大型稀疏复线性方程组双共轭梯度法

有限元复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.在一般双共轭梯度法的基础上,本文利用广义变分原理对内积进行了重新定义,使双共轭梯度法求解复线性方程组更为有效.数值算例表明这种双共轭梯度法结合全稀疏存贮方案的求解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.

Bi-conjugate Gradient Method of Large-scale Sparse and Complex Linear Equations

Coefficient matrix of complex linear equations from FEM is sparse and symmetrical,so fully sparse strategy only stores nonzero 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 biconjugate gradient method,we redefine inner products using general variation principle,which can make complex linear equations solving have high-performance.Numerical examples show that the bi-conjugate gradient method combining fully sparse strategy is available,effective and predominant for time and storage.Therefore it is applicable to solve systems of linear equations from FEM.