Robin-Schwarz algorithm for contact conductance heat transfer

Huan Zhang; YingXiang Xu; Huan Zhang; YingXiang Xu

doi:10.3934/math.2025821

AIMS Mathematics

2025, Volume 10, Issue 8: 18381-18397. doi: 10.3934/math.2025821

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Research article

Robin-Schwarz algorithm for contact conductance heat transfer

Huan Zhang ,
YingXiang Xu ^,

School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received: 05 June 2025 Revised: 31 July 2025 Accepted: 01 August 2025 Published: 13 August 2025
MSC : 65M55

This paper explored the optimized Schwarz method (OSM) for solving contact conductance heat transfer problems, with a particular emphasis on the impact of thermal contact resistance (TCR) on the convergence behavior of the OSM algorithm when the standard Robin transmission condition is applied. The presence of TCR introduces a challenging optimization problem, which was rigorously addressed to determine the optimal Robin parameter and describe the corresponding convergence behavior. Our analysis yielded several novel findings. First, an increase in TCR results in faster convergence of the OSM algorithm. Second, mesh-independent convergence was achieved in an asymptotic sense, contrasting with the mesh-dependent convergence observed in the absence of TCR. Third, unlike the deceleration caused by strong heterogeneity in the TCR-free scenario, increased heterogeneity contrast accelerates convergence. Thermal conductivity also contributes to convergence enhancement in a manner analogous to the effect of heterogeneity. These theoretical results were validated through numerical experiments, demonstrating the significant influence of TCR on the performance of the OSM algorithm in contact conductance heat transfer problems.
- optimized Schwarz method,
- contact conductance heat transfer,
- thermal contact resistance,
- domain decomposition,
- optimized transmission condition
Citation: Huan Zhang, YingXiang Xu. Robin-Schwarz algorithm for contact conductance heat transfer[J]. AIMS Mathematics, 2025, 10(8): 18381-18397. doi: 10.3934/math.2025821

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Abstract

This paper explored the optimized Schwarz method (OSM) for solving contact conductance heat transfer problems, with a particular emphasis on the impact of thermal contact resistance (TCR) on the convergence behavior of the OSM algorithm when the standard Robin transmission condition is applied. The presence of TCR introduces a challenging optimization problem, which was rigorously addressed to determine the optimal Robin parameter and describe the corresponding convergence behavior. Our analysis yielded several novel findings. First, an increase in TCR results in faster convergence of the OSM algorithm. Second, mesh-independent convergence was achieved in an asymptotic sense, contrasting with the mesh-dependent convergence observed in the absence of TCR. Third, unlike the deceleration caused by strong heterogeneity in the TCR-free scenario, increased heterogeneity contrast accelerates convergence. Thermal conductivity also contributes to convergence enhancement in a manner analogous to the effect of heterogeneity. These theoretical results were validated through numerical experiments, demonstrating the significant influence of TCR on the performance of the OSM algorithm in contact conductance heat transfer problems.

References

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