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

Research output: Contribution to journalArticle


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.


External organisations
  • University of Kassel
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computational Mathematics


  • Three dimensional problems, Preconditioning, Implicit methods, Navier–Stokes, Unsteady flows, Discontinuous Galerkin
Original languageEnglish
Pages (from-to)20-35
JournalJournal of Computational Physics
Publication statusPublished - 2013
Publication categoryResearch
Externally publishedYes

Bibliographic note

The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: External organization(s) (LUR000040), Numerical Analysis (011015004)