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<p>For large-scale topology optimization problems, the multigrid preconditioner conjugate gradient (MGPCG) solver is very effective for solving the nested finite-element equations. But the convergence rate of MGPCG strongly depends on the damping factor of the damped Jacobi smoother. Traditional experimental damping factor in multigrid preconditioner may cause slow rate of convergence and high computational costs in solving large-scale topology optimization problems. This work analyzes the limitations of the original adaptive damped Jacobi smoother proposed in Luo et&#xa0;al. (<CitationRef CitationID="CR12">2024</CitationRef>) and presents an enhanced adaptive damped Jacobi smoother. Specifically, an amplification factor is applied to the maximum eigenvalue obtained from the power method to make it not underestimated. The proposed enhanced adaptive damped Jacobi smoother provides a robust practical framework for automatic damping factor selection for large-scale topology optimization problems. The results of 2D and 3D examples demonstrate that the enhanced adaptive damped smoother either improves the convergence rate of the MGPCG solver and reduces the finite-element analysis time or delivers comparable performance, when compared with the original smoother.</p>

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An enhanced adaptive damped Jacobi smoother for efficient MGPCG solving in large-scale topology optimization

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Long Hu,
  • Tianyuan Qi,
  • Junpeng Zhao,
  • Chunjie Wang

摘要

For large-scale topology optimization problems, the multigrid preconditioner conjugate gradient (MGPCG) solver is very effective for solving the nested finite-element equations. But the convergence rate of MGPCG strongly depends on the damping factor of the damped Jacobi smoother. Traditional experimental damping factor in multigrid preconditioner may cause slow rate of convergence and high computational costs in solving large-scale topology optimization problems. This work analyzes the limitations of the original adaptive damped Jacobi smoother proposed in Luo et al. (2024) and presents an enhanced adaptive damped Jacobi smoother. Specifically, an amplification factor is applied to the maximum eigenvalue obtained from the power method to make it not underestimated. The proposed enhanced adaptive damped Jacobi smoother provides a robust practical framework for automatic damping factor selection for large-scale topology optimization problems. The results of 2D and 3D examples demonstrate that the enhanced adaptive damped smoother either improves the convergence rate of the MGPCG solver and reduces the finite-element analysis time or delivers comparable performance, when compared with the original smoother.