hp-Multigrid as Smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I. Multilevel analysis

  • Authors:

  • J. J. W. Van Der Vegt;S. Rhebergen

  • Affiliations:

  • Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 Enschede, AE, The Netherlands;Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 Enschede, AE, The Netherlands and School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

The hp-Multigrid as Smoother algorithm (hp-MGS) for the solution of higher order accurate space-time discontinuous Galerkin discretizations of advection dominated flows is presented. This algorithm combines p-multigrid with h-multigrid at all p-levels, where the h-multigrid acts as smoother in the p-multigrid. The performance of the hp-MGS algorithm is further improved using semi-coarsening in combination with a new semi-implicit Runge-Kutta method as smoother. A detailed multilevel analysis of the hp-MGS algorithm is presented to obtain more insight into the theoretical performance of the algorithm. As model problem a fourth order accurate space-time discontinuous Galerkin discretization of the advection-diffusion equation is considered. The multilevel analysis shows that the hp-MGS algorithm has excellent convergence rates, both for steady state and time-dependent problems, and low and high cell Reynolds numbers, including highly stretched meshes.