TY - JOUR
T1 - Field-of-values analysis of preconditioned linearized Rayleigh–Bénard convection problems
AU - Aulisa, Eugenio
AU - Bornia, Giorgio
AU - Howle, Victoria
AU - Ke, Guoyi
N1 - Publisher Copyright:
© 2019
PY - 2020/5/1
Y1 - 2020/5/1
N2 - In this paper we use the notion of field-of-values (FOV) equivalence of matrices to study a class of block-triangular preconditioners for the fixed-point linearization of the Rayleigh–Bénard convection problem discretized with inf–sup stable finite element spaces. First, sufficient conditions on the nondimensional parameters of the problem are determined in order to establish the FOV-equivalence between the system matrix and the preconditioners. Four upper triangular block preconditioners belonging to the general proposed class are then considered. Numerical experiments show that the Generalized Minimal Residual (GMRES) convergence is robust with respect to the mesh size for these preconditioned systems. We also compare the performance of the different preconditioners in terms of computational time.
AB - In this paper we use the notion of field-of-values (FOV) equivalence of matrices to study a class of block-triangular preconditioners for the fixed-point linearization of the Rayleigh–Bénard convection problem discretized with inf–sup stable finite element spaces. First, sufficient conditions on the nondimensional parameters of the problem are determined in order to establish the FOV-equivalence between the system matrix and the preconditioners. Four upper triangular block preconditioners belonging to the general proposed class are then considered. Numerical experiments show that the Generalized Minimal Residual (GMRES) convergence is robust with respect to the mesh size for these preconditioned systems. We also compare the performance of the different preconditioners in terms of computational time.
KW - Block preconditioning
KW - FOV-equivalence
KW - Incompressible flows
KW - Rayleigh–Bénard convection
UR - http://www.scopus.com/inward/record.url?scp=85075390154&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2019.112582
DO - 10.1016/j.cam.2019.112582
M3 - Article
AN - SCOPUS:85075390154
SN - 0377-0427
VL - 369
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 112582
ER -