Scalable two-level preconditioning and deflation based on a piecewise constant subspace for (SIP)DG systems for diffusion problems

van Slingerland, P.; Vuik, Cornelis

Scalable two-level preconditioning and deflation based on a piecewise constant subspace for (SIP)DG systems for diffusion problems

Journal article (2015)

Authors

P. van Slingerland Numerical Analysis -

Cornelis Vuik Numerical Analysis -

Research Group

Numerical Analysis () (TU Delft)

Deflation Two-level preconditioning Conjugate gradient method Diffusion problems Symmetric interior penalty Galerkin discretization

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Published Date

2015

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

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.