Research on the Fictitious Source Points of the Hybrid Fundamental Solution-Based Finite Element Method for Heat Conduction Problems

ZHANG Kai; WANG Keyong; QI Dongping

doi:10.21656/1000-0887.430077

Volume 44 Issue 4

Apr. 2023

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Article Navigation > Applied Mathematics and Mechanics > 2023 > 44(4): 431-440

ZHANG Kai, WANG Keyong, QI Dongping. Research on the Fictitious Source Points of the Hybrid Fundamental Solution-Based Finite Element Method for Heat Conduction Problems[J]. Applied Mathematics and Mechanics, 2023, 44(4): 431-440. doi: 10.21656/1000-0887.430077

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Research on the Fictitious Source Points of the Hybrid Fundamental Solution-Based Finite Element Method for Heat Conduction Problems

doi: 10.21656/1000-0887.430077

School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai 201620, P.R.China

Received Date: 2022-03-10
Rev Recd Date: 2022-05-15
Publish Date: 2023-04-01

Abstract

Abstract

The hybrid fundamental solution-based finite element method was proposed for heat conduction problems. Firstly, 2 independent fields were assumed: the intra-element temperature field approximated through the linear combination of fundamental solutions, and the auxiliary frame temperature field in the same form as that in the conventional finite element method. Then, a modified variational functional was employed to link the 2 independent fields and derive the finite element formulation. However, the accuracy of the method is strongly dependent on the distribution and the number of source points. The source points were usually placed on 2 fictitious boundaries outside the element: one is similar to the element shape, the other is a circular one. Furthermore, the dual fictitious boundary scheme was proposed for comparison with the above fictitious boundaries. With different configurations of source points, 2 typical numerical examples were given to demonstrate the validity and the insensitivity to mesh distortion of the proposed method.
- fundamental solution,
- finite element method,
- modified variational functional,
- fictitious boundary,
- mesh distortion

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References(19)

References

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