### Abstract

Original language | English |
---|---|

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 |
---|---|

Publisher | University of Twente, Department of Applied Mathematics |

No. | 1955 |

ISSN (Print) | 1874-4850 |

ISSN (Electronic) | 1874-4850 |

### Fingerprint

### 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

*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.

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*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.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows

T2 - Part I. Multilevel Analysis

AU - van der Vegt, Jacobus J.W.

AU - Rhebergen, Sander

PY - 2011/10

Y1 - 2011/10

N2 - 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.

AB - 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.

KW - METIS-279714

KW - Multigrid algorithms

KW - Runge-Kutta methods

KW - EWI-20657

KW - MSC-65M55

KW - MSC-65M60

KW - Discontinuous Galerkin methods

KW - MSC-76M10

KW - Space-time methods

KW - Fourier analysis

KW - Multi-level analysis

KW - IR-78251

KW - Higher order accurate discretizations

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -