A Numerical Algorithm For A Class Of Anisotropic Quasilinear Problems

Many scientific calculation and engineering problems are attributed to the boundary value problem of partial differential equations on unbounded domain.The traditional methods of solving boundary value problems,such as finite element method and finite difference method,are very effective for the problem of bounded domain,but it is difficult to get ideal accuracy in the problem of unbounded domain.By virtue of the principle of the natural boundary reduction,and introducing the typical artificial boundary,the original unbounded domain is decomposed into a small bounded domain and a typical boundary of unbounded domain: the finite element method is used for the standard bounded domain,the principle of the natural boundary reduction is adopted in an unbounded domain.For the unbounded problem,the coupling algorithm based on natural boundary reduction and the domain decomposition algorithm are very effective.This thesis is divided into two parts:In the first part,the non overlapping domain decomposition method(Dirichlet-Neumann alternating algorithm)is given to solve the anisotropic quasilinear problem.Based on the theory of natural boundary reduction and the idea of domain decomposition,the algrithm is offered,the natural boundary integral equation of the circular is otained,and the convergence of the algorithm is analyzed.Finally,numerical examples are given.In the second part,a class of anisotropic quasilinear problem with elliptic artificial boundary is studied,based on the Kirichhoff transformation,and the principle of the natural boundary reduction,the natural integral equation,and the coupling problem of the original problem are obtained.Moreover,the convergence of the approximate solution is given and numerical examples are posed to illustrate the feasibility and effectiveness of this method.