| In real world, we find that some problems of mechanics, acoustics and other areas can be attributed to the solution of exterior problems of differential equations, but because the region outside is unbounded, so boundless of these problems brings some difficulties of solution to these problems, we have gradually discovered the existence of methods to solve a series problems of bounded region can not be directly brought up, obviously, there are some limitations between these, therefore, in this case, the others methods have emerged, these methods for solving partial differential equations without boundary area shows superiority, among these, domain decomposition method is prominent, solving unbounded elliptic boundary value problem, we can not get the result we want relying on domain decomposition method, because even after we joined the artificial boundary, there are difficulties that we cannot avoid the existence of an unbounded region, so in the facing and dealing with this problem,people summarized that, we usually coupled finite element and boundary element method the artificial boundaries and the corresponding approximate boundary conditions are given, then we use the finite element method to solve bounded domain, then we combined with effective methods to solve some problems in the unbounded domain, to some extent, all of these could solve the problem we face.In this paper we mainly take anisotropic elliptic equations with constant coefficients as an example, to study the non-overlapping domain decomposition method of the anisotropy of the problem based on elliptic artificial boundary, and further discussion of iterative convergence of discrete problems and its relaxation factor of selection, and then get the conclusion we want. The paper is to promote artificial boundary of the ellipse from the circle, we derived a series of iterative error compression factor depending on the relaxation factor, finally the relaxation factor has been the best, and gives the numerical examples.
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