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 引用本文: 尚月强, 何银年. 定常Stokes方程一种基于完全区域分解的有限元并行算法[J]. 应用数学和力学, 2010, 31(5): 609-617.
SHANG Yue-qiang, HE Yin-nian. A Parallel Finite Element Algorithm Based on Full Domain Partition for the Stationary Stokes Equations[J]. Applied Mathematics and Mechanics, 2010, 31(5): 609-617. doi: 10.3879/j.issn.1000-0887.2010.05.012
 Citation: SHANG Yue-qiang, HE Yin-nian. A Parallel Finite Element Algorithm Based on Full Domain Partition for the Stationary Stokes Equations[J]. Applied Mathematics and Mechanics, 2010, 31(5): 609-617.

## 定常Stokes方程一种基于完全区域分解的有限元并行算法

##### doi: 10.3879/j.issn.1000-0887.2010.05.012

###### 作者简介:尚月强(1976- ),男,贵州人,副教授,博士(E-mail:yueqiangshang@gmai.lcom);何银年(1953- ),男,陕西人,教授,博士(联系人.E-mail:heyn@mai.lxjtu.edu.cn).
• 中图分类号: O246;O242.21

## A Parallel Finite Element Algorithm Based on Full Domain Partition for the Stationary Stokes Equations

• 摘要: 基于完全区域分解技巧,提出了一种求解定常Stokes方程的有限元并行算法．该算法中,所有子问题都是定义在整个求解区域上,但绝大部分自由度来自其所负责的子区域，从而使得算法稍加修改现有的串行程序即可实现相应的并行计算，实现简单，通信需求少．数值结果验证了算法的高效性．
•  [1] Mitchell W F. The full domain partition approach to distributing adaptive grids[J]. Appl Numer Math, 1998, 26(1/2):265-275. [2] Mitchell W F. Parallel adaptive multilevel methods with full domain partitions[J].Appl Numer Anal Comput Math, 2004, 1(1/2):36-48. [3] Adams R. Sobolev Spaces[M]. New York: Academic Press Inc，1975. [4] Ciarlet P G, Lions J L. Handbook of Numerical Analysis[M]. Vol Ⅱ，Finite Element Methods (Part Ⅰ). Amsterdam: Elsevier Science Publisher， 1991. [5] Girault V, Raviart P A. Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms[M].Berlin Heidelberg: Springer-Verlag， 1986. [6] Elman H C， Silvester D J, Wathen A J. Finite Elements and Fast Iterative Solvers:With Applications in Incompressible Fluid Dynamics[M].Oxford: Oxford University Press， 2005. [7] HE Yin-nian， XU Jin-cao， ZHOU Ai-hui, et al. Local and parallel finite element algorithms for the Stokes problem[J]. Numer Math, 2008, 109(3): 415-434.

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##### 出版历程
• 收稿日期:  2009-12-18
• 修回日期:  2010-04-15
• 刊出日期:  2010-05-15

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