论文部分内容阅读
点源三维地电场的求解是一大型数值计算问题.本文用有限差分方法求解,最后形成一个线性方程组Ax=b,这里A是大型稀疏的带状对称矩阵.解大型稀疏方程组的完全Cholesky分解直接算法,一般要求巨大的机器内存来存储系数矩阵A,而且计算速度极慢.因此引入不完全Cholesky共轭梯度(ICCG)算法及按行索引的稀疏存储模式,充分利用A的稀疏性,使得计算速度大大提高,而内存要求则大大减少,因此ICCG算法是地电三维正演的强有力工具.
The solution of three-dimensional electric field of point source is a large-scale numerical calculation problem. In this paper, we use the finite difference method to solve, and finally form a linear system of equations Ax = b, where A is a large sparse symmetrical strip matrix. The complete Cholesky decomposition direct algorithm for solving large sparse equations generally requires a huge amount of machine memory to store the coefficient matrix A and the computational speed is very slow. Therefore, the introduction of Incomplete Cholesky Conjugate Gradient (ICCG) algorithm and row-indexed sparse storage mode make full use of the sparsity of A, resulting in greatly increased computational speed and significantly reduced memory requirements. Therefore, ICCG algorithm is a three-dimensional forward modeling Powerful tool.