On the elimination of quadrature subcells for discontinuous functions in the eXtended Finite‐Element Method

By Giulio Ventura. 2006

227 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2c2896e29c44e7eeb0b2810dc7186614f0ef968c

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements (2009, background): “This leads to the following: upon mapping into the master element, an initially straight discontinuity may become curved (Ventura 2006); being the opposite also true.”
The extended/generalized finite element method: An overview of the method and its applications (2010, methodology): “This is the motivation for the description of the crack morphology by vector level-sets as proposed by Ventura et al. [192, 189] in the context of enriched methods and two-dimensional applications.”
The p-Version of the Finite Element and Finite Cell Methods (2017, background): “, 2013; Sudhakar and Wall, 2013) or the integrand (Ventura, 2006; Ventura and Benvenuti, 2014) to regain the accuracy of the integration.”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, background): “The numerical integration for elements cut by the discontinuity or containing the crack tip requires subdivision, except for very special cases [45].”
Extended finite element method with global enrichment (2015, methodology): “Other drawbacks of the method include blending problems between the enriched and the standard part of the approximation for which several solutions have been given [27,28,29,30,31,32] and problems in numerical integration which can be dealt with by using techniques such as element partitioning and s”
Local enrichment of the finite cell method for problems with material interfaces (2013, methodology): “Concerning the accurate integration on the cut cells, other approaches such as the estimation of the discontinuous integrands with the continuous functions [35–37], or local mesh generation are also applicable [38–40].”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, unknown): “…algorithms have also been devised for polynomial-precision quadrature rules that integrate discontinuous functions on either side of the crack (Ventura 2006; Holdych et al. 2008; Mousavi and Sukumar 2010b; Ventura and Benvenuti 2015); however, these approaches are still the subject of current…”
Equivalent polynomials for quadrature in Heaviside function enriched elements (2015, methodology): “This was accomplished by different techniques (including the use of the divergence theorem) in [11].”