NURBS swMATH ID: 2633 Software Authors: Legrain, Grégory Description: A NURBS enhanced extended finite element approach for unfitted CAD analysis. A NURBS enhanced extended finite element approach is proposed for the unfitted simulation of structures defined by means of CAD parametric surfaces. In contrast to classical X-FEM that uses levelsets to define the geometry of the computational domain, exact CAD description is considered here. Following the ideas developed in the context of the NURBS-enhanced finite element method, NURBS-enhanced subelements are defined to take into account the exact geometry of the interface inside an element. In addition, a high-order approximation is considered to allow for large elements compared to the size of the geometrical details (without loss of accuracy). Finally, a geometrically implicit/explicit approach is proposed for efficiency purpose in the context of fracture mechanics. In this paper, only 2D examples are considered: It is shown that optimal rates of convergence are obtained without the need to consider shape functions defined in the physical space. Moreover, thanks to the flexibility given by the Partition of Unity, it is possible to recover optimal convergence rates in the case of re-entrant corners, cracks and embedded material interfaces. Homepage: http://link.springer.com/article/10.1007%2Fs00466-013-0854-7 Keywords: X-FEM; NURBS-enhanced FEM; partition of unity; CAD Related Software: ISOGAT; CutFEM; GeoPDEs; Matlab; EBF3PanelOpt; SciPy; XFEM; FCMLab; LBFGS-B; TRON; SymPy; LAPACK; ParaView; FreeHyTE; Optimization Toolbox; rbMIT; DFVLR-SQP; IETI; polyquad; fminsearch Cited in: 27 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A NURBS enhanced extended finite element approach for unfitted CAD analysis. Zbl 1311.65017Legrain, Grégory 2013 all top 5 Cited by 79 Authors 3 Sevilla, Ruben 2 Bouclier, Robin 2 Geubelle, Philippe H. 2 Legrain, Gregory 2 Marco, Onofre 2 Najafi, Ahmad R. 2 Rabczuk, Timon 2 Safdari, Masoud 2 Schillinger, Dominik 1 Anitescu, Cosmin 1 Annavarapu, Chandrasekhar 1 Arias, Irene 1 Arroyo, Marino 1 Audoux, Yohann 1 Barbieri, Ettore 1 Bayesteh, H. 1 Behr, Marek A. 1 Bletzinger, Kai-Uwe 1 Bordas, Stéphane Pierre Alain 1 Chang, Xiaolin 1 Chanon, Ondine 1 Chen, Chong 1 Chen, Xudong 1 Cheng, Yonggang 1 Codony, David 1 Coelho, Marianna 1 Dede’, Luca 1 DeSimone, Antonio 1 Do Nguyen Van Vuong 1 Elgeti, Stefanie 1 Elguedj, Thomas 1 Fernández-Méndez, Sonia 1 Gervasio, Paola 1 Heltai, Luca 1 Hirschler, Thomas 1 Huerta, Antonio 1 Jiang, Wen 1 Kollmannsberger, Stefan 1 Kudela, László 1 Lin, Gao 1 Liu, Biao 1 Liu, Jun 1 Liu, Yingjie 1 Ma, Gang 1 Mohammdi, S. 1 Montemurro, Marco 1 Morlier, Joseph 1 Nguyen, Lam H. 1 Nguyen, Vinh Phu 1 Ong, Thanh Hai 1 Ostermeyer, Georg-Peter 1 Pailhès, Jérôme 1 Pan, Qing 1 Passieux, Jean-Charles 1 Quarteroni, Alfio M. 1 Rank, Ernst 1 Ródenas, Juan José 1 Roehl, Deane M. 1 Ruess, Martin 1 Shen, Ruyi 1 Song, Gan 1 Sottos, Nancy R. 1 Stavrev, Atanas 1 Tan, Marcus Hwai Yik 1 Thai, Chien Hoang 1 Tong, Yan 1 Tur, Manuel 1 Varduhn, Vasco 1 Wang, Qiao 1 Wu, Chunlin 1 Xu, Gang 1 Ye, Wenbin 1 Yin, Huiming 1 Zander, Nils 1 Zang, Quansheng 1 Zhang, Liangliang 1 Zhang, Yongjie Jessica 1 Zhou, Wei 1 Zlotnik, Sergio all top 5 Cited in 11 Serials 10 Computer Methods in Applied Mechanics and Engineering 3 Computational Mechanics 3 Applied Mathematical Modelling 2 Computers & Mathematics with Applications 2 Journal of Computational Physics 2 Engineering Analysis with Boundary Elements 1 International Journal for Numerical Methods in Engineering 1 Mathematics and Computers in Simulation 1 Journal of Scientific Computing 1 European Journal of Mechanics. A. Solids 1 Archives of Computational Methods in Engineering Cited in 5 Fields 20 Numerical analysis (65-XX) 15 Mechanics of deformable solids (74-XX) 3 Fluid mechanics (76-XX) 2 Partial differential equations (35-XX) 1 Classical thermodynamics, heat transfer (80-XX) Citations by Year