Hybridized Discontinuous Galerkin Methods for Wave Propagation
Author(s)
Fernandez del Campo, Pablo; Christophe, A.; Terrana, Sebastien; Nguyen, Ngoc C.; Peraire, Jaime
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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, Electromagnetism
Date issued
2018-09-05Department
Massachusetts Institute of Technology. Department of Aeronautics and AstronauticsJournal
Journal of Scientific Computing
Publisher
Springer Science+Business Media
Citation
Fernandez, P. et al. "Hybridized Discontinuous Galerkin Methods for Wave Propagation." Journal of Scientific Computing, vol.77, 3 (December 2018): 1566-1604. © 2018 Springer Science+Business Media
Version: Original manuscript
ISSN
0885-7474
1573-7691
Keywords
Theoretical Computer Science, General Engineering, Computational Theory and Mathematics, Software