Numerical Investigation of the Conditioning for Plane Wave Discontinuous Galerkin Methods

  • Scott Congreve
  • Joscha Gedicke
  • Ilaria PerugiaEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


We present a numerical study to investigate the conditioning of the plane wave discontinuous Galerkin discretization of the Helmholtz problem. We provide empirical evidence that the spectral condition number of the plane wave basis on a single element depends algebraically on the mesh size and the wave number, and exponentially on the number of plane wave directions; we also test its dependence on the element shape. We show that the conditioning of the global system can be improved by orthogonalization of the local basis functions with the modified Gram-Schmidt algorithm, which results in significantly fewer GMRES iterations for solving the discrete problem iteratively.



The authors have been funded by the Austrian Science Fund (FWF) through the project P 29197-N32. The third author has also been funded by the FWF through the project F 65.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Scott Congreve
    • 1
  • Joscha Gedicke
    • 1
  • Ilaria Perugia
    • 1
    Email author
  1. 1.University of ViennaFaculty of MathematicsViennaAustria

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