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<p>Two iterative methods are designed based on matrix splitting techniques to solve the double saddle point problems arising from the liquid crystal director model. These iterative methods exhibit unconditional convergence under certain conditions imposed on the Schur complement <i>S</i>. Additionally, we propose the new block diagonal (NBD) and new block triangular (NBT) preconditioners, which are derived from these iterative methods, and analyze the spectral properties of the corresponding preconditioned matrices. Finally, numerical experiments are conducted to validate the robustness and efficiency of the proposed iterative methods and preconditioners for solving the double saddle point problems in liquid crystal director modeling.</p>

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Two new block preconditioners for double saddle point problems arising from liquid crystal director modeling

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • Yu-Lan Liu,
  • Bo Wu

摘要

Two iterative methods are designed based on matrix splitting techniques to solve the double saddle point problems arising from the liquid crystal director model. These iterative methods exhibit unconditional convergence under certain conditions imposed on the Schur complement S. Additionally, we propose the new block diagonal (NBD) and new block triangular (NBT) preconditioners, which are derived from these iterative methods, and analyze the spectral properties of the corresponding preconditioned matrices. Finally, numerical experiments are conducted to validate the robustness and efficiency of the proposed iterative methods and preconditioners for solving the double saddle point problems in liquid crystal director modeling.