A Dirichlet-Neumann Alternating Algorithm For Biharmonic Equation Half-unbounded Domain

In this thesis, by the theory of the natural boundary reduction and the key idea of domain decomposition method (DDM), a Dirichlet-Neumann alternating algorithm based on the natural boundary reduction is devised for the solution of biharmonic equation in a half-infinite domain. The main work of this thesis is as follows.Firstly, an artificial boundary ?1 is introduced, the original problem is re-duced two subproblems in a bounded domain and a unbounded domain, respec-tively. Secondly, by means of results obtained by the natural boundary reduc-tion, a D-N alternating algorithm based on the natural boundary reduction is suggested, the discretization of the D-N alternating algorithm is given by fi-nite element methods, and the convergence of the D-N alternating algorithm is proved. Finally, Some numerical examples are presented to show the feasibility and effectiveness of the method given in this thesis.