The Fast Multipole Method And Its Application To The Multiple Floating Bodies And Hydroelasticity

In this thesis, the boundary element method and fast multipole technology are used to study the diffraction and radiation of rigid multiple floating bodies and elastic floating body in frequency domain.The interaction between waves and structure is a coupling problem. For a rigid multiple floating bodies system, the hydrodynamic interaction between the body must be calculated. For a elastic body, the amplitude of each node on the body is different. The two kinds of problems mentioned above make the coupling problems turn to more difficult. In this paper the boundary element method is used. Basing on the boundary integral equation which satisfied on the body surface, the radiation and diffraction velocity potentions can be obtained. For the rigid multiple floating bodies, the added mass and damping coefficient on each body are made of two parts:one part is due to the movement by itself, the other part is due to the other bodies. For elastic body, the heave amplitude of each point can be written as the summation of each mode component. At last the amplitude of the body response can be identified by the rigid motion equation and elastic motion equation respectively.The most important advantage of boundary element method is that the three dimensional problems are changed to two dimensional problems. The unknowns can be placed only on the surface of the computational domain. But the coefficient matrix is full. If the number of unknows is too large, it will need very large computer resources for storage and computation. In this paper, a fast multipole method is used to solve this problem. When the field point is far from the source point, the Green function in series form which satisfied the free surface boundary condition can be expanded in the cylinderical coordinate system by Graf's addition theorem, and calculated approximatly. The coefficient matrix needn't to be calculate in this method. And it combined with iterative method can reduce the memory storge and calculation times evidently.Free-term coefficient and CPV integrals are must be concerned when higher-order boundary element method is used. If a indirect method is used to calculate free-term coefficient and CPV integrals, another Green function will be added to the boundary integral equation. This will debase the efficiency of fast multipole method. In this paper a direct method is used to calculated free-term coefficient and CPV integrals. By the use in constant panel method and higher order boundary element method, the accuracy and efficitive of this method are be verified.Firstly, the interaction between the regular wave and two floating bodies are calculated. Then the programs of the fast multipole method applied to constant panel method and higher order boundary element method are developed. Subsequently, this program is used to solve the interaction between waves and multiple floating bodies. At last for the elastic body, this program is used to compare the results and the rate of convergence of several modes. The results in this paper have a good agreement with analytical results and published results.