求解非均匀介质问题的双共轭梯度方法

Solving Inhomogeneous Media Problems by Bi-Conjugate Gradient Method

分析非均匀介质条件下的电成像问题 ,在说明电成像仪的测量环境和测量原理之后 ,对这种复杂条件的电磁场问题 ,采用三维有限元方法进行分析。为了保证计算精度 ,在分析过程中 ,需要划分较多的空间网格 ,从而生成大型的有限元矩阵方程。对此大型矩阵方程 ,采用计算效率较高的双共轭梯度方法求解 ,给出了双共轭梯度方法的算法和利用该算法求解有限元矩阵方程时的收敛速度曲线 ,并对水平分层和倾斜分层两种典型情况下的非均匀介质成像问题进行分析 ,给出了模拟测量成像结果。

In this paper, electric imaging under inhomogeneous media conditions is analyzed. After the measurement circumstances and the measurement principle of electric imager are described, the three-dimensional finite element method is used for the analysis of this type of electromagnetic problems under complex conditions. For the purpose of high computing precision, the model is partitioned into a large amount of spatial elements during the analysis, then huge finite element matrix equations are generated. A high-efficiency solution based on bi-conjugate method is applied for huge equations. The algorithm of bi-conjugate method is given and the convergence rate is illustrated. Electric imaging measurement in horizontal and sloped beds is studied, and simulated images are also given.\;