多自由度块行压缩存储技术及大型稀疏方程组的求解

BLOCK COMPRESSED SPARSE ROW OF MULTIPLE DOF AND LARGE SPARSE LINEAR SYSTEM REAL DOMAIN SOLUTION

在地球物理电磁勘探领域有限元数值模拟中,最后都会得到一个大型稀疏的复系数线性方程组,受计算机内存空间的限制,必须根据有限元刚度矩阵的稀疏性对其进行压缩存储。由于电磁场有限元计算的自由度大都在三个以上,因而提出了适合多自由度的块按行压缩稀疏存储方案,并通过存储格式的转换,把块按行压缩方式转换成流行的,大型稀疏矩阵的行压缩存储格式,以便于求解。用求解大型稀疏方程组的Krylov子空间方法中的稳定双共轭梯度(Bicg-stab)方法,收敛速度快,精度高,而且稳定性好,结合ilu预处理技术,可以大大提高求解大型稀疏方程组的效率。

In electromagnetic finite element numerical simulation of geophysics, a large, sparse and complex coefficient matrix is obtained. Because of limitation of computer memory, finite element stiff matrix must be compressed to store. Since there are multiple degrees of freedom, block compressed sparse row technique fitting to more freedom than one is proposed, and transform block compressed sparse row to general compressed sparse row through format transform program. As stabilized biconjugate gradient(bicgstab)of krylov subspace iterative method in solving large and sparse coefficient linear systems are stable, have fast convergence and high accuracy, it can improve the efficiency to solve linear equations compared with ilu precondioner.