TY - JOUR
T1 - Augmented Lagrangian-based preconditioners for steady buoyancy driven flow
AU - Ke, G.
AU - Aulisa, E.
AU - Dillon, G.
AU - Howle, V.
N1 - Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/8
Y1 - 2018/8
N2 - In this paper, we apply the augmented Lagrangian (AL) approach to steady buoyancy driven flow problems. Two AL preconditioners are developed based on the variable's order, specifically whether the leading variable is the velocity or the temperature variable. Correspondingly, two non-augmented Lagrangian (NAL) preconditioners are also considered for comparison. An eigenvalue analysis for these two pairs of preconditioners is conducted to predict the rate of convergence for the GMRES solver. The numerical results show that the AL preconditioner pair is insensitive with respect to the mesh size, Rayleigh number, and Prandtl number in terms of GMRES iterations, resulting in a significantly more robust preconditioner pair compared to the NAL pair. Accordingly, the AL pair performs much better than the NAL pair in terms of computational time. For the AL pair, the preconditioner with velocity as the leading variable gives slightly better efficiency than the one with temperature as the leading variable.
AB - In this paper, we apply the augmented Lagrangian (AL) approach to steady buoyancy driven flow problems. Two AL preconditioners are developed based on the variable's order, specifically whether the leading variable is the velocity or the temperature variable. Correspondingly, two non-augmented Lagrangian (NAL) preconditioners are also considered for comparison. An eigenvalue analysis for these two pairs of preconditioners is conducted to predict the rate of convergence for the GMRES solver. The numerical results show that the AL preconditioner pair is insensitive with respect to the mesh size, Rayleigh number, and Prandtl number in terms of GMRES iterations, resulting in a significantly more robust preconditioner pair compared to the NAL pair. Accordingly, the AL pair performs much better than the NAL pair in terms of computational time. For the AL pair, the preconditioner with velocity as the leading variable gives slightly better efficiency than the one with temperature as the leading variable.
KW - Augmented Lagrangian preconditioners
KW - Buoyancy driven flow problems
KW - Eigenvalue analysis
KW - Finite element method
UR - http://www.scopus.com/inward/record.url?scp=85042698505&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2018.02.013
DO - 10.1016/j.aml.2018.02.013
M3 - Article
AN - SCOPUS:85042698505
SN - 0893-9659
VL - 82
SP - 1
EP - 7
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
ER -