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

Kasimir, Johannes LU ; Versbach, Lea M. LU ; Birken, Philipp LU ; Gassner, Gregor J. and Klöfkorn, Robert LU orcid (2021) 14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020 In World Congress in Computational Mechanics and ECCOMAS Congress 600. p.1-12
Abstract

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... (More)

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.

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Please use this url to cite or link to this publication:
author
; ; ; and
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
keywords
Compressible Flow, Discontinuous Galerkin, Finite Volume, Multigrid Preconditioners
host publication
Fluid Dynamics and Transport Phenomena
series title
World Congress in Computational Mechanics and ECCOMAS Congress
volume
600
pages
12 pages
conference name
14th World Congress of Computational Mechanics and ECCOMAS Congress, WCCM-ECCOMAS 2020
conference location
Virtual, Online
conference dates
2021-01-11 - 2021-01-15
external identifiers
  • scopus:85122067492
DOI
10.23967/wccm-eccomas.2020.212
language
English
LU publication?
yes
id
0b353d5d-eb90-486c-bb42-1562430fec5c
date added to LUP
2022-03-04 10:34:21
date last changed
2022-06-29 14:33:14
@inproceedings{0b353d5d-eb90-486c-bb42-1562430fec5c,
  abstract     = {{<p>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 L<sub>2</sub> 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 L<sub>2</sub> projection from this paper result in the best convergence speed up.</p>}},
  author       = {{Kasimir, Johannes and Versbach, Lea M. and Birken, Philipp and Gassner, Gregor J. and Klöfkorn, Robert}},
  booktitle    = {{Fluid Dynamics and Transport Phenomena}},
  keywords     = {{Compressible Flow; Discontinuous Galerkin; Finite Volume; Multigrid Preconditioners}},
  language     = {{eng}},
  pages        = {{1--12}},
  series       = {{World Congress in Computational Mechanics and ECCOMAS Congress}},
  title        = {{An finite volume based multigrid preconditioner for dg-sem for convection-diffusion}},
  url          = {{http://dx.doi.org/10.23967/wccm-eccomas.2020.212}},
  doi          = {{10.23967/wccm-eccomas.2020.212}},
  volume       = {{600}},
  year         = {{2021}},
}