A New Block Preconditioner for Double Saddle Point Systems Arising from Liquid Crystal Directors Modeling

doi:10.1007/s42967-023-00361-y

Communications on Applied Mathematics and Computation ›› 2025, Vol. 7 ›› Issue (5): 1652-1664.doi: 10.1007/s42967-023-00361-y

• ORIGINAL PAPERS • 上一篇

A New Block Preconditioner for Double Saddle Point Systems Arising from Liquid Crystal Directors Modeling

Jian-Jun Zhang^1,2, Jia-Qi Liu^1,2

1. Department of Mathematics, Shanghai University, Shanghai, 200444, China;
2. Newtouch Center for Mathematics of Shanghai University, Shanghai, 200444, China

收稿日期:2023-09-05 修回日期:2023-11-27 接受日期:2023-12-04 出版日期:2024-02-26 发布日期:2024-02-26
通讯作者: Jian-Jun Zhang,E-mail:jjzhang@staff.shu.edu.cn E-mail:jjzhang@staff.shu.edu.cn
基金资助:
The authors are grateful to Prof. Ai-Li Yang for providing the codes of BT and TPBT preconditioners, and are grateful to Prof. Fang Chen for providing the codes of the IAPSS preconditioner. The project is partially supported by the Natural Science Foundation of Shanghai, China (Grant No. 23ZR1422400).

A New Block Preconditioner for Double Saddle Point Systems Arising from Liquid Crystal Directors Modeling

Jian-Jun Zhang^1,2, Jia-Qi Liu^1,2

1. Department of Mathematics, Shanghai University, Shanghai, 200444, China;
2. Newtouch Center for Mathematics of Shanghai University, Shanghai, 200444, China

Received:2023-09-05 Revised:2023-11-27 Accepted:2023-12-04 Online:2024-02-26 Published:2024-02-26
Contact: Jian-Jun Zhang,E-mail:jjzhang@staff.shu.edu.cn E-mail:jjzhang@staff.shu.edu.cn
Supported by:
The authors are grateful to Prof. Ai-Li Yang for providing the codes of BT and TPBT preconditioners, and are grateful to Prof. Fang Chen for providing the codes of the IAPSS preconditioner. The project is partially supported by the Natural Science Foundation of Shanghai, China (Grant No. 23ZR1422400).

摘要/Abstract

摘要： We develop and investigate a new block preconditioner for a class of double saddle point (DSP) problems arising from liquid crystal directors modeling using a finite element scheme. We analyze the spectral properties of the preconditioned matrix. Numerical results are provided to evaluate the behavior of preconditioned iterative methods using the new preconditioner.

关键词: Iterative methods, Krylov methods, Preconditioning, Liquid crystals (LCs), Saddle point problems

Abstract: We develop and investigate a new block preconditioner for a class of double saddle point (DSP) problems arising from liquid crystal directors modeling using a finite element scheme. We analyze the spectral properties of the preconditioned matrix. Numerical results are provided to evaluate the behavior of preconditioned iterative methods using the new preconditioner.

Key words: Iterative methods, Krylov methods, Preconditioning, Liquid crystals (LCs), Saddle point problems

Jian-Jun Zhang, Jia-Qi Liu. A New Block Preconditioner for Double Saddle Point Systems Arising from Liquid Crystal Directors Modeling[J]. Communications on Applied Mathematics and Computation, 2025, 7(5): 1652-1664.

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A New Block Preconditioner for Double Saddle Point Systems Arising from Liquid Crystal Directors Modeling

A New Block Preconditioner for Double Saddle Point Systems Arising from Liquid Crystal Directors Modeling

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