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The dimension splitting element-free Galerkin method for 3D transient heat conduction problems

  • ZhiJuan Meng
  • Heng Cheng
  • LiDong Ma
  • YuMin ChengEmail author
Article

Abstract

By transforming a 3D problem into some related 2D problems, the dimension splitting element-free Galerkin (DSEFG) method is proposed to solve 3D transient heat conduction problems. The improved element-free Galerkin (IEFG) method is used for 2D transient heat conduction problems, and the finite difference method is applied in the splitting direction. The discretized system equation is obtained based on the Galerkin weak form of 2D problem; the essential boundary conditions are imposed with the penalty method; and the finite difference method is employed in the time domain. Four exemplary problems are chosen to verify the efficiency of the DSEFG method. The numerical solutions show that the efficiency and precision of the DSEFG method are greater than ones of the IEFG method for 3D problems.

Keywords

improved element-free Galerkin (IEFG) method dimension splitting method finite difference method dimension splitting element-free Galerkin (DSEFG) method transient heat conduction problem 

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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • ZhiJuan Meng
    • 1
    • 2
  • Heng Cheng
    • 3
  • LiDong Ma
    • 4
  • YuMin Cheng
    • 1
    Email author
  1. 1.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai UniversityShanghaiChina
  2. 2.School of Applied ScienceTaiyuan University of Science and TechnologyTaiyuanChina
  3. 3.Department of Civil EngineeringShanghai UniversityShanghaiChina
  4. 4.School of Materials Science and EngineeringTaiyuan University of Science and TechnologyTaiyuanChina

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