大型稀疏线性方程组的改进ICCG方法

An Improved ICCG Method for Large Scale Sparse Linear Equations

有限元线性方程组的系数矩阵一般具有稀疏性和对称性的特点,全稀疏存贮方法就是利用这些特点,只存贮对称部分的非零元素,采用链表式管理,既节省存贮空间,又便于动态更改.在带双门槛值ICCG方法的基础上,加上适当的对角元修正策略,得到一种新的改进的ICCG方法,能够确保方程组高效准确的分解和求解.数值算例证明,该算法在时间和存贮上都较为占优,可靠高效,能够应用于有限元线性方程组的求解.

Based on incomplete Cholesky decomposition with two thresholds,we propose an improved incomplete Cholesky conjugate gradient（ICCG） method with diagonal elements modification.It ensures accurate and efficient decomposition and solution of large scale sparse linear equations. The method shows advantage in computing time and storage requirment.It is applicable to solve the systems of linear equations from FEM finite element method.