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.
|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|
|Number of pages||13|
|Publication status||Published - Aug 2010|
|Name||Notes on Numerical Fluid Mechanics and Multidisciplinary Design|
- Discontinuous Galerkin finite element method