基于多层增量未知元方法的一类三维对流扩散方程的研究  

A Class of Generalized Three Dimensional Convection-Diffusion Equations with Multi-Level Incremental Unknowns Method

作　　者：杨爱利[1] 伍渝江[1] 宋伦继[1] 

机构地区：[1]兰州大学数学与统计学院,兰州730000

出　　处：《数学物理学报（A辑）》2009年第3期564-572,共9页Acta Mathematica Scientia

基　　金：甘肃省科技计划(0804NKCA073);兰州大学理论物理与数学纯基础科学基金(Lzu07003)资助

摘　　要：对于一类一般形式的三维对流扩散方程,运用有限差分方法,在增量未知元方法(IU)下,可以得到一个IU型正定但非对称的线性方程组。其系数矩阵条件数要远远优于不用IU方法的情形。考虑到IU方法的这一优点,作者在文中将IU方法与几种经典的迭代方法相结合,来求解上述系统。作者从理论上对该系统的IU型系数矩阵条件数进行了估计,并通过数值试验验证了这几种IU型迭代方法的有效性。With the finite difference discretization techniques, the authors get a nonsymmetric and positive-definite linear system when considering a class of generalized three-dimensional convection-diffusion equations even if they have variable coefficients. Considering that the condition number of incremental unknowns（IU）-type coefficient matrix is much better than the matrix without IU（see [1]）, the authors use the IU method in conjunction with several classical iterative methods to approximate the solution of the system. After estimating the condition number of IU-type coefficient matrix, the authors numerically confirm that these IU-type iterative methods are much more efficient.

关 键 词：增量未知元方法 对流扩散方程 迭代方法. 

分 类 号：O241.82[理学—计算数学]