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

数学物理学报 ›› 2009, Vol. 29 ›› Issue (3): 564-572.

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

(兰州大学数学与统计学院兰州 730000)

收稿日期:2007-03-07 修回日期:2008-12-18 出版日期:2009-06-25 发布日期:2009-06-25
基金资助:
甘肃省科技计划(0804NKCA073)和兰州大学理论物理与数学纯基础科学基金(Lzu07003)资助

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

(School of Mathematics and Statistics, Lanzhou Univeristy, Lanzhou 730000)

Received:2007-03-07 Revised:2008-12-18 Online:2009-06-25 Published:2009-06-25
Supported by:
甘肃省科技计划(0804NKCA073)和兰州大学理论物理与数学纯基础科学基金(Lzu07003)资助

摘要/Abstract

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^[1]. 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.

关键词: 增量未知元方法, 对流扩散方程, 迭代方法

Abstract:

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.

Key words: Incremental unknowns, Convection-diffusion equations with variable coefficients, Iterative methods

中图分类号:

杨爱利, 伍渝江, 宋伦继. 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[J]. 数学物理学报, 2009, 29(3): 564-572.

YANG Ai-Li, WU Yu-Jiang, SONG Lun-Ji. A Class of Generalized Three Dimensional Convection-Diffusion Equations with Multi-Level Incremental Unknowns Method[J]. Acta mathematica scientia,Series A, 2009, 29(3): 564-572.

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