The application of boundary element method (BEM) is difficult for some large practical problems. In this paper a fast multipole expansion method (FMM) in the cylindrical coordinate system is used in BEM for wave diffraction/radiation problems of structures. This method can reduce the memory requirements and the operation count to O(N). When this method is used in HOBEM, a direct method is implemented for computing the free-term coefficient and the Cauchy principal value (CPV) integral. In order to verify this method, the added mass, the radiation damping and the excited force loads on floating boxes and cylinders are calculated and compared with available analytical results. The comparison shows that the present calculations have a good agreement with the analytical results. To take advantage of the method, we carried out a series of convergent experiments on the CPM and the HOBEM. The conclusion can be drawn that it is hard to obtain convergent results by the CPM, especial for the added mass and the radiation damping; but the convergence of the HOBEM is very fast.


BEM is usually more effective than other methods such as FEM and FDM when the fluid domain is infinite. If a proper Green function is applied, it only needs to arrange unknowns on the body surface. This will reduce the computer memory requirement and computation cost greatly. However application of this method has some difficult to very large problems. This is because that both the operation count and the memory requirements for the matrix equation setup are of the order O(N2), where N is the number of unknowns. When size of a body is biggish, very large computer resources are required for storage and computation.

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