Kapl, M., Buchegger, F., Bercovier, M., Jüttler, B.: Isogeometric analysis with geometrically continuous functions on planar multi-patch geometries. Hughes, T.J.R., Cottrell, J.A., Bazilevs, Y.: Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Hoschek, J., Lasser, D.: Fundamentals of computer aided geometric design. Hernández Encinas, L., Muñoz Masqué, J.: A short proof of the generalized Faà di Bruno’s formula. Guo, Y., Ruess, M.: Nitsche’s method for a coupling of isogeometric thin shells and blended shell structures. Groisser, D., Peters, J.: Matched G k-constructions always yield C k-continuous isogeometric elements. Gomez, H., Nogueira, X.: An unconditionally energy-stable method for the phase field crystal equation. Gomez, H., De Lorenzis, L.: The variational collocation method. In: ECCOMAS Multidisciplinary Jubilee Symposium: New Computational Challenges in Materials, Structures, and Fluids, pp 1–16. Gomez, H., Calo, V.M., Hughes, T.J.R.: Isogeometric analysis of phase–field models: application to the Cahn–Hilliard equation. Gómez, H., Calo, V.M., Bazilevs, Y., Hughes, T.J.: Isogeometric analysis of the Cahn–Hilliard phase-field model. Academic Press, New York (1997)įischer, P., Klassen, M., Mergheim, J., Steinmann, P., Müller, R.: Isogeometric analysis of 2D gradient elasticity. John Wiley & Sons, England Chichester (2009)įarin, G.: Curves and surfaces for computer-aided geometric design. 47, 93–113 (2016)Ĭottrell, J.A., Hughes, T.J.R., Bazilevs, Y.: Isogeometric analysis: toward integration of CAD and FEA. 112599, 357 (2019)Ĭollin, A., Sangalli, G., Takacs, T.: Analysis-suitable G 1 multi-patch parametrizations for C 1 isogeometric spaces. 62, 294–310 (2018)Ĭhan, C., Anitescu, C., Rabczuk, T.: Strong multipatch C 1-coupling for isogeometric analysis on2Dand 3D domains. 101814, 78 (2020)Ĭhan, C., Anitescu, C., Rabczuk, T.: Isogeometric analysis with strong multipatch C 1-coupling. 52–53, 106–125 (2017)īlidia, A., Mourrain, B., Xu, G.: Geometrically smooth spline bases for data fitting and simulation. Springer, New York (2017)īlidia, A., Mourrain, B., Villamizar, N.: G 1-smooth splines on quad meshes with 4-split macro-patch elements. Lecture Notes of the Unione Matematica Italiana. 200(13), 1367–1378 (2011)īercovier, M., Matskewich, T.: Smooth Bézier surfaces over unstructured quadrilateral meshes. 23, 157–287 (2014)īenson, D.J., Bazilevs, Y., Hsu, M.C., Hughes, T.J.: A large deformation, rotation-free, isogeometric shell. 295, 446–469 (2015)īeirão da Veiga, L., Buffa, A., Sangalli, G., Vázquez, R.: Mathematical analysis of variational isogeometric methods. 20(11), 2075–2107 (2010)īartezzaghi, A., Dedè, L., Quarteroni, A.: Isogeometric analysis of high order partial differential equations on surfaces.
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197(1), 160–172 (2007)Īuricchio, F., Beirão da Veiga, L., Hughes, T.J.R., Reali, A., Sangalli, G.: Isogeometric collocation methods. Springer (2015)Īuricchio, F., Beirão da Veiga, L., Buffa, A., Lovadina, C., Reali, A., Sangalli, G.: A fully locking-free isogeometric approach for plane linear elasticity problems: a stream function formulation. (eds.) Isogeometric Analysis and Applications 2014, pp 73–101. 284, 1073–1097 (2015)Īpostolatos, A., Breitenberger, M., Wüchner, R., Bletzinger, K.U.: Domain decomposition methods and kirchhoff-love shell multipatch coupling in isogeometric analysis. Moreover, we use the C s-smooth spline functions to perform L 2 approximation on bilinearly parameterized multi-patch domains, where the obtained numerical results indicate an optimal approximation power of the constructed C s-smooth subspace.Īnitescu, C., Jia, Y., Zhang, Y.J., Rabczuk, T.: An isogeometric collocation method using superconvergent points. We further present the construction of a basis for this C s-smooth subspace, which consists of simple and locally supported functions. More precisely, we study for s ≥ 1 the space of C s-smooth isogeometric spline functions defined on planar, bilinearly parameterized multi-patch domains, and generate a particular C s-smooth subspace of the entire C s-smooth isogeometric multi-patch spline space. 360:112684, 2020 for the construction of C 1-smooth and C 2-smooth isogeometric spline spaces over particular planar multi-patch geometries to the case of C s-smooth isogeometric multi-patch spline spaces of degree p, inner regularity r and of a smoothness s ≥ 1, with p ≥ 2 s + 1 and s ≤ r ≤ p − s − 1. In this work, we extend the recent methods Kapl et al.
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vertices with valencies different from four, is a current and challenging topic of research in the framework of isogeometric analysis. The design of globally C s-smooth ( s ≥ 1) isogeometric spline spaces over multi-patch geometries with possibly extraordinary vertices, i.e.