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

• We consider a solver for the discontinuous Galerkin method.
• We use the Symmetric Interior Penalty variant.
• The deflated solver appears to be scalable.
• Our solver is independent of the jump in the coefficients.

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.