级,很难满足大范围多未知量问题的计算需要。本文基于高阶边界元方法,应用预修正快速傅里叶变换方法,使计算量与存储量分别降低至O(NlogN)和O(N)量级,并得到一个连续的压强分布以适应结构设计的要求,同时可以通过使用满足无限水深自由水面边界条件的格林函数来克服多极子展开方法无法应用于深水问题的缺点。计算结果表明,该方法特别适用于多未知量问题的计算,在提高计算效率的同时也保证了计算精度。

Boundary element method（BEM） has been widely applied in the field of wave interaction with offshore structures,but it is still difficult to resolve the large-scale problems because of computer storage and computing cost by O（N2） order for traditional BEM.the precorrected fast Fourier transform method（pFFT） combined with higher-order boundary element method is developed to reduce the computing cost and the required memory by O（N） order in frequency-domain analyses.The continuous pressure distribution can be obtained for the structural design.Using a free-surface Green function for infinite depth,the disadvantage of fast multipole boundary element method,i.e.,unable to solve infinite deep water wave problems,can be overcome.Numerical examinations show that the pFFT method has more evident advantages in saving memory and computing time,especially for large-scale problems,over the traditional BEM.