Spectral approximation properties of isogeometric analysis with variable continuity

Hughes, 2005, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 4135, 10.1016/j.cma.2004.10.008 Bazilevs, 2010, Isogeometric analysis using T-splines, Comput. Methods Appl. Mech. Engrg., 199, 229, 10.1016/j.cma.2009.02.036 Cottrell, 2006, Isogeometric analysis of structural vibrations, Comput. Methods Appl. Mech. Engrg., 195, 5257, 10.1016/j.cma.2005.09.027 Cottrell, 2007, Studies of refinement and continuity in isogeometric structural analysis, Comput. Methods Appl. Mech. Engrg., 196, 4160, 10.1016/j.cma.2007.04.007 Cottrell, 2009 Hughes, 2008, Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: comparison of p-method finite elements with k-method NURBS, Comput. Methods Appl. Mech. Engrg., 197, 4104, 10.1016/j.cma.2008.04.006 Hughes, 2010, Efficient quadrature for NURBS-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 199, 301, 10.1016/j.cma.2008.12.004 Hughes, 2014, Finite element and NURBS approximations of eigenvalue, boundary-value, and initial-value problems, Comput. Methods Appl. Mech. Engrg., 272, 290, 10.1016/j.cma.2013.11.012 Gómez, 2008, Isogeometric analysis of the Cahn–Hilliard phase-field model, Comput. Methods Appl. Mech. Engrg., 197, 4333, 10.1016/j.cma.2008.05.003 V.M. Calo, H. Gomez, Y. Bazilevs, G. Johnson, T.J.R. Hughes, Simulation of engineering applications using isogeometric analysis, in: Proceedings of Tera Grid, 2008. Auricchio, 2013, Locking-free isogeometric collocation methods for spatial Timoshenko rods, Comput. Methods Appl. Mech. Engrg., 263, 113, 10.1016/j.cma.2013.03.009 Collier, 2012, The cost of continuity: A study of the performance of isogeometric finite elements using direct solvers, Comput. Methods Appl. Mech. Engrg., 213, 353, 10.1016/j.cma.2011.11.002 Collier, 2013, The cost of continuity: performance of iterative solvers on isogeometric finite elements, SIAM J. Sci. Comput., 35, A767, 10.1137/120881038 Collier, 2014, On the computational efficiency of isogeometric methods for smooth elliptic problems using direct solvers, Internat. J. Numer. Methods Engrg., 100, 620, 10.1002/nme.4769 Garcia, 2017, The value of continuity: Refined isogeometric analysis and fast direct solvers, Comput. Methods Appl. Mech. Engrg., 316, 586, 10.1016/j.cma.2016.08.017 Garcia, 2017, Optimally refined isogeometric analysis, Procedia Comput. Sci., 108, 808, 10.1016/j.procs.2017.05.283 Thompson, 1994, Complex wavenumber Fourier analysis of the p-version finite element method, Comput. Mech., 13, 255, 10.1007/BF00350228 Ainsworth, 2004, Discrete dispersion relation for hp-version finite element approximation at high wave number, SIAM J. Numer. Anal., 42, 553, 10.1137/S0036142903423460 Bazilevs, 2007, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Engrg., 197, 173, 10.1016/j.cma.2007.07.016 Kolman, 2014, Complex wavenumber Fourier analysis of the B-spline based finite element method, Wave Motion, 51, 348, 10.1016/j.wavemoti.2013.09.003 Dedè, 2015, Isogeometric numerical dispersion analysis for two-dimensional elastic wave propagation, Comput. Methods Appl. Mech. Engrg., 284, 320, 10.1016/j.cma.2014.09.013 Strang, 1973 Puzyrev, 2017, Dispersion-optimized quadrature rules for isogeometric analysis: modified inner products, their dispersion properties, and optimally blended schemes, Comput. Methods Appl. Mech. Engrg., 320, 421, 10.1016/j.cma.2017.03.029 Piegl, 1997 Schillinger, 2012, An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces, Comput. Methods Appl. Mech. Engrg., 249, 116, 10.1016/j.cma.2012.03.017 Dokken, 2013, Polynomial splines over locally refined box-partitions, Comput. Aided Geom. Design, 30, 331, 10.1016/j.cagd.2012.12.005 Dalcin, 2016, PetIGA: A framework for high-performance isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 308, 151, 10.1016/j.cma.2016.05.011 Sarmiento, 2017, PetIGA-MF: a multi-field high-performance toolbox for structure-preserving B-splines spaces, J. Comput. Sci., 18, 117, 10.1016/j.jocs.2016.09.010 De Falco, 2011, GeoPDEs: a research tool for isogeometric analysis of PDEs, Adv. Eng. Softw., 42, 1020, 10.1016/j.advengsoft.2011.06.010 Pauletti, 2015, Igatools: An isogeometric analysis library, SIAM J. Sci. Comput., 37, C465, 10.1137/140955252 Calo, 2017, Quadrature blending for isogeometric analysis, Procedia Comput. Sci., 108, 798, 10.1016/j.procs.2017.05.143 Ainsworth, 2010, Optimally blended spectral-finite element scheme for wave propagation and nonstandard reduced integration, SIAM J. Numer. Anal., 48, 346, 10.1137/090754017 V.M. Calo, Q. Deng, V. Puzyrev, Dispersion optimized quadratures for isogeometric analysis, 2017, Submitted for publication. ArXiv preprint: https://arxiv.org/abs/1702.04540. Deng, 2018, Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 328, 554, 10.1016/j.cma.2017.09.025 Bartoň, 2017, Generalization of the Pythagorean eigenvalue error theorem and its application to isogeometric analysis