An finite volume based multigrid preconditioner for dg-sem for convection-diffusion

Johannes Kasimir, Lea M. Versbach, Philipp Birken, Gregor J. Gassner, Robert Klöfkorn

Research output: Chapter in Book/Report/Conference proceedingPaper in conference proceedingpeer-review


The goal of our research is the construction of efficient Jacobian-free preconditioners for high order Discontinuous Galerkin (DG) discretizations with implicit time integration. We are motivated by three-dimensional unsteady compressible flow applications, which often result in large stiff systems. Implicit time integrators overcome the impact upon restrictive CFL conditions on explicit ones but leave the problem to solve huge nonlinear systems. In this paper we consider a multigrid preconditioning strategy for Jacobian-free Newton-Krylov (JFNK) methods for the solution of algebraic equation systems arising from implicit Discontinuous Galerkin (DG) discretizations. The preconditioner is defined by an auxiliary first order Finite Volume (FV) discretization that refines the original DG mesh, but can still be implemented algebraically. Different options exist to define the grid transfer between DG and FV. We suggest an ad hoc assignment of the unknowns as well as L2 projections. We present new numerical results for the two-dimensional convection-diffusion equation in combination with the different transfer options, which demonstrate the quality and efficiency of the suggested preconditioner with regards to convergence speed up and CPU time. The suggested L2 projection from this paper result in the best convergence speed up.

Original languageEnglish
Title of host publicationFluid Dynamics and Transport Phenomena
Number of pages12
Publication statusPublished - 2021
Event14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020 - Virtual, Online
Duration: 2021 Jan 112021 Jan 15

Publication series

NameWorld Congress in Computational Mechanics and ECCOMAS Congress


Conference14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020
CityVirtual, Online

Subject classification (UKÄ)

  • Computational Mathematics

Free keywords

  • Compressible Flow
  • Discontinuous Galerkin
  • Finite Volume
  • Multigrid Preconditioners


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