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Abstract <p>Using the idea in [Cao Y., Jiang M.-Q., Zheng Y.-L., A splitting preconditioner for saddle point problems, Numer. Linear Algebra Appl. <b>18</b>, 875–895 (2011)], we present a parameterized block splitting (PBS) iteration method for solving the double saddle point problems arising from liquid crystal director modeling. We prove that the iteration method is unconditionally convergent. Then the induced preconditioner is used to accelerate the convergence of the Krylov subspace methods for solving the systems. Furthermore, spectral properties of the PBS preconditioned matrix are discussed and analyzed in detail. Numerical experiments not only verify the correctness of the theoretical results, but also show the efficiency of the proposed preconditioner.</p>

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A Parameterized Block Splitting Iteration Method for Double Saddle Point Problems Arising from Liquid Crystal Director Modeling

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Jun Li,
  • Lingsheng Meng,
  • Xiangtuan Xiong

摘要

Abstract

Using the idea in [Cao Y., Jiang M.-Q., Zheng Y.-L., A splitting preconditioner for saddle point problems, Numer. Linear Algebra Appl. 18, 875–895 (2011)], we present a parameterized block splitting (PBS) iteration method for solving the double saddle point problems arising from liquid crystal director modeling. We prove that the iteration method is unconditionally convergent. Then the induced preconditioner is used to accelerate the convergence of the Krylov subspace methods for solving the systems. Furthermore, spectral properties of the PBS preconditioned matrix are discussed and analyzed in detail. Numerical experiments not only verify the correctness of the theoretical results, but also show the efficiency of the proposed preconditioner.