A new block triangular preconditioner for three-by-three block saddle-point problem

Jun Li; Xiangtuan Xiong

Applications of Mathematics (2024)

  • Volume: 69, Issue: 1, page 67-91
  • ISSN: 0862-7940

Abstract

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In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties are also discussed. Finally, numerical experiments are provided to show the effectiveness of the NBT preconditioner.

How to cite

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Li, Jun, and Xiong, Xiangtuan. "A new block triangular preconditioner for three-by-three block saddle-point problem." Applications of Mathematics 69.1 (2024): 67-91. <http://eudml.org/doc/299204>.

@article{Li2024,
abstract = {In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties are also discussed. Finally, numerical experiments are provided to show the effectiveness of the NBT preconditioner.},
author = {Li, Jun, Xiong, Xiangtuan},
journal = {Applications of Mathematics},
keywords = {three-by-three block saddle-point problems; matrix splitting; convergence; preconditioning; GMRES method},
language = {eng},
number = {1},
pages = {67-91},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A new block triangular preconditioner for three-by-three block saddle-point problem},
url = {http://eudml.org/doc/299204},
volume = {69},
year = {2024},
}

TY - JOUR
AU - Li, Jun
AU - Xiong, Xiangtuan
TI - A new block triangular preconditioner for three-by-three block saddle-point problem
JO - Applications of Mathematics
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 69
IS - 1
SP - 67
EP - 91
AB - In this paper, to solve the three-by-three block saddle-point problem, a new block triangular (NBT) preconditioner is established, which can effectively avoid the solving difficulty that the coefficient matrices of linear subsystems are Schur complement matrices when the block preconditioner is applied to the Krylov subspace method. Theoretical analysis shows that the iteration method produced by the NBT preconditioner is unconditionally convergent. Besides, some spectral properties are also discussed. Finally, numerical experiments are provided to show the effectiveness of the NBT preconditioner.
LA - eng
KW - three-by-three block saddle-point problems; matrix splitting; convergence; preconditioning; GMRES method
UR - http://eudml.org/doc/299204
ER -

References

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