@book{ebcc59aa446b4b259916d96ddfb28d49,

title = "HP-multigrid as smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows: Part I. Multilevel Analysis",

abstract = "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 low and high cell Reynolds numbers and on highly stretched meshes.",

keywords = "METIS-279714, Multigrid algorithms, Runge-Kutta methods, EWI-20657, MSC-65M55, MSC-65M60, Discontinuous Galerkin methods, MSC-76M10, Space-time methods, Fourier analysis, Multi-level analysis, IR-78251, Higher order accurate discretizations",

author = "{van der Vegt}, {Jacobus J.W.} and Sander Rhebergen",

year = "2011",

month = oct,

language = "English",

series = "Memorandum / Department of Applied Mathematics",

publisher = "University of Twente",

number = "1955",

address = "Netherlands",

}