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Subcell finite volume multigrid preconditioning for high-order discontinuous Galerkin methods

Birken, Philipp LU ; Gassner, Gregor and Versbach, Lea Miko LU (2019) In International Journal of Computational Fluid Dynamics 33(9). p.353-361
Abstract
We suggest a new multigrid preconditioning strategy for use in Jacobian-free Newton–Krylov (JFNK) methods for the solution of algebraic equation systems arising from implicit Discontinuous Galerkin (DG) discretisations. To define the new preconditioner, use is made of an auxiliary first-order finite volume discretisation that refines the original DG mesh, but can still be implemented algebraically. As smoother, we consider the pseudo-time iteration W3 with a symmetric Gauss–Seidel-type approximation of the Jacobian. As a proof of concept numerical tests are presented for the one-dimensional Euler equations, demonstrating the potential of the new approach.
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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
High order methods, Multigrid preconditioner, Discontinuous Galerkin method, finite volume method
in
International Journal of Computational Fluid Dynamics
volume
33
issue
9
pages
9 pages
publisher
Taylor & Francis
external identifiers
  • scopus:85074040074
ISSN
1061-8562
DOI
10.1080/10618562.2019.1667983
project
Efficient Solvers for Space-Time Discontinuous Galerkin Spectral Element Methods
language
English
LU publication?
yes
id
f1a18fbe-d75d-434e-9a6c-77f61f65d656
date added to LUP
2019-09-19 14:36:22
date last changed
2024-01-31 08:33:15
@article{f1a18fbe-d75d-434e-9a6c-77f61f65d656,
  abstract     = {{We suggest a new multigrid preconditioning strategy for use in Jacobian-free Newton–Krylov (JFNK) methods for the solution of algebraic equation systems arising from implicit Discontinuous Galerkin (DG) discretisations. To define the new preconditioner, use is made of an auxiliary first-order finite volume discretisation that refines the original DG mesh, but can still be implemented algebraically. As smoother, we consider the pseudo-time iteration W3 with a symmetric Gauss–Seidel-type approximation of the Jacobian. As a proof of concept numerical tests are presented for the one-dimensional Euler equations, demonstrating the potential of the new approach.}},
  author       = {{Birken, Philipp and Gassner, Gregor and Versbach, Lea Miko}},
  issn         = {{1061-8562}},
  keywords     = {{High order methods; Multigrid preconditioner; Discontinuous Galerkin method; finite volume method}},
  language     = {{eng}},
  month        = {{09}},
  number       = {{9}},
  pages        = {{353--361}},
  publisher    = {{Taylor & Francis}},
  series       = {{International Journal of Computational Fluid Dynamics}},
  title        = {{Subcell finite volume multigrid preconditioning for high-order discontinuous Galerkin methods}},
  url          = {{http://dx.doi.org/10.1080/10618562.2019.1667983}},
  doi          = {{10.1080/10618562.2019.1667983}},
  volume       = {{33}},
  year         = {{2019}},
}