A non-conformal eXtended Finite Element approach: Integral matching Xfem
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Cited by (22)
Crack analysis using numerical manifold method with strain smoothing technique and corrected approximation for blending elements
2020, Engineering Analysis with Boundary ElementsCitation Excerpt :In the blending elements, the partition of unity is not satisfied, and thus unwanted terms are introduced in the approximation, degrading the accuracy of XFEM significantly. The problem arising from blending elements has been widely discussed in XFEM and several modifications have been made to improve the performance [2,28,29]. In NMM, blending elements related problems for material discontinuities has been discussed by An et al. [80].
Interface solutions of partial differential equations with point singularity
2019, Journal of Computational and Applied MathematicsA unified enrichment approach addressing blending and conditioning issues in enriched finite elements
2019, Computer Methods in Applied Mechanics and EngineeringStable GFEM (SGFEM): Improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics
2015, Computer Methods in Applied Mechanics and EngineeringCitation Excerpt :The GFEM/XFEM relies on the enrichment of approximation spaces with a priori selected functions in localized sub-domains of the analysis domain for accurate response prediction in those regions. This leads to finite elements which are only partially enriched—the so-called blending elements [20,10,21–26]. The discretization error in these elements are, in general, higher than in non-blending elements.
The Orthonormalized Generalized Finite Element Method-OGFEM: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions
2015, Computer Methods in Applied Mechanics and EngineeringCitation Excerpt :In applications where discontinuities, singularities and/or large gradients have a local character, these enrichments can be merely employed locally. Unfortunately, this strategy does not always lead to a further improvement of the computational efficiency since a local enrichment introduces so-called blending elements which reduce the convergence rate [11–18]. Furthermore, the numerical solution obtained with the GFEM/XFEM is often perturbed by round-off errors as a result of an ill-conditioned stiffness matrix [11,15,19–35].
DIC identification and X-FEM simulation of fatigue crack growth based on the Williams' series
2015, International Journal of Solids and StructuresCitation Excerpt :Therefore, this analytical patch is made compatible with a localized multigrid approach (Passieux et al., 2010). This integral matching avoids half-enriched elements (often called blending elements) that come from the partition of unity method (Chahine et al., 2011). By comparison with the HAX-FEM (Réthoré et al., 2010) overlapping method, such a matching improves the accuracy of the solution, in particular the SIF evaluation.