Developments in Overlapping Schwarz Preconditioning of High-Order Nodal Discontinuous Galerkin Discretizations

  • Luke N. Olson
  • Jan S. Hesthaven
  • Lucas C. Wilcox
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 55)


Recent progress has been made to more robustly handle the increased complexity of high-order schemes by focusing on the local nature of the discretization. This locality is particularly true for many Discontinuous Galerkin formulations and is the focus of this paper. The contributions of this paper are twofold. First, novel observations regarding various flux representations in the discontinuous Galerkin formulation are highlighted in the context of overlapping Schwarz methods. Second, we conduct additional experiments using high-order elements for the indefinite Helmholtz equation to expose the impact of overlap.


Coarse Grid Spectral Element Method Interior Penalty Schwarz Method GMRES Iteration 
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© Springer 2007

Authors and Affiliations

  • Luke N. Olson
    • 1
  • Jan S. Hesthaven
    • 1
  • Lucas C. Wilcox
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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