摘要
本文提出一种将有限元单元刚度矩阵直接集成压缩格式的总体刚度矩阵的方法,并针对其线性系统设计了预处理的重启动GMRES(m)并行求解器.集成方法使用了一个"关联结点"的数据结构,它用来记录网格中节点的关联信息,作为集成过程的中间媒介.这种方法能减少大量的存储空间,简单且高效.求解器分别使用Jacobi和稀疏近似逆(SPAI)预条件子.二维和三维弹性力学问题的数值试验表明,在二维情形下,SPAI预条件子具有很好的加速收敛效果和并行效率;在三维情形下,Jacobi预条件子更能减少迭代收敛时间.
A technique to assemble element stiffness matrix to global stiffness matrix stored in compressed storage format and two parallel preconditioned Restarted GMRES （m） solvers for sparse linear systems based on FEM are presented. The assembly method uses a data structure named associated node which record the information about the connection of nodes in the mesh as intermediaries. This method can save large memory and is simple and effective. The solvers are preconditioned by Jacobi and sparse approximate inverse （SPAI） preconditioner, respectively. Numerical experiments about 2D and 3D elasticity mechanics problems show that SPAI preconditioner is more effective to reduce the number of iterations and has good parallel efficiency for 2D problem, and Jacobi preconditioner can reduce more convergence time for 3D problem.
出处
《数值计算与计算机应用》
CSCD
2012年第3期230-240,共11页
Journal on Numerical Methods and Computer Applications
基金
国家基础研究计划(2010CB832702)
国家自然科学基金(10972215)资助
