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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (3): 445-461.doi: 10.3969/j.issn.1005-3085.2015.03.013

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三维定常/非定常Stokes方程的维数分裂算法(英)

魏红波1,    侯延仁1,2   

  1. 1- 西安交通大学数学与统计学院，西安 710049
    2- 西安交通大学计算地学研究中心，西安 710049
  • 收稿日期:2013-11-01 接受日期:2014-05-26 出版日期:2015-06-15 发布日期:2015-08-15
  • 基金资助:
    国家自然科学基金 (11171269)；教育部博士点基金 (20110201110027).

Dimension Splitting Algorithms for Three Dimensional Steady/Unsteady Stokes Equations

WEI Hong-bo1,   HOU Yan-ren1,2   

  1. 1- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
    2- Center for Computational Geosciences, Xi'an Jiaotong University, Xi'an 710049
  • Received:2013-11-01 Accepted:2014-05-26 Online:2015-06-15 Published:2015-08-15
  • Supported by:
    The National Natural Science Foundation of China (11171269); the Ph.D. Programs Foundation of Ministry of Education of China (20110201110027).

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摘要： 本文针对三维柱形区域提出了定常/非定常Stokes方程基于一致分裂格式的维数分裂算法(DSA)．文章推导了三维定常/非定常Stokes方程维数分裂方法的数值迭代格式．新算法的优势在于一系列的二维问题能够并行执行，而且数值计算中避免了三维网格的生成．大量的数值结果表明新算法既能获得最优收敛阶，而且能获得比采用四面体元求解更精确的逼近解．最后，通过采用并行求解新算法能够得到比较好的加速比和并行效率．

关键词: 维数分裂算法, 一致分裂格式, Stokes方程, 并行求解技术

Abstract:

In the three dimensional (3D) cylindrical kind domain, the finite-element dimension splitting algorithm (DSA) of steady/unsteady Stokes equation based on a consistent splitting scheme is proposed in this paper. The numerical schemes of steady/unsteady Stokes equation based on the DSA are presented. The advantages of the DSA are that our numerical schemes can be easily solved in parallel with several processors, and only 2D meshes instead of 3D meshes are involved in the numerical implementation. A great number of numerical results show that the DSA algorithm can be up to the optimal convergence rates, and obtain more accurate approximate solution than the 3D Galerkin finite-element method with 4-node tetrahedron elements. Finally, the good speed-up and parallel efficiency of the DSA are obtained by a parallel solving technique.

Key words: dimension splitting algorithm, consistent splitting scheme, Stokes equation, parallel solving technique

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