| The Seepage problem is an important field in fluid mechanics, and is one of important subjects in rock civil engineering and hydroelectric engineering. These problems can be deduced to Laplace or Possion equation. The boundary element method has been widely used in Seepage problem, which was developed rapidly in late70s.When using the boundary element method to solve the boundary-value problems of Laplace equation, different boundary reduction approaches will lead to different boundary integral equation,and there exist several methods to solve the boundary integral equation. In this paper the direct boundary integral equation deduced by Green's formula and the fundamental solution is considered to solve Seepage problem. After the boundary is discrete, the numerical solution is gained by solving linear system of equations and by calculating the discrete integration expression of solution. This paper presents the analytical formula and the Gaussian quadrature for the integration formula.With the rapid developing of science and technology, how to solve so many large scale science and engineering problems becomes a difficult subject. Domain decomposition method, which decomposes the domain that a problem is given into sub-domains, has the advantage of reducing the large problem into smaller ones and reducing the complex problem into simpler ones and decomposing string pattern computing to parallel ones, and allows parallel computing. Domain decomposition method, as the main one to solve these problems, receives much recognition. In this paper we apply a non-overlapping domain decomposition method combining direct boundary element formulation to solve Seepage problems, and calculating orthotropic case in several domains.Constant element is used in the computing program of this paper, which is written by Fortran90. The numerical experiments tested are given, which demonstrated that the method in this paper is reliable and effective.
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