大规模p型有限元方程组的修正SSOR-PCG解法  

Modified SSOR-PCG Solver for Large-Scale p-Version FEM Equations

作　　者：程昭[1] 陈胜宏[2] 田胜利 葛修润 

机构地区：[1]上海交通大学岩土力学与工程研究所,上海200030 [2]武汉大学水利水电学院,武汉430072

出　　处：《上海交通大学学报》2002年第11期1608-1611,共4页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金资助项目 (5 99790 2 1)

摘　　要：结合 p型有限元方程组的系数矩阵具有对称性、正定性、稀疏性和阶谱性等特点 ,用修正的对称逐步超松弛预处理共轭梯度法来求解大规模 p型自适应有限元方程组 ,可以减少每步迭代的主要计算量 ;利用上一个自适应步的结果初始化迭代序列 ,可以减少迭代次数 ,使得总迭代次数和计算时间较原方法大为减少 .理论和算例均表明 ,这是求解大规模A modified symmetric successive over relaxation preconditioned conjugated gradient (SSOR PCG) solver was used to solve the equations based on the symmetric, positive definite, sparse and hierarchical characteristic of p version of the adaptive finite element method (FEM) equations. The solving cost of each iterative step is diminished; with the results of the last adaptive step transferred to the present adaptive step as a portion of the iterative initiation, the iterating number is declined as well. The methods make the iterating number and solving time be reduced compared with the traditional SSOR PCG solver. The analysis and example both indicate that it is an efficient method to solve large scale p version of adaptive FEM equations.

关 键 词：工程结构 有限元方法 P型 数值分析 改进方法 

分 类 号：O242.21[理学—计算数学] TB11[理学—数学]