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Multigrid Optimization for Space-Time Discontinuous Galerkin Discretizations of Advection Dominated Flows

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

Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 113))

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.

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Authors and Affiliations

  1. Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    S. Rhebergen & J. J. W. van der Vegt

  2. National Aerospace Laboratory NLR, P.O. Box 90502, 1006 BM, Amsterdam, The Netherlands

    H. van der Ven

Authors
  1. S. Rhebergen
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  2. J. J. W. van der Vegt
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  3. H. van der Ven
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Editor information

Editors and Affiliations

  1. German Aerospace Center (DLR), Braunschweig, Germany

    Norbert Kroll

  2. Airbus Deutschland GmbH, Bremen, Germany

    Heribert Bieler

  3. von Karman Institute for Fluid Dynamics (VKI), Rhode-St-Genese, Belgium

    Herman Deconinck

  4. ONERA, Châtillon, France

    Vincent Couaillier

  5. NLR, Amsterdam, The Netherlands

    Harmen van der Ven

  6. EADS Deutschland, Manching, Germany

    Kaare Sørensen

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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: Kroll, N., Bieler, H., Deconinck, H., Couaillier, V., van der Ven, H., Sørensen, K. (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, vol 113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03707-8_18

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  • DOI: https://doi.org/10.1007/978-3-642-03707-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03706-1

  • Online ISBN: 978-3-642-03707-8

  • eBook Packages: EngineeringEngineering (R0)

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