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A stable and efficient infinite meshfree approach for solving half-space eat conduction problems

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Abstract

This study introduces an innovative dynamic infinite meshfree method for robust and efficient solutions to half-space problems. This approach seamlessly couples this method with the nodal integral reproducing kernel particle method to discretize half-spaces defined by an artificial boundary. The infinite meshfree shape function is uniquely constructed using the 1D reproducing kernel shape function combined with the boundary singular kernel method, ensuring the Kronecker delta property on artificial boundaries. Coupled with the wave-transfer function, the proposed approach models dissipation actions effectively. The infinite domain simulation employs the dummy node method, enhanced by Newton–Cotes integrals. To ensure solution stability and convergence, our approach is based on the Galerkin weak form of the domain integral method. To combat the challenges of instability and imprecision, we integrated the stabilized conforming nodal integration method and the naturally stable nodal integration. The proposed methods efficacy is validated through various benchmark problems, with preliminary results showcasing superior precision and stability.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This study was supported by the National Science and Technology Council (NSTC), Taiwan, under project contract numbers MOST 111-2221-E-006-036 and NSTC 112-2625-M-006-006. Assistance with the illustrations by Kuan-Ting Lin is also acknowledged and appreciated.

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  1. Department of Civil Engineering, National Cheng Kung University, Tainan, 70101, Taiwan

    Kuan-Chung Lin, Ting-Wei Chen & Huai-Liang Hsieh

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  1. Kuan-Chung Lin
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  2. Ting-Wei Chen
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  3. Huai-Liang Hsieh
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Correspondence to Kuan-Chung Lin.

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Lin, KC., Chen, TW. & Hsieh, HL. A stable and efficient infinite meshfree approach for solving half-space eat conduction problems. Engineering with Computers (2024). https://doi.org/10.1007/s00366-024-01960-w

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