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Journal of Scientific Computing

, Volume 77, Issue 3, pp 1566–1604 | Cite as

Hybridized Discontinuous Galerkin Methods for Wave Propagation

  • P. Fernandez
  • A. Christophe
  • S. Terrana
  • N. C. Nguyen
  • J. Peraire
Article
  • 82 Downloads

Abstract

We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main features, display numerical results to illustrate their performance, and conclude with bibliography notes. The main ingredients in devising these DG methods are (1) a local Galerkin projection of the underlying partial differential equations at the element level onto spaces of polynomials of degree k to parametrize the numerical solution in terms of the numerical trace; (2) a judicious choice of the numerical flux to provide stability and consistency; and (3) a global jump condition that enforces the continuity of the numerical flux to obtain a global system in terms of the numerical trace. These DG methods are termed hybridized DG methods, because they are amenable to hybridization (static condensation) and hence to more efficient implementations. They share many common advantages of DG methods and possess some unique features that make them well-suited to wave propagation problems.

Keywords

Hybridized discontinuous Galerkin methods Wave propagation Fluids Solids Electrogmagnetism 

Notes

Acknowledgements

The authors acknowledge the Air Force Office of Scientific Research (FA9550-15-1-0276 and FA9550-16-1-0214), the NASA (NNX16AP15A), and Pratt & Whitney for supporting this work. P. Fernandez also acknowledges the financial support from the Zakhartchenko and “la Caixa” Fellowships.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.MIT Department of Aeronautics and AstronauticsCambridgeUSA

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