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<p>For the double saddle point problems (DSPPs) that arise in liquid crystal director modeling, we introduce a modified preconditioned quasi shift-splitting (MPQSS) iteration method. The convergent properties of the MPQSS iteration algorithm are carefully analyzed. Based on the MPQSS iteration method, two quasi shift-splitting (SS) preconditioners are developed. The spectral properties of the preconditioned DSPP matrices with these new preconditioners are thoroughly investigated. The implementations of the new preconditioners avoid direct and precise construction of the relevant Schur complement matrices, thereby enhancing the efficiency of the algorithms. Mathematical tests validate the reliability and effectiveness of the new methods by assessing the performance of the Krylov subspace method after being preconditioned with the new preconditioners.</p>

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A modified preconditioned quasi shift-splitting method for double saddle point problems with liquid crystal director modeling

  • 期刊论文

  • 发表日期：

    2025年1月9日

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  • Sheng-Wei Zhou,
  • Wei-Hong Zhang,
  • Mei-Ling Zhang

摘要

For the double saddle point problems (DSPPs) that arise in liquid crystal director modeling, we introduce a modified preconditioned quasi shift-splitting (MPQSS) iteration method. The convergent properties of the MPQSS iteration algorithm are carefully analyzed. Based on the MPQSS iteration method, two quasi shift-splitting (SS) preconditioners are developed. The spectral properties of the preconditioned DSPP matrices with these new preconditioners are thoroughly investigated. The implementations of the new preconditioners avoid direct and precise construction of the relevant Schur complement matrices, thereby enhancing the efficiency of the algorithms. Mathematical tests validate the reliability and effectiveness of the new methods by assessing the performance of the Krylov subspace method after being preconditioned with the new preconditioners.