大型稀疏线性方程组新的ICCG方法

A NEW ICCG METHOD OF 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,即节省存贮空间,又便于动态更改．在完全Cholesky分解的基础上,构造出了新的预处理方法,应用适当的对角元修正策略,得到了一种新的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．

Coefficient matrix of linear equations fully sparse strategy stores only nonzero from FEM is sparse and symmetrical, so elements of symmetrical part with chain pattern management. Not only storage scale is small, but also storage structure is convenient for dynamic change. Based on the complete Cholesky decomposition, this paper creates a new incomplete Cholesky conjugate gradient （ICCG） method with diagonal elements modification. The new method can decompose exactly and solve linear equations effectively. Numerical examples show that the method is available, effective and predominant for time and storage. Therefore it is applicable to solve systems of linear equations from FEM.