The Coupling Of NBEM And FEM For Schr(?)dinger Equations In Two-dimensional Unbounded Domains

In this thesis,we investigete the coupling of natural boundary element method(NBEM)and finite element method(FEM)for the Schr(?)dinger equation in an exterior two-dimensional domain.The Schr(?)dinger equation in an exterior two-dimensional domain is first discretized in time by the Newmark method,leading to a time-stepping scheme,where an exterior Helmholtz problem has to be solved in each time step.Secondly,we introduce a circular artificial boundary,a boundary condition on the circular artificial boundary is obtained by the natural boundary reduction,and a variational problem of the coupled problem is given.The well-posedness of the variational problem obtioned is analyzed,and finite element discretization is employed to solve this variational problem.Finally,some numerical examples are presented to illustrate the feasibility and effectiveness of the method.