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Local and Parallel Finite Element Algorithm Based on the Partition of Unity for Incompressible Flows

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Abstract

By combining two-grid method with domain decomposition method, a new local and parallel finite element algorithm based on the partition of unity is proposed for the incompressible flows. The interesting points in this algorithm lie in (1) a class of partition of unity is derived by a given triangulation, which guides the domain decomposition (2) the globally fine grid correction step is decomposed into a series of local linearized residual problems on some subdomains and (3) the global continuous finite element solution is obtained by assembling all local solutions together using the partition of unity functions. Some numerical simulations are presented to demonstrate the high efficiency and flexibility of the new algorithm.

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Author information

Authors and Affiliations

  1. Department of Mathematics, East China Normal University, Shanghai, China

    Haibiao Zheng

  2. School of Science, Donghua University, Shanghai, China

    Jiaping Yu

  3. School of Mechanical Engineering and Automation, Harbin Institute of Technology, Shenzhen Graduate School, Shenzhen, 518055, China

    Feng Shi

Authors
  1. Haibiao Zheng
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  2. Jiaping Yu
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  3. Feng Shi
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Corresponding author

Correspondence to Haibiao Zheng.

Additional information

H. Zheng was partially supported by NSF of China with Grant Nos. 11201369, 11171269, 11271298 and Tianyuan Fund for Mathematics with No. 11326224. J. Yu was partially supported by NSF of China with Grant No. 11471071 and NSF of Shanghai with Grant No. 14ZR1401200 and the Fundamental Research Funds for the Central Universities. F. Shi was partially supported by NSFC (Project 11401563), by Guangdong Natural Science Foundation (Project S201204007760), by Tianyuan Fund for Mathematics of the NSFC (Project 11226314), and China Postdoctoral Science Foundation (Project 2014M560252).

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Zheng, H., Yu, J. & Shi, F. Local and Parallel Finite Element Algorithm Based on the Partition of Unity for Incompressible Flows. J Sci Comput 65, 512–532 (2015). https://doi.org/10.1007/s10915-014-9979-x

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  • DOI: https://doi.org/10.1007/s10915-014-9979-x

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