HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I. Multilevel Analysis

Jacobus J.W. van der Vegt, Sander Rhebergen

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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 low and high cell Reynolds numbers and on highly stretched meshes.
Original languageEnglish
Place of PublicationEnschede
PublisherUniversity of Twente, Department of Applied Mathematics
Number of pages35
Publication statusPublished - Oct 2011

Publication series

NameMemorandum / Department of Applied Mathematics
PublisherUniversity of Twente, Department of Applied Mathematics
No.1955
ISSN (Print)1874-4850
ISSN (Electronic)1874-4850

Fingerprint

advection
advection-diffusion equation
analysis
Reynolds number

Keywords

  • METIS-279714
  • Multigrid algorithms
  • Runge-Kutta methods
  • EWI-20657
  • MSC-65M55
  • MSC-65M60
  • Discontinuous Galerkin methods
  • MSC-76M10
  • Space-time methods
  • Fourier analysis
  • Multi-level analysis
  • IR-78251
  • Higher order accurate discretizations

Cite this

van der Vegt, J. J. W., & Rhebergen, S. (2011). HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I. Multilevel Analysis. (Memorandum / Department of Applied Mathematics; No. 1955). Enschede: University of Twente, Department of Applied Mathematics.
van der Vegt, Jacobus J.W. ; Rhebergen, Sander. / HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows : Part I. Multilevel Analysis. Enschede : University of Twente, Department of Applied Mathematics, 2011. 35 p. (Memorandum / Department of Applied Mathematics; 1955).
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van der Vegt, JJW & Rhebergen, S 2011, HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I. Multilevel Analysis. Memorandum / Department of Applied Mathematics, no. 1955, University of Twente, Department of Applied Mathematics, Enschede.

HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows : Part I. Multilevel Analysis. / van der Vegt, Jacobus J.W.; Rhebergen, Sander.

Enschede : University of Twente, Department of Applied Mathematics, 2011. 35 p. (Memorandum / Department of Applied Mathematics; No. 1955).

Research output: Book/ReportReportProfessional

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van der Vegt JJW, Rhebergen S. HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I. Multilevel Analysis. Enschede: University of Twente, Department of Applied Mathematics, 2011. 35 p. (Memorandum / Department of Applied Mathematics; 1955).