In this paper, we apply the natural boundary element method to solve initialboundary value problem of parabolic equation. By Fourier expansion, we obtainthe natural integral equation of the problem and its Poisson integral formula overexterior circular domain. Meanwhile, the numerical implementation of the natural integral equation is given. At last some numerical examples are presented toillustrate feasibility and efficiency of our method.
In this paper, we investigate an overlapping domain decomposition algorithm for elliptic boundary value problems over an infinite domain with concave angles.The algorithm is constructed, and its convergence is discussed. The finite element method and natural boundary element are alternatively applied to solve a bounded subdomain and a typical unbounded subdomain. It has overcome the difficulty met in standard domain decomposition method for problems with unbounded domains.The convergence rate is analysed in details for a typical domain. Finally, some numerical example are presented to show effectiveness of our method.
