数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (2): 572-588.doi: 10.1007/s10473-020-0218-2

• 论文 • 上一篇    下一篇

EXPANDABLE PARALLEL FINITE ELEMENT METHODS FOR LINEAR ELLIPTIC PROBLEMS

杜光芝   

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
  • 收稿日期:2019-02-27 修回日期:2019-06-18 出版日期:2020-04-25 发布日期:2020-05-26
  • 作者简介:Guangzhi DU,E-mail:guangzhidu@gmail.com
  • 基金资助:
    Subsidized by NSFC (11701343) and partially supported by NSFC (11571274, 11401466).

EXPANDABLE PARALLEL FINITE ELEMENT METHODS FOR LINEAR ELLIPTIC PROBLEMS

Guangzhi DU   

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
  • Received:2019-02-27 Revised:2019-06-18 Online:2020-04-25 Published:2020-05-26
  • Supported by:
    Subsidized by NSFC (11701343) and partially supported by NSFC (11571274, 11401466).

摘要: In this article, two kinds of expandable parallel finite element methods, based on two-grid discretizations, are given to solve the linear elliptic problems. Compared with the classical local and parallel finite element methods, there are two attractive features of the methods shown in this article: 1) a partition of unity is used to generate a series of local and independent subproblems to guarantee the final approximation globally continuous; 2) the computational domain of each local subproblem is contained in a ball with radius of $O(H)$ ($H$ is the coarse mesh parameter), which means methods in this article are more suitable for parallel computing in a large parallel computer system. Some a priori error estimation are obtained and optimal error bounds in both $H^1$-normal and $L^2$-normal are derived. Finally, numerical results are reported to test and verify the feasibility and validity of our methods.

关键词: Two-grid method, expandable method, partition of unity, parallel algorithm, finite element method

Abstract: In this article, two kinds of expandable parallel finite element methods, based on two-grid discretizations, are given to solve the linear elliptic problems. Compared with the classical local and parallel finite element methods, there are two attractive features of the methods shown in this article: 1) a partition of unity is used to generate a series of local and independent subproblems to guarantee the final approximation globally continuous; 2) the computational domain of each local subproblem is contained in a ball with radius of $O(H)$ ($H$ is the coarse mesh parameter), which means methods in this article are more suitable for parallel computing in a large parallel computer system. Some a priori error estimation are obtained and optimal error bounds in both $H^1$-normal and $L^2$-normal are derived. Finally, numerical results are reported to test and verify the feasibility and validity of our methods.

Key words: Two-grid method, expandable method, partition of unity, parallel algorithm, finite element method

中图分类号: 

  • 65N15