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The interpolating dimension splitting element-free Galerkin method for 3D potential problems

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Abstract

In this paper, based on the improved interpolating moving least-squares (IMLS) method and the dimension splitting method, the interpolating dimension splitting element-free Galerkin (IDSEFG) method for three-dimensional (3D) potential problems is proposed. The key of the IDSEFG method is to split a 3D problem domain into many related two-dimensional (2D) subdomains. The shape function is constructed by the improved IMLS method on the 2D subdomains, and the Galerkin weak form based on the dimension splitting method is used to obtain the discretized equations. The discrete equations on these 2D subdomains are coupled by the finite difference method. Take the improved element-free Galerkin (IEFG) method as a comparison, the advantage of the IDSEFG method is that the essential boundary conditions can be enforced directly. The effects of the number of nodes, the direction of dimension splitting, and the parameters of the influence domain on the calculation accuracy are studied through four numerical examples, the numerical solutions of the IDSEFG method are compared with the numerical solutions of the IEFG method and the analytical solutions. It is verified that the numerical solutions of the IDSEFG method are highly consistent with the analytical solution, and the calculation efficiency of this method is significantly higher than that of the IEFG method.

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Funding

National Natural Science Foundation of China, Grant/Award Number: 11571223.

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Authors and Affiliations

  1. Department of Civil Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200444, China

    Qian Wu & Miaojuan Peng

  2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Yumin Cheng

Authors
  1. Qian Wu
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  2. Miaojuan Peng
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  3. Yumin Cheng
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Correspondence to Miaojuan Peng or Yumin Cheng.

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Wu, Q., Peng, M. & Cheng, Y. The interpolating dimension splitting element-free Galerkin method for 3D potential problems. Engineering with Computers 38 (Suppl 4), 2703–2717 (2022). https://doi.org/10.1007/s00366-021-01408-5

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