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The interpolating
EFG method for steady heat conduction problems in anisotropic
materials
Xiaofeng Liu, Fengbin Liu and Heng Cheng |
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Vol. 20 (2025), No. 5, 511–528
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Abstract |
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This paper employs the interpolation moving least-squares (IMLS) approximation to construct the shape functions and combines it with the Galerkin weak form for 3D steady anisotropic heat conduction equations, proposing an interpolated element-free Galerkin (IEFG) method for solving this problem. Unlike the traditional EFG method, this approach allows for direct imposition of Dirichlet boundary conditions when solving partial differential equations, thereby enhancing computational efficiency or accuracy. Five numerical examples are given, and comparing the IEFG method with EFG method. The results demonstrate that the IMLS-based IEFG method exhibits good convergence and accuracy in solving such problems. Its effectiveness in analyzing anisotropic heat conduction problems is further validated though comparison with both exact solutions and the EFG ones. The numerical results indicate that the proposed method reduces the errors and demonstrates its potential for addressing complex anisotropic heat conduction problems. |
Keywords
meshless method, interpolating element-free Galerkin
method, singular weight function, anisotropic steady heat
conduction
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Milestones
Received: 4 September 2025
Revised: 30 September 2025
Accepted: 12 October 2025
Published: 21 November 2025
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Authors |
| Xiaofeng Liu | |
| School of Applied Science Taiyuan University of Science and Technology Taiyuan, 030024 China |
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| Fengbin Liu | |
| College of Aeronautics and
Astronautics Shanxi Key Laboratory of Material Strength and Structural Shock Taiyuan University of Technology Taiyuan, 030024 China |
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| Heng Cheng | |
| School of Applied Science Taiyuan University of Science and Technology Taiyuan, 030024 China |
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| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
