TY - JOUR
T1 - Block triangular preconditioners for linearization schemes of the Rayleigh–Bénard convection problem
AU - Ke, Guoyi
AU - Aulisa, Eugenio
AU - Bornia, Giorgio
AU - Howle, Victoria
N1 - Publisher Copyright:
Copyright © 2017 John Wiley & Sons, Ltd.
PY - 2017/10
Y1 - 2017/10
N2 - In this paper, we compare two block triangular preconditioners for different linearizations of the Rayleigh–Bénard convection problem discretized with finite element methods. The two preconditioners differ in the nested or nonnested use of a certain approximation of the Schur complement associated to the Navier–Stokes block. First, bounds on the generalized eigenvalues are obtained for the preconditioned systems linearized with both Picard and Newton methods. Then, the performance of the proposed preconditioners is studied in terms of computational time. This investigation reveals some inconsistencies in the literature that are hereby discussed. We observe that the nonnested preconditioner works best both for the Picard and for the Newton cases. Therefore, we further investigate its performance by extending its application to a mixed Picard–Newton scheme. Numerical results of two- and three-dimensional cases show that the convergence is robust with respect to the mesh size. We also give a characterization of the performance of the various preconditioned linearization schemes in terms of the Rayleigh number.
AB - In this paper, we compare two block triangular preconditioners for different linearizations of the Rayleigh–Bénard convection problem discretized with finite element methods. The two preconditioners differ in the nested or nonnested use of a certain approximation of the Schur complement associated to the Navier–Stokes block. First, bounds on the generalized eigenvalues are obtained for the preconditioned systems linearized with both Picard and Newton methods. Then, the performance of the proposed preconditioners is studied in terms of computational time. This investigation reveals some inconsistencies in the literature that are hereby discussed. We observe that the nonnested preconditioner works best both for the Picard and for the Newton cases. Therefore, we further investigate its performance by extending its application to a mixed Picard–Newton scheme. Numerical results of two- and three-dimensional cases show that the convergence is robust with respect to the mesh size. We also give a characterization of the performance of the various preconditioned linearization schemes in terms of the Rayleigh number.
KW - Rayleigh–Bénard convection
KW - block preconditioning
KW - finite element methods
KW - incompressible flows
KW - multiphysics
UR - http://www.scopus.com/inward/record.url?scp=85015197447&partnerID=8YFLogxK
U2 - 10.1002/nla.2096
DO - 10.1002/nla.2096
M3 - Article
AN - SCOPUS:85015197447
SN - 1070-5325
VL - 24
JO - Numerical Linear Algebra with Applications
JF - Numerical Linear Algebra with Applications
IS - 5
M1 - e2096
ER -