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A Parallel Iterative Finite Element Method for the Linear Elliptic Equations

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Abstract

By combining the two-grid discretization with the partition of unity method, a parallel iterative finite element method for the linear elliptic equations is proposed and investigated. Since the construction of the partition of unity is based on the coarse mesh triangulation, the computational domain of each subproblem can be divided automatically and the number of subproblems can be arbitrarily huge as the coarse mesh parameter H tends to zero. That means our method can be easily implemented in high performance supercomputers or cluster of workstations. Theoretical results based on a priori error estimation of the scheme are obtained, which indicate that our method can reach the optimal convergence orders within a few two-grid iterations. Numerical results are reported to assess the theoretical results.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Guangzhi Du

  2. School of Mathematical Sciences, University of Jinan, Jinan, 250022, China

    Liyun Zuo

Authors
  1. Guangzhi Du
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  2. Liyun Zuo
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Correspondence to Guangzhi Du.

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Subsidized by NSFC (Grant No. 11701343) and partially supported by NSFC (Grant No. 11801332),

Subsidized by the Provincial Natural Science Foundation of Shandong (Grant No. ZR2017BA027)

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Du, G., Zuo, L. A Parallel Iterative Finite Element Method for the Linear Elliptic Equations. J Sci Comput 85, 35 (2020). https://doi.org/10.1007/s10915-020-01348-0

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  • DOI: https://doi.org/10.1007/s10915-020-01348-0

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