嵌套简单ILU分解代数预处理方法  

PRECONDITIONING METHODS WITH NESTED SIMPLE ILU DECOMPOSITION

作　　者：张振跃[1] 王靖[1] 方敏[1] 应文隆[1] 

机构地区：[1]浙江大学理学院数学系,杭州310027

出　　处：《计算数学》2004年第2期193-210,共18页Mathematica Numerica Sinica

基　　金：国家基础研究计划"973"项目(G19990328);北京应用物理与计算数学研究所计算物理重点实验室基金项目资助。

摘　　要：In this paper, we propose a nested simple incomplete LU decomposition (NSILU) method for preconditioning iterative methods for solving largely scale and sparse ill-conditioned hnear systems. NSILU consists of some numerical techniques such as simple modification of Schur complement, compression of ill-condition structure by permutation, nested simple ILU, and inner-outer iteration. We give detailed error analysis of NSILU and estimations of condition number of the preconditioned coefficient matrix, together with numerical comparisons. We also show an analysis of inner accuracy strategies for the inner-outer iteration approach. Our new approach NSILU is very efficient for linear systems from a kind of two-dimensional nonlinear energy equations with three different temperature variables, where most of the calculations centered around solving large number of discretized and illconditioned linear systems in large scale. Many numerical experiments are given and compared in costs of flops, CPU times, and storages to show the efficiency and effectiveness of the NSILU preconditioning method. Numerical examples include middle-scale real matrices of size n = 3180 or n = 6360, a real apphcation of solving about 755418 linear systems of size n = 6360, and a simulation of order n=814080 with structures and properties similar as the real ones.In this paper, we propose a nested simple incomplete LU decomposition (NSILU) method for preconditioning iterative methods for solving largely scale and sparse ill-conditioned linear systems. NSILU consists of some numerical techniques such as simple modification of Schur complement, compression of ill-condition structure by permutation, nested simple ILU, and inner-outer iteration. We give detailed error analysis of NSILU and estimations of condition number of the preconditioned coefficient matrix, together with numerical comparisons. We also show an analysis of inner accuracy strategies for the inner-outer iteration approach. Our new approach NSILU is very efficient for linear systems from a kind of two-dimensional nonlinear energy equations with three different temperature variables, where most of the calculations centered around solving large number of discretized and ill-conditioned linear systems in large scale. Many numerical experiments are given and compared in costs of flops, CPU times, and storages to show the efficiency and effectiveness of the NSILU preconditioning method. Numerical examples include middle-scale real matrices of size n = 3180 or n = 6360, a real application of solving about 755418 linear systems of size n = 6360, and a simulation of order n ?814080 with structures and properties similar as the real ones.

关 键 词：嵌套 代数预处理 线性代数方程组 内外迭代法 多介质能量方程 

分 类 号：O241[理学—计算数学]