Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows

Sander Rhebergen; Jacobus J.W. van der Vegt; H. van der Ven

doi:10.1007/978-3-642-03707-8_18

Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows

Sander Rhebergen, Jacobus J.W. van der Vegt, H. van der Ven

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

5 Citations (Scopus)

198 Downloads (Pure)

Abstract

The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of two- and three-level multigrid algorithms. This gives the spectral radius of the error transformation operator which predicts the asymptotic rate of convergence of the multigrid algorithm. In the optimization process we therefore choose to minimize the spectral radius of the error transformation operator. We specifically consider optimizing h-multigrid methods with explicit Runge-Kutta type smoothers for second and third order accurate space-time discontinuous Galerkin finite element discretizations of the 2D advection-diffusion equation. The optimized schemes are compared with current h-multigrid techniques employing Runge-Kutta type smoothers. Also, the efficiency of h-, p- and hp-multigrid methods for solving the Euler equations of gas dynamics with a higher order accurate space-time DG method is investigated.

Original language	Undefined
Title of host publication	ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications
Editors	Norbert Kroll, Heribert Bieler, Herman Deconinck, Vincent Couallier, Harmen van der Ven, Kaare Sorensen
Place of Publication	Berlin
Publisher	Springer
Pages	257-269
Number of pages	13
ISBN (Print)	978-3-642-03706-1
DOIs	https://doi.org/10.1007/978-3-642-03707-8_18
Publication status	Published - Aug 2010

Publication series

Name	Notes on Numerical Fluid Mechanics and Multidisciplinary Design
Publisher	Springer-Verlag
Number	113
Volume	113

Keywords

IR-73356
METIS-270769
EWI-17723
Multigrid
Discontinuous Galerkin finite element method

Access to Document

10.1007/978-3-642-03707-8_18

Cite this

Rhebergen, S., van der Vegt, J. J. W., & van der Ven, H. (2010). Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows. In N. Kroll, H. Bieler, H. Deconinck, V. Couallier, H. van der Ven, & K. Sorensen (Eds.), ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications (pp. 257-269). (Notes on Numerical Fluid Mechanics and Multidisciplinary Design; Vol. 113, No. 113). Springer. https://doi.org/10.1007/978-3-642-03707-8_18

Rhebergen, Sander ; van der Vegt, Jacobus J.W. ; van der Ven, H. / Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows. ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications. editor / Norbert Kroll ; Heribert Bieler ; Herman Deconinck ; Vincent Couallier ; Harmen van der Ven ; Kaare Sorensen. Berlin : Springer, 2010. pp. 257-269 (Notes on Numerical Fluid Mechanics and Multidisciplinary Design; 113).

@inbook{7a1e566625a942f697fd7990467ed42c,

title = "Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows",

abstract = "The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of two- and three-level multigrid algorithms. This gives the spectral radius of the error transformation operator which predicts the asymptotic rate of convergence of the multigrid algorithm. In the optimization process we therefore choose to minimize the spectral radius of the error transformation operator. We specifically consider optimizing h-multigrid methods with explicit Runge-Kutta type smoothers for second and third order accurate space-time discontinuous Galerkin finite element discretizations of the 2D advection-diffusion equation. The optimized schemes are compared with current h-multigrid techniques employing Runge-Kutta type smoothers. Also, the efficiency of h-, p- and hp-multigrid methods for solving the Euler equations of gas dynamics with a higher order accurate space-time DG method is investigated.",

keywords = "IR-73356, METIS-270769, EWI-17723, Multigrid, Discontinuous Galerkin finite element method",

author = "Sander Rhebergen and {van der Vegt}, {Jacobus J.W.} and {van der Ven}, H.",

note = "10.1007/978-3-642-03707-8_18 ",

year = "2010",

month = aug,

doi = "10.1007/978-3-642-03707-8_18",

language = "Undefined",

isbn = "978-3-642-03706-1",

series = "Notes on Numerical Fluid Mechanics and Multidisciplinary Design",

publisher = "Springer",

number = "113",

pages = "257--269",

editor = "Norbert Kroll and Heribert Bieler and Herman Deconinck and Vincent Couallier and {van der Ven}, Harmen and Kaare Sorensen",

booktitle = "ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications",

address = "Germany",

}

Rhebergen, S, van der Vegt, JJW & van der Ven, H 2010, Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows. in N Kroll, H Bieler, H Deconinck, V Couallier, H van der Ven & K Sorensen (eds), ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, no. 113, vol. 113, Springer, Berlin, pp. 257-269. https://doi.org/10.1007/978-3-642-03707-8_18

Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows. / Rhebergen, Sander; van der Vegt, Jacobus J.W.; van der Ven, H.
ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications. ed. / Norbert Kroll; Heribert Bieler; Herman Deconinck; Vincent Couallier; Harmen van der Ven; Kaare Sorensen. Berlin: Springer, 2010. p. 257-269 (Notes on Numerical Fluid Mechanics and Multidisciplinary Design; Vol. 113, No. 113).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

TY - CHAP

T1 - Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows

AU - Rhebergen, Sander

AU - van der Vegt, Jacobus J.W.

AU - van der Ven, H.

N1 - 10.1007/978-3-642-03707-8_18

PY - 2010/8

Y1 - 2010/8

N2 - The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of two- and three-level multigrid algorithms. This gives the spectral radius of the error transformation operator which predicts the asymptotic rate of convergence of the multigrid algorithm. In the optimization process we therefore choose to minimize the spectral radius of the error transformation operator. We specifically consider optimizing h-multigrid methods with explicit Runge-Kutta type smoothers for second and third order accurate space-time discontinuous Galerkin finite element discretizations of the 2D advection-diffusion equation. The optimized schemes are compared with current h-multigrid techniques employing Runge-Kutta type smoothers. Also, the efficiency of h-, p- and hp-multigrid methods for solving the Euler equations of gas dynamics with a higher order accurate space-time DG method is investigated.

AB - The goal of this research is to optimize multigrid methods for higher order accurate space-time discontinuous Galerkin discretizations. The main analysis tool is discrete Fourier analysis of two- and three-level multigrid algorithms. This gives the spectral radius of the error transformation operator which predicts the asymptotic rate of convergence of the multigrid algorithm. In the optimization process we therefore choose to minimize the spectral radius of the error transformation operator. We specifically consider optimizing h-multigrid methods with explicit Runge-Kutta type smoothers for second and third order accurate space-time discontinuous Galerkin finite element discretizations of the 2D advection-diffusion equation. The optimized schemes are compared with current h-multigrid techniques employing Runge-Kutta type smoothers. Also, the efficiency of h-, p- and hp-multigrid methods for solving the Euler equations of gas dynamics with a higher order accurate space-time DG method is investigated.

KW - IR-73356

KW - METIS-270769

KW - EWI-17723

KW - Multigrid

KW - Discontinuous Galerkin finite element method

U2 - 10.1007/978-3-642-03707-8_18

DO - 10.1007/978-3-642-03707-8_18

M3 - Chapter

SN - 978-3-642-03706-1

T3 - Notes on Numerical Fluid Mechanics and Multidisciplinary Design

SP - 257

EP - 269

BT - ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications

A2 - Kroll, Norbert

A2 - Bieler, Heribert

A2 - Deconinck, Herman

A2 - Couallier, Vincent

A2 - van der Ven, Harmen

A2 - Sorensen, Kaare

PB - Springer

CY - Berlin

ER -

Rhebergen S, van der Vegt JJW, van der Ven H. Multigrid optimization for space-time discontinuous Galerkin discretizations of advection dominated flows. In Kroll N, Bieler H, Deconinck H, Couallier V, van der Ven H, Sorensen K, editors, ADIGMA - A European Initiative on the Development of Adaptive Higher-Order Variational Methods for Aerospace Applications. Berlin: Springer. 2010. p. 257-269. (Notes on Numerical Fluid Mechanics and Multidisciplinary Design; 113). doi: 10.1007/978-3-642-03707-8_18