Zheng Hong, Ge Xiu-run. Improved Preconditoned Conjugate Gradient Method and Its Application in F. E. A. for Engineering[J]. Applied Mathematics and Mechanics, 1993, 14(4): 353-361.
Citation: Zheng Hong, Ge Xiu-run. Improved Preconditoned Conjugate Gradient Method and Its Application in F. E. A. for Engineering[J]. Applied Mathematics and Mechanics, 1993, 14(4): 353-361.

Improved Preconditoned Conjugate Gradient Method and Its Application in F. E. A. for Engineering

  • Received Date: 1992-05-30
  • Publish Date: 1993-04-15
  • In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method(PCCG). The theorems discuss respectively the qualitative property of the iterative solution and the construction principle of the iterative matrix. The authors put forward a new incompletely LU factorizing technique for non-M-matrix and the method of constructing the iterative matrix. This improved PCCG is used to calculate the ill-conditioned problems and large-scale three-dimensional finite element problems, and simultaneously contrasted with other methods. The abnormal phenomenon is analyzed when PCCG is used to solve the system of ill-conditioned equations, It is shown that the method proposed in this paper is quite effective in solving the system of large-scale finite element equations and the system of ill-conditioned equations.
  • loading
  • [1]
    Purasinghe,R.and R.Muller,Improved iterative solution for finite element analysis on microcomputers,Microcomputers in Civil Engineering,4,7(1989),91-97.
    [2]
    Crisfield,M.A.,Finite Element and Solution Procedures for Structural Analysis,Vol.1,Linear Analysis,Swansea:UK(1986),197-223.
    [3]
    Hughes,T.J.R.,An element-by-element algorithm for problems of structural and solid mechanics,Comput.Methods Appl.Mech.Eng.,36(1983),241-254.
    [4]
    Jennings.A.,Matrix Computation for Engineers and Scientists,John Wiley,New York(1977).
    [5]
    蔡大用,《数值代数》,清华大学出版社(1987).
    [6]
    蒋尔雄,《对称矩阵计算》,上海科学技术出版社(1984).
    [7]
    杨家岭、郑宏、葛修润,清江隔河岩重力拱坝坝体与复杂地基相互作用的三维有限元分析,岩土力学,(4)(1989),5-19.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1645) PDF downloads(659) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return