| In this thesis,based on the theory of the natural boundary reduction,the natural boundary element method for three-dimensional Klein-Gordon exterior problems are investigated.Firstly,we discrete the governing equation in time by the Taylor expansion,and solve a exterior three-dimensional modified Helmholtz equation at each time step,and the natural integral equation and the Poisson integral formula are given by the principle of natural boundary reduction.Secondly,some properties of the natural integral operator are studied,the numerical implementation of the natural integral equation is discussed in details,and error estimates of the solution are given.Finally,some numerical experiments are presented to demonstrate the feasibility and effectiveness of this method. |
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