In this paper, an exact analytical method is developed for the problem of wave radiation by a uniform cylinder in front of a vertical wall. Based on the image principle, the hydrodynamic problem of a cylinder in front of a vertical wall is transformed into the equivalent problem of double cylinders in unbounded fluid domain. Consequently, an analytical method of eigenfunction expansion is adopted to calculate the radiation of the cylinder due to the motion in surge, sway, roll and pitch, respectively. Moreover, numerical analysis has been carried out in detail in order to discuss the influences of the distance between the cylinder and the vertical wall and water depth on the added mass and radiation damping of the cylinder. It is shown that added mass and damping of the cylinder in front of a vertical wall are evidently different from those in case of the cylinder in unbounded fluid domain from the numerical results. It is also found that the added mass and radiation damping oscillate with wave number, and the oscillating frequency increases with the increasing of the distance between the cylinder and the wall.

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.

In this paper, the principle of mirror image is used to transform the problem of wave diffraction from a circular cylinder in front of orthogonal vertical walls into the problem of diffraction of four symmetric incident waves from four symmetrically arranged circular cylinders, and then the eigenfunction expansion of velocity potential and Grafs addition theorem are used to give the analytical solution to the wave diffraction problem. The relation of the total wave force on cylinder to the distance between the cylinder and orthogonal vertical walls and the incidence angle of wave is also studied by numerical computation.

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。

高阶边界元法以较常数元方法计算精度高存储低而在工程计算中得到了广泛的应用，但由于其平方存储和计算量的本质，无法应用于大型工程问题中。本文将快速多极子方法(FMM)应用于高阶边界元中从而使其计算量和存储量分别降为O(N log N)和O(N)。通过无限区域中水流绕射算例的数值计算，对FMM高阶边界元法与传统高阶边界元法的运算速度和内存消耗进行了分析对比，结果表明对于大型计算问题FMM高阶边界元算法更加有效。