A two-parameter block triangular preconditioner for double saddle point problem arising from liquid crystal directors modeling

To improve the performance of block triangular (BT) preconditioner, we develop a two-parameter BT (TPBT) preconditioner for a double saddle point problem arising from liquid crystal directors modeling. Theoretical analysis shows that all the eigenvalues of the TPBT preconditioned coefficient matrix...

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Bibliographic Details
Published in:Numerical algorithms 2022-03, Vol.89 (3), p.987-1006
Main Authors: Zhu, Jun-Li, Wu, Yu-Jiang, Yang, Ai-Li
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Computer Science
Crystals
Efficiency
Eigenvalues
Iterative methods
Lagrange multiplier
Liquid crystals
Mathematical models
Numeric Computing
Numerical Analysis
Original Paper
Parameters
Polynomials
Saddle points
Theory of Computation
Upper bounds
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Summary:To improve the performance of block triangular (BT) preconditioner, we develop a two-parameter BT (TPBT) preconditioner for a double saddle point problem arising from liquid crystal directors modeling. Theoretical analysis shows that all the eigenvalues of the TPBT preconditioned coefficient matrix are real and located in an interval (0, 2) no matter which value the spectral radius of matrix D − 1 C A − 1 C T is chosen. Moreover, an upper bound of the degree of the minimal polynomial of the TPBT preconditioned coefficient matrix is also obtained. Inasmuch as the efficiency of the TPBT preconditioner depends on the values of its parameters, we further derive a class of fast and effective formulas to compute the quasi-optimal values of the parameters involved in the TPBT preconditioner. Finally, numerical results are reported to illustrate the feasibility and the efficiency of the TPBT preconditioner.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-021-01142-5