A Fast Multipole Method (FMM) is developed as a numerical approach to the reduction of the computational cost and requirement memory capacity for a large in solving large-scale problems. In this paper it is applied to the boundary integral equation method (BIEM) for current diffraction from arbitrary 3D bodies. The boundary integral equation is discretized by higher order elements, the FMM is applied to avoid the matrix/ vector product, and the resulting algebraic equation is solved by the Generalized Conjugate Residual method (GCR). Numerical examination shows that the FMM is more efficient than the direct evaluation method in computational cost and storage of computers.

A fully nonlinear irregular wave tank has been developed using a three-dimensional higher-order boundary element method (HOBEM)in the time domain. The Laplace equation is solved at each time step by an integral equation method. Based on image theory, a new Green function is applied in the whole fluid domain so that only the incident surface and free surface are discretized for the integral equation. The fully nonlinear free surface boundary conditions are integrated with time to update the wave profile and boundary values on it by a semi-mixed Eulerian–Lagrangian time marching scheme. The incident waves are generated by feeding analytic forms on the input boundary and a ramp function is introduced at the start of simulation to avoid the initial transient disturbance. The outgoing waves are sufficiently dissipated by using a spatially varying artificial damping on the free surface before they reach the downstream boundary. Numerous numerical simulations of linear and nonlinear waves are performed and the simulated results are compared with the theoretical input waves.

利用时域高阶边界元方法建立了模拟极限波浪运动的完全非线性数值模型,其中自由水面满足完全非线性自由水面条件。采用半混合欧拉2拉格朗日方法追踪流体瞬时水面,运用四阶Runge2Kut ta 方法更新下一时间步的波面和速度势,同时应用镜像格林函数消除水槽两个侧面和 底面上的积分。研究中利用波浪聚焦的方法产生极限波浪,并且在水槽中开展了物理模型实验,将测点试验数据与数值结果进行了对比,两者吻合得很好。对极限波浪运动的非线性和流域内速度分布进行了研究。

应用镜像原理，将正交直墙前单个圆柱在静水中的振荡问题，转化为4个对称布置圆柱在静水中的振荡问题，由此应用速度势的特征函数展开法，建立了正交直墙前直立圆柱振荡问题的解析解。通过数值计算研究了圆柱与正交直墙间距离大小、水深等因素对附加质量和辐射阻尼的影响。计算结果表明，正交直墙前圆柱上的附加质量和辐射阻尼将明显增大，且随着波数的变化而发生振荡;不同水深中圆柱的附加质量和辐射阻尼在低频区与水深成线性关系。

在众多水波问题，尤其是非线性水波问题求解中，巨大计算量和存储量一直是人们试图克服和解决的重点与难点。本文通过对简单Green函数基本解1/r做多极子展开，并应用到去奇异边界元法中求解三维水波问题。通过无限区域中水流对圆球绕射算例的数值计算，验证了多极子去奇异边界元法能给出高精度的满意结果，与传统边界元方法相比避免了边界积分中奇异性的单独处理并将计算量和存储量均降到了O(NIg N)和O(N)数量级，同时对完全非线性水波问题的时域模拟也得出了令人满意的结果，验证了该方法在处理大计算量问题中所具有的优势。