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Fast multipole singular boundary method for Stokes flow problems

Author

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  • Qu, Wenzhen
  • Chen, Wen
  • Fu, Zhuojia
  • Gu, Yan

Abstract

This paper firstly employs the fast multipole method (FMM) to accelerate the singular boundary method (SBM) solution of the Stokes equation. We present a fast multipole singular boundary method (FMSBM) based on the combination of the SBM and the FMM. The proposed FMSBM scheme reduces CPU operations and memory requirements by one order of magnitude, namely O(N) (where N is the number of boundary nodes). Thus, the strategy overcomes costly expenses of the SBM due to its dense interpolation matrix while keeping its major merits being free of mesh, boundary-only discretization, and high accuracy in the solution of the Stokes equation. The performance of this scheme is tested to a few benchmark problems. Numerical results demonstrate its efficiency, accuracy and applicability.

Suggested Citation

  • Qu, Wenzhen & Chen, Wen & Fu, Zhuojia & Gu, Yan, 2018. "Fast multipole singular boundary method for Stokes flow problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 146(C), pages 57-69.
    • Handle: RePEc:eee:matcom:v:146:y:2018:i:c:p:57-69
    DOI: 10.1016/j.matcom.2017.10.001
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    References listed on IDEAS

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    1. Beneš, Michal, 2007. "The qualitative properties of the Stokes and Navier–Stokes system for the mixed problem in a nonsmooth domain," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 76(1), pages 8-12.
    2. Lin, Ji & Chen, Wen & Wang, Fuzhang, 2011. "A new investigation into regularization techniques for the method of fundamental solutions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1144-1152.
    3. Li, Xiaolin, 2011. "Development of a meshless Galerkin boundary node method for viscous fluid flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(2), pages 258-280.
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