Discontinuous enrichment in finite elements with a partition of unity method

By John Dolbow, Nicolas Moës, Ted Belytschko. 2000

483 citations recorded by the source corpus.

We present an approximate analytical method to evaluate efficiently and accurately the call blocking probabilities in wavelength routing networks with multiple classes of calls. The model is fairly general and allows each source-destination pair to service calls of different classes, with each call occupying one wavelength per link. Our approximate analytical approach involves two steps. The arrival process of calls on some routes is first modified slightly to obtain an approximate multiclass network model. Next, all classes of calls on a particular route are aggregated to give an equivalent single-class model. Thus, path decomposition algorithms for single-class wavelength routing networks may be readilt extended to the multiclass case. This article is a first step towards understanding the issues arising in wavelength routing networks that serve multiple classes of customers.

Subfields: Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/bdfc0b2e7fdda5e472dffe7ba69ea88d80c5c852

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In Mechanics of Materials

Citations in the corpus

Dynamic crack propagation under mixed-mode loading – Comparison between experiments and X-FEM simulations (2007, methodology): “The eXtended Finite Element Method (X-FEM) (Moës et al., 1999; Dolbow et al., 2000; Belytschko et al., 2001; Réthoré et al., 2005) is chosen for the simulations because the cracks are not described explicitly by the 0020-7683/$ - see front matter 2007 Elsevier Ltd.”
Combined extended and superimposed finite element method for cracks (2004, methodology): “Other applications of step function for elements completely cut by a crack can be found in References [2–5].”
A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries (2006, methodology): “done for each grain following standard techniques [4] (at this stage, nodes that do not pass the area test, as proposed in [32], are not enriched).”
Cracking particles: a simplified meshfree method for arbitrary evolving cracks (2004, methodology): “Experimental data is available, see References [53, 54] or Reference [55], but for different dimensions.”
Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation (2003, methodology): “The X-FEM has been successfully applied to 2-dimensional static and quasi-static crack growth problems (Mo€ e es et al., 1999; Dolbow, 1999; Dolbow et al., 2000a,b; Dolbow et al., 2001; Mo€ e es and Belytschko, 2002), with its extension to modeling holes, and branched and intersecting cracks…”
A discontinuous‐Galerkin‐based immersed boundary method (2008, background): “Though the specific enrichment near the boundary proposed here has not yet been explored, many others have, such as the discontinuous enrichments of Dolbow et al [17] or Chessa and Belytschko [13], or the additional pressure basis functions with discontinuous gradient proposed by Coppola-Owen and Co”
An adaptive spacetime discontinuous Galerkin method for cohesive models of elastodynamic fracture (2010, methodology): “Rather than introduce discontinuity surfaces on element interiors, as in [22, 21, 23], we use adaptive spacetime meshing operations to generate new cohesive surfaces in the SDG discretization that align with evolving crack trajectories.”
Element‐local level set method for three‐dimensional dynamic crack growth (2009, methodology): “[9] introduced step function enrichments for the finite element basis that can model discontinuities independent of the mesh topology and called the method XFEM.”
eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfaces (2010, methodology): “On this gure, the reference response surface is obtained with a collection of deterministic X-FEM computations for dierent positions of the hal-00455646, version 1 -11 Feb 2010 EXTENDED STOCHASTIC FINITE ELEMENT METHOD 19 interface (with a ψ 1 enrichment).”
A three dimensional large deformation meshfree method for arbitrary evolving cracks (2007, methodology): “To describe this discontinuity, the displacement is decomposed into continuous and discontinuous parts as in [3, 19, 30]: u(X, t) = u(X, t) + u(X, t) (9)”
A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries (2012, methodology): “: +1 217 244 7648; fax E-mail address: geubelle@illinois.edu (P.H. Geubel a b s t r a c t An interface-enriched generalized finite element method (GFEM) is introduced for 3D problems with discontinuous gradient fields.”
Modeling three‐dimensional crack propagation—A comparison of crack path tracking strategies (2008, methodology): “To overcome this deficiency, Belytschko and co-workers [7, 8] introduced a technique to successfully capture smooth failure surfaces: the celebrated extended finite element method.”