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Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations

Birken, Philipp LU ; Gregor, Gassner; Mark, Haas and Claus-Dieter, Munz (2013) In Journal of Computational Physics 240. p.20-35
Abstract
We compare different block preconditioners in the context of parallel time adaptive higher order implicit time integration using Jacobian-free Newton–Krylov (JFNK) solvers for discontinuous Galerkin (DG) discretizations of the three dimensional time dependent Navier–Stokes equations. A special emphasis of this work is the performance for a relative high number of processors, i.e. with a low number of elements on the processor. For high order DG discretizations, a particular problem that needs to be addressed is the size of the blocks in the Jacobian. Thus, we propose a new class of preconditioners that exploits the hierarchy of modal basis functions and introduces a flexible order of the off-diagonal Jacobian blocks. While the standard... (More)
We compare different block preconditioners in the context of parallel time adaptive higher order implicit time integration using Jacobian-free Newton–Krylov (JFNK) solvers for discontinuous Galerkin (DG) discretizations of the three dimensional time dependent Navier–Stokes equations. A special emphasis of this work is the performance for a relative high number of processors, i.e. with a low number of elements on the processor. For high order DG discretizations, a particular problem that needs to be addressed is the size of the blocks in the Jacobian. Thus, we propose a new class of preconditioners that exploits the hierarchy of modal basis functions and introduces a flexible order of the off-diagonal Jacobian blocks. While the standard preconditioners ‘block Jacobi’ (no off-blocks) and full symmetric Gauss–Seidel (full off-blocks) are included as special cases, the reduction of the off-block order results in the new scheme ROBO-SGS. This allows us to investigate the impact of the preconditioner’s sparsity pattern with respect to the computational performance. Since the number of iterations is not well suited to judge the efficiency of a preconditioner, we additionally consider CPU time for the comparisons. We found that both block Jacobi and ROBO-SGS have good overall performance and good strong parallel scaling behavior. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Three dimensional problems, Preconditioning, Implicit methods, Navier–Stokes, Unsteady flows, Discontinuous Galerkin
in
Journal of Computational Physics
volume
240
pages
20 - 35
publisher
Elsevier
external identifiers
  • Scopus:84874462327
ISSN
0021-9991
DOI
10.1016/j.jcp.2013.01.004
language
English
LU publication?
no
id
972dad84-a206-49ff-9830-79fdea6345ba (old id 7862234)
date added to LUP
2015-09-09 10:43:13
date last changed
2016-10-13 04:47:02
@misc{972dad84-a206-49ff-9830-79fdea6345ba,
  abstract     = {We compare different block preconditioners in the context of parallel time adaptive higher order implicit time integration using Jacobian-free Newton–Krylov (JFNK) solvers for discontinuous Galerkin (DG) discretizations of the three dimensional time dependent Navier–Stokes equations. A special emphasis of this work is the performance for a relative high number of processors, i.e. with a low number of elements on the processor. For high order DG discretizations, a particular problem that needs to be addressed is the size of the blocks in the Jacobian. Thus, we propose a new class of preconditioners that exploits the hierarchy of modal basis functions and introduces a flexible order of the off-diagonal Jacobian blocks. While the standard preconditioners ‘block Jacobi’ (no off-blocks) and full symmetric Gauss–Seidel (full off-blocks) are included as special cases, the reduction of the off-block order results in the new scheme ROBO-SGS. This allows us to investigate the impact of the preconditioner’s sparsity pattern with respect to the computational performance. Since the number of iterations is not well suited to judge the efficiency of a preconditioner, we additionally consider CPU time for the comparisons. We found that both block Jacobi and ROBO-SGS have good overall performance and good strong parallel scaling behavior.},
  author       = {Birken, Philipp and Gregor, Gassner and Mark, Haas and Claus-Dieter, Munz},
  issn         = {0021-9991},
  keyword      = {Three dimensional problems,Preconditioning,Implicit methods,Navier–Stokes,Unsteady flows,Discontinuous Galerkin},
  language     = {eng},
  pages        = {20--35},
  publisher    = {ARRAY(0x9c2e208)},
  series       = {Journal of Computational Physics},
  title        = {Preconditioning for modal discontinuous Galerkin methods for unsteady 3D Navier-Stokes equations},
  url          = {http://dx.doi.org/10.1016/j.jcp.2013.01.004},
  volume       = {240},
  year         = {2013},
}