A discontinuous Galerkin method with Lagrange multipliers for the solution of Helmholtz problems in the mid-frequency regime

By Charbel Farhat, I. Harari, U. Hetmaniuk. 2003

272 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/fb87fa4110e0ac65400f37420739a30dafbc7c06

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Hybridizable discontinuous Galerkin p‐adaptivity for wave propagation problems (2013, background): “Embedding the oscillatory behavior of the solution in the approximating functions is another option to improve accuracy, see for instance [6, 7, 8, 9, 10, 11, 12].”
PLANE WAVE DISCONTINUOUS GALERKIN METHODS: ANALYSIS OF THE h-VERSION ∗, ∗∗ (2009, methodology): “This has been attempted in the partition of unity (PUM) finite element method [3,20,25,26,28], the discontinuous enrichment approach [14,15,33], in the context of least squares approaches [27,32], and in the so-called “Variational Theory of Complex Rays” (VTCR) approach [29].”
A Numerical Study on the Weak Galerkin Method for the Helmholtz Equation (2013, methodology): “To the end of alleviating the pollution eﬀect, various continuous or discontinuous ﬁnite element methods have been developed in the literature for solving the Helmholtz equation with large wave numbers [4, 5, 26, 27, 8, 9, 16, 17, 18, 3, 12, 14, 15, 20].”
A comparison of wave‐based discontinuous Galerkin, ultra‐weak and least‐square methods for wave problems (2011, methodology): “First, a general system of first-order conservation equations is considered here whereas the method in [8] is devised for the case of a scalar second-order equation.”
Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods (2008, unknown): “[20, 23].”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “For more information on the DEM, the interested reader is refered to works by Farhat and coworkers [72, 41, 40, 99, 140, 145, 107].”
A Plane Wave Virtual Element Method for the Helmholtz Problem (2015, background): “, [22, 23, 33, 48]); through weighted residual formulations (like in the variational theory of complex rays [35, 45], or in the wave based method [20, 21]).”
To appear in the ACM SIGGRAPH conference proceedings Modular Bases for Fluid Dynamics (unknown): “To enforce coupling constraints arising on the boundaries between subdomains, one can add penalty terms [Farhat et al. 2001; Farhat et al. 2003; Tezaur et al. 2008; Zhang et al. 2006], or enforce strict compliance via Lagrange multipliers [Babuška 1973; Farhat et al. 2000; Tezaur and Farhat 2006].”
A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers (2009, methodology): “However, as was observed in [9, 13, 22], the accuracy of the solution delivered by DEM is significantly higher than that delivered by the standard finite element method of comparable order of convergence.”
High‐order continuous and discontinuous Galerkin methods for wave problems (2013, methodology): “Two DG methods are studied: compact discontinuous Galerkin (CDG) [34] because it introduces the smallest stencil, as interior penalty [32], and hybridizable discontinuous Galerkin (HDG) [35–37, 40] because it reduces the global solve to the DOF on the sides —similarly to CG with static condensation,”