A novel numerical method combining Eigenfunction matching method (EMM) and 3D Rankine source method is developed to investigate wave-body interaction over a sloping bottom. The extended EMM is proposed to create an incident wave model over the sloping bottom, thereby obtaining the Froude-Krylov force and Neumann data on wet surfaces of the floating body for the diffraction problem. A 3D Rankine source method concerning the sloping bottom is developed, in which the free surface and seabed are both divided into the inner domain and outer domain. Source panels are placed in an exponential manner in the latter domain, by which the far field radiation condition is well satisfied. To verify the proposed method, comparisons with other mathematical models involving added mass and damping coefficients, wave exciting forces and motion RAOs by a floating hemisphere and a LNG carrier are carried out.

提出了一种结合特征函数匹配法（EMM）和3D兰金源方法的新型数值方法，以研究倾斜底部的波体相互作用。提出了扩展的EMM以在倾斜底部上创建入射波模型，从而获得浮体湿表面上的Froude-Krylov力和Neumann数据，以解决衍射问题。提出了一种与倾斜底部有关的3D Rankine震源方法，该方法将自由面和海床都分为内部区域和外部区域。源面板以指数方式放置在后一个域中，通过该域可以很好地满足远场辐射条件。为了验证所提出的方法，将其与其他数学模型进行比较，其中包括增加的质量和阻尼系数，