Two-level Fourier analysis of a multigrid approach for discontinuous Galerkin discretisation
In this paper we study a multigrid method for the solution of a linear second order elliptic equation, discretized by discontinuous Galerkin (DG) methods, andwe give a detailed analysis of the convergence for different block-relaxation strategies.We find that point-wise block-partitioning gives much better results than the classical cell-wise partitioning.Both for the Baumann-Oden and for the symmetric DG method,with and without interior penalty, the block relaxation methods (Jacobi,Gauss-Seidel and symmetric Gauss-Seidel) give excellent smoothing procedures in a classical multigrid setting.Independent of the mesh size, simple MG cycles give convergence factors 0.075 -- 0.4 per iteration sweep for the different discretisation methods studied.
|Iterative methods for linear systems (msc 65F10), Stability and convergence of numerical methods (msc 65N12), Error bounds (msc 65N15), Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (msc 65N30), Multigrid methods; domain decomposition (msc 65N55)|
|Life Sciences (theme 5), Energy (theme 4)|
|Modelling, Analysis and Simulation [MAS]|
Hemker, P.W, Hoffmann, W, & van Raalte, M.H. (2002). Two-level Fourier analysis of a multigrid approach for discontinuous Galerkin discretisation. Modelling, Analysis and Simulation [MAS]. CWI.