\(hp\)-Multigrid as Smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. II: Optimization of the Runge-Kutta smoother

DOI10.1016/j.jcp.2012.05.037zbMath1284.65130OpenAlexW2130038841MaRDI QIDQ2446724

J. J. W. van der Vegt, Sander Rhebergen

Publication date: 22 April 2014

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2012.05.037

zbMATH Keywords

Fourier analysisRunge-Kutta methodsdiscontinuous Galerkin methodsmultilevel analysismultigrid algorithmsspace-time methodshigher order accurate discretizations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55)

Related Items

An efficient adaptive mesh refinement (AMR) algorithm for the discontinuous Galerkin method: applications for the computation of compressible two-phase flows, A fast spectral element solver combining static condensation and multigrid techniques, Time-multipatch discontinuous Galerkin space-time isogeometric analysis of parabolic evolution problems, Robust multigrid for high-order discontinuous Galerkin methods: a fast Poisson solver suitable for high-aspect ratio Cartesian grids, Theoretical and practical aspects of space-time DG-SEM implementations, A space-time hybridizable discontinuous Galerkin method for incompressible flows on deforming domains, Efficient solvers of discontinuous Galerkin discretization for the Cahn-Hilliard equations, \(hp\)-Multigrid as Smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. I: Multilevel analysis, \(p\)-multigrid high-order discontinuous Galerkin solution of compressible flows, Local Fourier Analysis of Multigrid for Hybridized and Embedded Discontinuous Galerkin Methods, Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs, Entropy stable space-time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws, Solution of cavitating compressible flows using discontinuous Galerkin discretisation

Uses Software

• Wesseling
• LFA

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• \(p\)-multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
• Coupling \(p\)-multigrid to geometric multigrid for discontinuous Galerkin formulations of the convection-diffusion equation
• Multigrid methods. Proceedings of the Conference Held at Köln-Porz, November 23-27, 1981
• Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
• Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. I: General formulation.
• \(hp\)-Multigrid as Smoother algorithm for higher order discontinuous Galerkin discretizations of advection dominated flows. I: Multilevel analysis
• \(h\)-multigrid for space-time discontinuous Galerkin discretizations of the compressible Navier-Stokes equations
• High-order discontinuous Galerkin methods using an \(hp\)-multigrid approach
• A \(p\)-multigrid discontinuous Galerkin method for the Euler equations on unstructured grids
• High‐order accuratep‐multigrid discontinuous Galerkin solution of the Euler equations
• On the Solution of Block-Tridiagonal Systems Arising from Certain Finite-Difference Equations