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<p>For multi-domain heat conduction problems with complex interfaces, we present an efficient multi-domain fast multipole boundary element method (MD-FMMBEM) integrated with a high-performance preconditioning strategy. Traditional fast multipole boundary element method (FMMBEM) preconditioners struggle with multi-domain problems due to the lack of invertible diagonal submatrices at interface regions, limiting their effectiveness. To address this challenge, we propose a novel “global tree-subtree” structure combined with an innovative equation numbering strategy. The global tree ensures consistent cell alignment at interfaces within the subtree structure, while a continuous numbering scheme for interface elements enables the formation of invertible submatrices. This lays a solid foundation for robust preconditioner construction. By incorporating this strategy, we develop a preconditioned MD-FMMBEM (P-MD-FMMBEM) that significantly improves robustness and computational efficiency. Numerical experiments demonstrate that the proposed method achieves efficiency comparable to traditional FMMBEM for standard heat transfer conditions, including continuous interfaces, interfacial thermal resistance, and interfacial convection. More importantly, in ultra-large-scale, multi-interface problems, it exhibits superior accuracy, faster convergence, and enhanced stability. Our approach not only provides an efficient solution for multi-domain heat conduction but also opens new avenues for tackling complex multi-physics coupling problems.</p>

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An advanced preconditioning strategy for multi-domain fast multipole BEM with complex interfaces

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Jiayue Hou,
  • Yongqiang Chen

摘要

For multi-domain heat conduction problems with complex interfaces, we present an efficient multi-domain fast multipole boundary element method (MD-FMMBEM) integrated with a high-performance preconditioning strategy. Traditional fast multipole boundary element method (FMMBEM) preconditioners struggle with multi-domain problems due to the lack of invertible diagonal submatrices at interface regions, limiting their effectiveness. To address this challenge, we propose a novel “global tree-subtree” structure combined with an innovative equation numbering strategy. The global tree ensures consistent cell alignment at interfaces within the subtree structure, while a continuous numbering scheme for interface elements enables the formation of invertible submatrices. This lays a solid foundation for robust preconditioner construction. By incorporating this strategy, we develop a preconditioned MD-FMMBEM (P-MD-FMMBEM) that significantly improves robustness and computational efficiency. Numerical experiments demonstrate that the proposed method achieves efficiency comparable to traditional FMMBEM for standard heat transfer conditions, including continuous interfaces, interfacial thermal resistance, and interfacial convection. More importantly, in ultra-large-scale, multi-interface problems, it exhibits superior accuracy, faster convergence, and enhanced stability. Our approach not only provides an efficient solution for multi-domain heat conduction but also opens new avenues for tackling complex multi-physics coupling problems.