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Solving double saddle point problems via three-parameter preconditioning method with physical application

delete2025-09-22
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PRE
AI
Q
Qin, Junquan
J
Jun Li *
DOI：10.1002/zamm.70221delete
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Abstract

Abstract

En 中文
In this work, a three-parameter (TP) preconditioner, as a generalization of the block preconditioner proposed by Chen et al. (F. Chen, B.-C. Ren, Appl. Math. Lett. 136, [2023], 108445), is established for solving the double saddle point problems. The new preconditioner has two distinct features: (i) the iteration method produced by the TP preconditioner is unconditionally convergent, and (ii) it is different from the block preconditioner in that the corresponding residual equation can avoid solving the linear subsystem with coefficient matrix being Schur complement matrix. Next, the selection of three parameters is discussed in details by adopting the strategy of making the eigenvalue distribution of the preconditioned matrix more clustered. Numerical examples arising from the liquid crystal directors model and the mixed Stokes-Darcy model are given to show the efficiency of the proposed preconditioner.
Keywords:
ITERATIVE METHODS
FORMULATION
PARAMETER

Journal

Z
ZAMM-Zeitschrift fur Angewandte Mathematik und Mechanik
IF:
3.2
Papers:
255
Citations:
5.5K

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