HP-Multigrid as Smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part II: Optimization of the Runge-Kutta smoother

Jacobus J.W. van der Vegt, Sander Rhebergen

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    Abstract

    Using a detailed multilevel analysis of the complete hp-Multigrid as Smoother algorithm accurate predictions are obtained of the spectral radius and operator norms of the multigrid error transformation operator. This multilevel analysis is used to optimize the coefficients in the semi-implicit Runge–Kutta smoother, such that the spectral radius of the multigrid error transformation operator is minimal under properly chosen constraints. The Runge–Kutta coefficients for a wide range of cell Reynolds numbers and a detailed analysis of the performance of the hp-MGS algorithm are presented. In addition, the computational complexity of the hp-MGS algorithm is investigated. The hp-MGS algorithm is tested on a fourth order accurate space–time discontinuous Galerkin finite element discretization of the advection–diffusion equation for a number of model problems, which include thin boundary layers and highly stretched meshes, and a non-constant advection velocity. For all test cases excellent multigrid convergence is obtained.
    Original languageEnglish
    Pages (from-to)7564-7583
    Number of pages20
    JournalJournal of computational physics
    Volume231
    Issue number22
    DOIs
    Publication statusPublished - 2012

    Keywords

    • Space–time methods
    • EWI-22712
    • Fourier analysis
    • Multi-level analysis
    • IR-83461
    • Discontinuous Galerkin methods
    • Higher order accurate discretizations
    • Runge–Kutta methods
    • METIS-293255
    • Multigrid algorithms

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