### 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 language | English |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Number of pages | 35 |

Publication status | Published - Oct 2011 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
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Publisher | University of Twente, Department of Applied Mathematics |

No. | 1955 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### 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

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## 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.