Natural Boundary Element Methods For Outer Problems Of The Three-Dimensional Wave Equation

In this thesis,by the theory of natural boundary reduction of elliptic boundary problem,the natural boundary element method for a three-dimensional exterior wave problem is investigated.Firstly,the governing equation is discretized in time by the Taylor expansion method,leading to a time-stepping scheme,where a three-dimensional exterior elliptic problem has to be solved at each time step.Secondly,the series expansion of the solution function is carried out by using the spherical harmonic functions,the results of natural boundary reduction are obtained and the properties of natural integral operators are studied.Thirdly,the natural integral equation are performed by finite element method,the numerical solution of the natural integral equation is obtained,and the value of the function at any point is obtained by Poisson integral formula.Finally,some theoretical analysis are given,some numerical experiments are presented to illustrate the feasibility and effectiveness of the method.