Rapid Solution Techniques Study With Preconditioned Iterative Methods Of Large-scale Sparse Equation Group

The numerical analysis of finite element method (FEM) is an important means of modern engineering refined design, having become an indispensable engineering tool for designers. The FEM and other numerical computation finally go to solve a large-scale linear equation group, most contradiction of which involves with very time-consuming and storage occupying computational efforts. The solving methodology and storing way to the equation group from FEM greatly affect the computational efficiency. Therefore, it is very valuable for theoretical and engineering application to study cost-effective algorithm and its optimization procedures to solve the equation group.Based on the adequate study of general method to solve linear equation group, this thesis employs incomplete Cholesky conjugate gradient (ICCG) method for the numerical stability and efficiency of solution process. In order to eliminate morbidity of FEM coefficient matrix and speed up its convergency, this thesis proposes a newly effective incomplete Cholesky decomposition preconditioned method and suggests some improved preconditioned schemes to the current popular ICCG methods. This thesis takes the fully sparse strategy for the storage and decomposition of the sparse and symmetrical matrix of FEM equations such that it makes lowest storing requirement to computer. The combination of ICCG method and fully sparse storage structure can greatly improve the algorithmic efficiency for FEM solution of large scaled sparse linear equation group.The major research work in this thesis includes building up the fully sparse storage structure for global stiffness matrix from FEM, implementing the algorithmic program and solving large-scaled sparse linear equation group by ICCG method. Numerical examples show that incomplete Cholesky decomposition preconditioned methods proposed by the thesis are available, and that the combination of ICCG method and fully sparse storage structure is effective, reliable and applicable to modern structural analysis.