TY - JOUR
T1 - Scalable two-level preconditioning and deflation based on a piecewise constant subspace for (SIP)DG systems for diffusion problems
AU - van Slingerland, P.
AU - Vuik, C.
PY - 2015
Y1 - 2015
N2 - This paper is focused on the preconditioned Conjugate Gradient (CG) method for linear systems resulting from Symmetric Interior Penalty (discontinuous) Galerkin (SIPG) discretizations for stationary diffusion problems. In particular, it concerns two-level preconditioning strategies where the coarse space is based on piecewise constant DG basis functions. In this paper, we show that both the two-level preconditioner and the corresponding BNN (or ADEF2) deflation variant yield scalable convergence of the CG method (independent of the mesh element diameter). These theoretical results are illustrated by numerical experiments.
AB - This paper is focused on the preconditioned Conjugate Gradient (CG) method for linear systems resulting from Symmetric Interior Penalty (discontinuous) Galerkin (SIPG) discretizations for stationary diffusion problems. In particular, it concerns two-level preconditioning strategies where the coarse space is based on piecewise constant DG basis functions. In this paper, we show that both the two-level preconditioner and the corresponding BNN (or ADEF2) deflation variant yield scalable convergence of the CG method (independent of the mesh element diameter). These theoretical results are illustrated by numerical experiments.
KW - Conjugate gradient method
KW - Deflation
KW - Diffusion problems
KW - Symmetric interior penalty Galerkin discretization
KW - Two-level preconditioning
UR - http://www.scopus.com/inward/record.url?scp=84907362734&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2014.06.028
DO - 10.1016/j.cam.2014.06.028
M3 - Article
AN - SCOPUS:84907362734
SN - 0377-0427
VL - 275
SP - 61
EP - 78
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
ER -