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<p>This paper presents an automatic domain decomposition algorithm based on dihedral angle-constrained optimization. Our algorithm prevents the formation of unacceptably small angles or intersections between interface mesh and elements of subdomains. Dihedral angles between the mesh and the cutting plane are used to identify which segmented boundaries require optimization. When optimized boundaries satisfy the dihedral angle constraints yet are still unsuitable for interface mesh generation, the problem is addressed by local transformations of the cutting plane, including translation and rotation. Furthermore, if geometric proximity exists between nodes not located on the segmented boundary and the cutting plane, then such nodes and boundary mesh edge of their connected mesh are imposed as constraints on the meshing boundary to resolve the proximity. The proposed algorithm was applied to three complex models to demonstrate its capability for parallel domain decomposition and tetrahedral mesh generation. The effectiveness and robustness of our algorithm are confirmed through mesh generation analysis and quality verification based on the collapse parameter.</p>

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Dihedral angle constraint-driven optimization for automatic domain decomposition and parallel tetrahedral generation

  • 期刊论文

  • 发表日期：

    2026年6月2日

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  • Haidong Wang,
  • Siqi Yin,
  • Feiqi Wang,
  • Xin Hu,
  • Yumin Huang,
  • Xiangyang Y. Cui

摘要

This paper presents an automatic domain decomposition algorithm based on dihedral angle-constrained optimization. Our algorithm prevents the formation of unacceptably small angles or intersections between interface mesh and elements of subdomains. Dihedral angles between the mesh and the cutting plane are used to identify which segmented boundaries require optimization. When optimized boundaries satisfy the dihedral angle constraints yet are still unsuitable for interface mesh generation, the problem is addressed by local transformations of the cutting plane, including translation and rotation. Furthermore, if geometric proximity exists between nodes not located on the segmented boundary and the cutting plane, then such nodes and boundary mesh edge of their connected mesh are imposed as constraints on the meshing boundary to resolve the proximity. The proposed algorithm was applied to three complex models to demonstrate its capability for parallel domain decomposition and tetrahedral mesh generation. The effectiveness and robustness of our algorithm are confirmed through mesh generation analysis and quality verification based on the collapse parameter.