Boundary Element Method With Overlapping Domain Decomposition For Parabolic Equation

Boundary element method is a numerical method for solving partial differential equations. There are several formulations of boundary element method (BEM) applied to solve a parabolic differential equation.The approach,which employs time- dependent fundamental solution,allows longer time steps in time integration than other approaches,and this can cut down on time for computer implementation with high precision.Domain decomposition method,which decompose the domain that a given problem is to be solved into subdomains,has the advantages of reducing the large problem into smaller ones and reducing the complex problem into simpler ones,and allows parallel computing.In this paper, we apply an overlapping domain decomposition method combining a boundary element formulation with time-dependent fundamental solution to solve a diffusion equation. Firstly, by domain decomposition, the problem divided into two problems on subdomains, and then we solve the initial-Boundary problems by boundry element method on each subdomain. A Fortran program is compiled with parallel algorithm and some numerical examples are presented to illustrate feasibility and efficiency of the method. The numerical experiments showed that the convergence rate of the method is dependent with the overlapping degree of the subdomains.