Coupling p-multigrid to geometric multigrid for discontinuous Galerkin formulations of the convection–diffusion equation

✍ Scribed by Brendan S. Mascarenhas; Brian T. Helenbrook; Harold L. Atkins

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 360 KB
• Volume: 229
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2010.01.020

✦ Synopsis

An improved p-multigrid algorithm for discontinuous Galerkin (DG) discretizations of convection-diffusion problems is presented. The general p-multigrid algorithm for DG discretizations involves a restriction from the p ¼ 1 to p ¼ 0 discontinuous polynomial solution spaces. This restriction is problematic and has limited the efficiency of the p-multigrid method. For purely diffusive problems, Helenbrook and Atkins have demonstrated rapid convergence using a method that restricts from a discontinuous to continuous polynomial solution space at p ¼ 1. It is shown that this method is not directly applicable to the convection-diffusion (CD) equation because it results in a central-difference discretization for the convective term. To remedy this, ideas from the streamwise upwind Petrov-Galerkin (SUPG) formulation are used to devise a transition from the discontinuous to continuous space at p ¼ 1 that yields an upwind discretization. The results show that the new method converges rapidly for all Peclet numbers.