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1,228 citations
...[62]and applied to the edges of a solid....
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...This approach with ψ (x) = 1 has been intensively investigated in the frame of the PUM [117, 16], GFEM [169, 20, 19] and hp-cloud method [66, 62, 136]....
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1,112 citations
...The recognition and use of partition of unity enrichment strategy to solve boundary-value problems with internal boundaries is due to Oden and co-workers [4] [5] [9] [10] ± the numerical technique was coined as the generalized ®nite-element method (GFEM)....
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976 citations
...(2000) [62–71]....
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...One such example is the so-called ‘generalized finite element method’ (GFEM), which was developed based on the partition of unity principle (Duarte et al., 2000; Strouboulis et al., 2000, 2001) [73– 75]....
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...…developed for fracture analysis with minimal or no re-meshing, as reported in Belytschko and Black (1999), Belytschko et al. (2001), Daux et al. (2000), Duarte et al. (2000, 2001), Dolbow et al. (2000), Jirasek and Zimmermann (2001a, b), Mo.es et al. (1999) and Sukumar et al. (2000) [62–71]....
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718 citations
...The first works in GFEM involved global enrichments of the approximation space; however, as early as 2000, local enrichment for singularities at sharp corners were also developed [34]....
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681 citations
...GFEM uses concepts from the partition of unity [11], where...
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5,324 citations
5,049 citations
...[4,5,32]), xa x a, ya, za are the coordinates of the node a, ha is the diameter of the largest ®nite element sharing the node a and N is the number of nodes in the mesh....
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3,276 citations
...The generalized nite element method (GFEM) was proposed independently by Babu ska and colleagues [1,2, 12 ] (under the names special nite element methods, generalized nite element method and nite element partition of unity method) and by Duarte and Oden [6{9, 15] (under the names hp clouds and cloud-based hp nite element method)....
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...In the case of nite element partitions of unity, the clouds ! are simply the union of the nite elements sharing a vertex node (see, for example, [ 12 , 15])....
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...For a more detailed discussion we refer the interested reader to [2, 7, 12 , 15] and the references therein....
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3,082 citations
...Recent surveys on meshless methods can be found in [6,8]....
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2,748 citations
