Natural Boundary Element Method For 3D Non--homogeneous Exterior Parabolic Problems

In this thesis,based on the theory of the natural boundary reduction,the natural boundary element method for three–dimensional non–homogeneous exterior parabolic problems are studied.Firstly,the non–homogeneous parabolic equation is discredized in time by the Taylor expansion method,leading to a time–stepping scheme,where a exterior three–dimensional modified Helmholtz equation has to be solved at each time step.Secondly,the natural integral equation and Poisson integral equation are obtained by the principle of the natural boundary reduction(NBR),and some properties of natural integral operators are discussed.Thirdly,some numerical methods for solving the natural integral equation are proposed.Finally,some numerical experiments are presented to illustrate the feasibility and effectiveness of the method.