Exact and approximating boundary conditions for the parabolic problems on unbounded domains
Exact and approximating boundary conditions for the parabolic problems on unbounded domains
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DOI：
10.1016/s0898-1221(02)00180-3
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发表时间：
2002-09
影响因子：
2.9
通讯作者：
Houde Han;Zhongyi Huang
中科院分区：
文献类型：
--
作者：
Houde Han;Zhongyi Huang
本文研究了无界区域上二维热传导方程问题的数值解。对于给定的问题，我们引入一个人工边界Γ来限定计算区域。在人工边界上，我们提出了一个精确的边界条件，将给定问题化为有限计算区域上的热方程初边值问题，并与原问题等价。并给出了一系列近似的人工边界条件。然后在有限计算域上用有限差分法和有限元法求解约化问题。最后通过数值算例验证了本文方法的可行性和有效性。
In this paper, the numerical solutions of the problems of heat equation in two dimensions on unbounded domains are considered. For a given problem, we introduce an artificial boundary Γ to finite the computational domain. On the artificial boundary Γ, we propose an exact boundary condition to reduce the given problem to an initial-boundary problem of heat equation on the finite computational domain, which is equivalent to the original problem. Furthermore, a series of approximating artificial boundary conditions is given. Then the finite difference method and finite element method are used to solve the reduced problem on the finite computational domain. Finally, the numerical examples show the feasibility and effectiveness of the method given in this paper.