基于预修正快速傅里叶变换高阶边界元方法的多体水动力分析

高阶边界元方法在求解波浪对海上建筑物作用问题中具有诸多优势，但由于它所形成的矩阵是一个满阵，计算量和存储量均为未知量的平方量级，很难满足如多体水动力分析等大尺度多未知量问题的计算需要。本文采用预修正快速傅里叶变换高阶边界元方法（pFFT-HOBEM），将计算量和存储量均降低到未知量的线性量级。通过对不同未知量时该方法与传统边界元法的计算量与存储量的对比，以及该方法自身各步骤计算时间的对比，研究了不同pFFT网格方案对计算量和存储量的影响，并提出了基于计算时间最小化原则的pFFT网格优化方法。采用本文方法研究了四柱结构在不同频率波浪作用下的作用力及波面分布，并对近场干涉发生时的物理现象进行了分析和讨论。

A precorrected-FFT higher-order boundary element method for multi-bodies hydrodynamic analyses

Higher-order boundary element method (HOBEM) has been widely applied in the field of wave interaction with offshore structures,but it is still difficult to resolve the large scale problems such as multi-bodies hydrodynamics due to computer storage and computing cost being increased by O(N²) order.In this paper,a pre-corrected Fast Fourier Transform higher-order boundary element method (pFFT-HOBEM) is developed to reduce the computational time and computer memory by O(N) order.According to the comparison between pFFT-HOBEM and traditional HOBEM with different number of unknowns and the analysis about the computing cost at different parts of pFFT-HOBEM,the efficiency of present method to different mesh variable is studied.The optimal variable of pFFT mesh was recommended to minimize the time cost.Based on the present method,the hydrodynamic behavior of a four-cylinder structure and the near trapping phenomena is investigated.