Kasimir et al 2021 - Revision history

Move page script: Move page script moved page Birken et al 2021a to Kasimir et al 2021

2021-04-16T14:28:54Z

Move page script moved page Birken et al 2021a to Kasimir et al 2021

Scipediacontent at 07:32, 12 March 2021

2021-03-12T07:32:02Z

Scipediacontent at 07:31, 12 March 2021

2021-03-12T07:31:26Z

Scipediacontent: Scipediacontent moved page Draft Content 286954867 to Birken et al 2021a

2021-03-11T16:31:28Z

Scipediacontent moved page Draft Content 286954867 to Birken et al 2021a

Scipediacontent: Created page with "== Abstract == The goal of our research is the construction of efficient Jacobian-free preconditioners for high order Discontinuous Galerkin (DG) discretizations with implici..."

2021-03-11T16:31:25Z

Created page with "== Abstract == The goal of our research is the construction of efficient Jacobian-free preconditioners for high order Discontinuous Galerkin (DG) discretizations with implici..."

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== 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 (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

== Full document ==
<pdf>Media:Draft_Content_286954867p4700.pdf</pdf>

← Older revision	Revision as of 14:28, 16 April 2021
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 == 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 (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.
+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.
 == Full document ==
 <pdf>Media:Draft_Content_286954867p4700.pdf</pdf>

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