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

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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).

Abstract

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

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