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A Domain Decomposition Solver for the Discontinuous Enrichment Method for the Helmholtz Equation

  • Charbel Farhat
  • Radek Tezaur
  • Jari Toivanen
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 91)

Abstract

The discontinuous enrichment method (DEM) [4] for the Helmholtz equation approximates the solution as a sum of a piecewise polynomial continuous function and element-wise supported plane waves [5]. A weak continuity of the plane wave part is enforced using Lagrangemultipliers. The plane wave enrichment improves the accuracy of solutions considerably. In the mid-frequency range, severalfold savings in terms of degrees of freedom over comparable higher order polynomial discretizations have been observed, which translates into even larger savings in compute time [6, 9]. The partition of unity method [8] and the ultra weak variational formulation [1] also employ plane waves in the construction of discretizations. It was shown recently in [10] that DEM without the polynomial field is computationally more efficient than these methods.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Aeronautics & AstronauticsStanford UniversityStanfordUSA

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