The Coupling Of NBEM And FEM For Klein-Gordon Equations

In this thesis, based on the theory of the natural boundary reduction, we study the coupling of natural boundary element method (NBEM) and finite ele-ment method (FEM) for Klein-Gordon equations.By means of Newmark method, the governing equation is first discretized in time, leading to a time-stepping scheme, where the original problem has to be solved at each time step. By the principle of the natural boundary reduction, we derive the Poisson integral formulae and the natural integral equation of the Helmholtz problem related to time step. An artificial boundary is introduced, the coupled variational problem is obtained, the well-posedness of the variational problem obtained is analyzed, and finite element discretization is employed to solved this variational problem. Finally, some numerical examples are presented to illustrate the feasibility and effectiveness of the algorithm.