Research Of Iterative Methods For Linear Systems Arising From Hydrodynamic Analysis Of Floating Bodies With Boundary Element Method

With the development of marine transportation, the dimensions of offshore structures become larger and the structures are more and more complicated. And also there have been a lot of catamaran and multi-body problem. Due to the increasing number of panels, it will cost us more and more CPU time to solve the linear systems arising from the diffraction-radiation analysis of floating bodies with boundary element methods. As for large offshore structures, it will consume us several days to solve the linear systems using traditional direct method, which is not acceptable for engineering application. In order to improve the effectiveness, we will analysis the features of linear systems and select the suitable solver.The structures of coefficient matrices in linear systems play a very important role in choosing the appropriate method. This paper will do some researches on the behavior of the matrices arising from the boundary method of different models from the viewpoint of condition number. Through the researches on different iterative methods, with the characteristic of coefficient matrices, we finally make sure the most appropriate iterative method in theory. After writing the iterative method program, the solutions of linear systems using iterative method are certified by the results using direct method. In order to improve the effectiveness of the iterative program, we use the incomplete LU factorization as the preconditioner to reduce the number of iteration. For different offshore structures, the preconditioner will be different. The iterative method is not always faster than direct method for all the linear systems. Based on the floating point operations calculation, we finally get an optimization algorithm between these two methods.Firstly, this thesis will introduce the potential theories of floating bodies in wave and the linear system arising from the diffraction and radiation computation. And we also give out the physical significance of the elements in the linear system. Using condition number program, this paper analysis the characteristics of coefficient matrices of linear systems arising from the 3D frequency-domain analysis of floating bodies without speed. It has shown that the condition number of coefficient matrices will become larger with the increasing of frequencies and panels. Through distributing the panels on the interior free surface, the effectiveness of irregular frequencies can be reduced. But the condition number of matrices in other frequencies will increase. The solver based on the GMRES approach is faster than the direct method for the given linear systems. As for the high frequencies, the number of iteration can be reduced by the incomplete LU factorization preconditioner. And the preconditioner should be different for structures which has different interior free surface. Comparing the flops of direct method with that of GMRES, we can get a judgment formula. As for different linear systems, we can select the faster solver between the two methods through the formula.