The Discontinuous Enrichment Method

By Charbel Farhat, I. Harari, Leopoldo P. Franca. 2000

400 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/ada76134a8e6ffba2becc34ed6f07c323027e70e

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

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]).”
A survey of finite element methods for time-harmonic acoustics (2006, methodology): “In the discontinuous enrichment method (DEM), standard finite element polynomials are retained for the coarse scales, and enriched within each element by nonconforming free-space homogeneous solutions representing fine scales, with continuity enforced in the variational formulation [85].”
To appear in the ACM SIGGRAPH conference proceedings Modular Bases for Fluid Dynamics (neutral): “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].”
Discontinuous Galerkin methods for non‐linear elasticity (2006, background): “For situations in which a fine microstructure is developed the nonconforming approximation is likely to allow a localized enrichment of the discrete functional space, in the spirit of [20, 18, 13].”
A domain decomposition method for discontinuous Galerkin discretizations of Helmholtz problems with plane waves and Lagrange multipliers (2009, methodology): “In DEM and its DGM variant [8, 22, 25, 23], the latter approach is adopted.”
A comparison of wave‐based discontinuous Galerkin, ultra‐weak and least‐square methods for wave problems (2011, methodology): “At the moment, the choice of discretization for the Lagrange multiplier is based on a set of heuristics proposed in the literature, see for instance [4] and [5].”
Efficiency of high‐order elements for continuous and discontinuous Galerkin methods (2013, methodology): “Nevertheless, even in this case, high order elements are more competitive than low order ones as shown numerically in [9, 10] and also in [20] where a hybrid discontinuous enrichment method [21] is compared with an ultra-weak variational formulation [22] and a partition of unity method [23], the thr”
On methods for stabilizing constraints over enriched interfaces in elasticity (2009, methodology): “The challenge of enforcing constraints across an internal discontinuity produced by an enriched solution field has some similarities to the numerics of other problems, including enforcing Dirichlet constraints on an enriched field and enforcing continuity constraints in meshfree, discontinuous enric”
Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods (2008, methodology): “[20], but in the latter, Lagrange multipliers are used to weakly enforce continuity between enriched and unenriched subdomains.”
The embedded discontinuous Galerkin method: application to linear shell problems (2007, methodology): “Before proving Theorem 2.1, it is worth to briefly compare the EDG method (with Lagrange multipliers ∈Mh continuous on Eh\ D) with two related methods, the multiscale discontinuous Galerkin (MDG) method [37] and the discontinuous enrichment method (DEM) [38].”
Multiscale enrichment based on partition of unity (2005, methodology): “Special functions can be also introduced locally using Lagrange multipliers [ 44 ] or by means of the DG method [40], but the question of stability cannot be easily resolved, and the implementation of such methods requires major changes to existing finite element codes.”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “The special structure of the enrichment differentiates the PUM, GFEM, and XFEM from other methods which add terms to the standard FE approximation such as for example the global-local FEM [130, 134] or the discontinuous enrichment method [39, 72, 99].”