hp-Multigrid as Smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I. Multilevel analysis

作者：van der Vegt J J W^*; Rhebergen S

来源：Journal of Computational Physics, 2012, 231(22): 7537-7563.

DOI：10.1016/j.jcp.2012.05.038

• Multigrid algorithms
• Discontinuous Galerkin methods
• Higher order accurate discretizations
• Space-time methods
• Runge-Kutta methods
• Fourier analysis
• Multilevel analysis

The hp-Multigrid as Smoother algorithm (hp-MGS) for the solution of higher order accurate space-time discontinuous Galerkin discretizations of advection dominated flows is presented. This algorithm combines p-multigrid with h-multigrid at all p-levels, where the h-multigrid acts as smoother in the p-multigrid. The performance of the hp-MGS algorithm is further improved using semi-coarsening in combination with a new semi-implicit Runge-Kutta method as smoother. A detailed multilevel analysis of the hp-MGS algorithm is presented to obtain more insight into the theoretical performance of the algorithm. As model problem a fourth order accurate space-time discontinuous Galerkin discretization of the advection-diffusion equation is considered. The multilevel analysis shows that the hp-MGS algorithm has excellent convergence rates, both for steady state and time-dependent problems, and low and high cell Reynolds numbers, including highly stretched meshes.

• 出版日期2012-9-15