三维非均匀介质成像问题的区域分解方法
Domain decomposition method applied to three-dimensional inhomogeneous media imaging
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摘要: 在利用数值方法分析非均匀介质问题时,容易生成大型系数矩阵,从而在求解时常常造成计算机内存不足或者计算时间过长。该文利用区域分解方法对三维非均匀介质成像问题进行分析,通过将求解区域划分为几个子区域,在子区域上以迭代求解子问题的方式解决以上问题。文中给出的迭代收敛速度曲线证明区域分解算法的收敛速度很快。该文对一些复杂的非均匀介质问题给出了模拟测量成像的结果。Abstract: When numerical methods are used to solve the inhomogeneous media problems, generally, the large coefficient matrixes are generated. This results in the shortage of memory or very long computing time. In this paper, the domain decomposition method is applied to three-dimensional inhomogeneous media imaging. By means of dividing the domain into a few subdomains and iteratively solving the small problems on these subdomains, the large problem can be efficiently solved. The iterative curve shows the fast convergence rate. The imaging results of some complex inhomogeneous media problems are given in this paper.
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