Research On FMM-BEM Algorithm Based On Improved Free Surface Green's Function

The boundary element method is one of the main methods to solve the interaction between waves and offshore structures.The traditional BEM transforms the integral domain of the integral equation to the boundary by Gauss theorem,which reduces the amount of calculation and improves the computational efficiency.However,due to the dense coefficient matrix of the boundary integral equation discretized by the traditional BEM,the computational complexity increases geometrically with the increase of the scale of the structure,which leads to the decrease of the computational efficiency of large offshore structures.In this paper,the Green's function which satisfies the free surface boundary conditions is improved to overcome the shortcomings of the traditional boundary element method in the hydrodynamic calculation of large offshore structures and multi floating offshore structures.It is applied to the fast multipole boundary element method,an improved fast multipole boundary element method is proposed.The improved method is applied to the numerical calculation of coupled hydrodynamic forces of multi floating structures,and the efficiency and accuracy of the improved method are verified by numerical examples.The main work of this paper is divided into the following three aspects:Firstly,the numerical algorithm theory of fast multipole technique combined with boundary element method,and the implementation process of the algorithm,and analyzes the advantages of fast multipole boundary element method compared with traditional boundary element method.Secondly,based on the potential flow theory,a new Green's function is proposed by improving the Green's function satisfying the free surface condition.The new Green's function is applied to the fast multipole boundary method.An improved FMM-BEM algorithm is proposed.Numerical examples show that compared with the traditional BEM,the computation time and storage capacity of the improved algorithm are improved.Finally,an improved fast multipole boundary element method is used to calculate the coupled hydrodynamic forces of multi floating offshore structures.The results provide a basis for the design of wave energy devices based on floating carriers.