Isogeometric spline forests

Computer Methods in Applied Mechanics and Engineering

Volumn 269, Issue , 2014, Pages 222-264

  Scott, M A ^a   Thomas, D C ^b   Evans, E J ^c  

^a Department of Electrical and Computer Engineering   (United States)

^b Brigham Young University   (United States)

^c BRIGHAM YOUNG UNIVERSITY   (United States)

Author keywords

Adaptive mesh refinement; Advection diffusion; Hierarchical splines; Isogeometric analysis

Indexed keywords

ADAPTIVE MESH REFINEMENT; ADVECTION-DIFFUSION; ADVECTION-DIFFUSION PROBLEM; COMPLEX GEOMETRIES; FULLY INTEGRATED; HIERARCHICAL BASIS; HIERARCHICAL SPLINES; ISOGEOMETRIC ANALYSIS;

COMPUTATIONAL METHODS; COMPUTER APPLICATIONS;

FORESTRY;

COMPUTATION; FORESTRY;

EID: 84888779109     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2013.10.024     Document Type: Article

References (76)

1. Forsey D.R., Bartels R.H. Hierarchical B-spline refinement. ACM SIGGRAPH Computer Graphics 1988, 22(4):205-212.
2. Vuong A., Giannelli C., Jüttler B., Simeon B. A hierarchical approach to adaptive local refinement in isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 2011, 200(49-52):3554-3567.
3. Giannelli C., Jüttler B., Speleers H. THB-splines: The truncated basis for hierarchical splines. Computer Aided Geometric Design 2012, 29(7):485-498.
4. Schillinger D., Dedé L., Scott M.A., Evans J.A., Borden M.J., Rank E., Hughes T.J.R. An isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces. Computer Methods in Applied Mechanics and Engineering 2012, 249-252:116-150.
5. Schillinger D., Evans J.A., Reali A., Scott M.A., Hughes T.J.R. Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations. Computer Methods in Applied Mechanics and Engineering 2013, 267:170-232.
6. Hughes T.J.R., Cottrell J.A., Bazilevs Y. Isogeometric analysis: CAD, finite elements NURBS, exact geometry, and mesh refinement. Computer Methods in Applied Mechanics and Engineering 2005, 194:4135-4195.
7. Cottrell J.A., Hughes T.J.R., Bazilevs Y. Isogeometric analysis: Toward Integration of CAD and FEA 2009, Wiley, Chichester.
8. Akkerman I., Bazilevs Y., Calo V., Hughes T.J.R., Hulshoff S. The role of continuity in residual-based variational multiscale modeling of turbulence. Computational Mechanics 2008, 41:371-378.
9. Bazilevs Y., Calo V.M., Cottrell J.A., Hughes T.J.R., Reali A., Scovazzi G. Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows. Computer Methods in Applied Mechanics and Engineering 2007, 197:173-201.
10. Bazilevs Y., Akkerman I. Large eddy simulation of turbulent Taylor-Couette flow using isogeometric analysis and residual-based variational multiscale method. Journal of Computational Physics 2010, 229:3402-3414.
11. Bazilevs Y., Michler C., Calo V.M., Hughes T.J.R. Isogeometric variational multiscale modeling of wall-bounded turbulent flows with weakly enforced boundary conditions on unstretched meshes. Computer Methods in Applied Mechanics and Engineering 2010, 199(13-16):780-790.
12. Bazilevs Y., Calo V.M., Zhang Y., Hughes T.J.R. Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Computational Mechanics 2006, 38:310-322.
13. Bazilevs Y., Calo V.M., Hughes T.J.R., Zhang Y. Isogeometric fluid-structure interaction: theory, algorithms, and computations. Computational Mechanics 2008, 43:3-37.
14. Zhang Y., Bazilevs Y., Goswami S., Bajaj C., Hughes T.J.R. Patient-specific vascular NURBS modeling for isogeometric analysis of blood flow. Computer Methods in Applied Mechanics and Engineering 2007, 196:2943-2959.
15. Bazilevs Y., Gohean J.R., Hughes T.J.R., Moser R.D., Zhang Y. Patient-specific isogeometric fluid-structure interaction analysis of thoracic aortic blood flow due to implantation of the Jarvik 2000 left ventricular assist device. Computer Methods in Applied Mechanics and Engineering 2009, 198(45-46):3534-3550.
16. Auricchio F., da Veiga L.B., Lovadina C., Reali A. The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity: mixed FEMs versus NURBS-based approximations. Computer Methods in Applied Mechanics and Engineering 2010, 199:314-323.
17. Auricchio F., da Veiga L.B., Buffa A., Lovadina C., Reali A., Sangalli G. A fully locking-free isogeometric approach for plane linear elasticity problems: A stream function formulation. Computer Methods in Applied Mechanics and Engineering 2007, 197:160-172.
18. Elguedj T., Bazilevs Y., Calo V.M., Hughes T.J.R. B- and F- projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements. Computer Methods in Applied Mechanics and Engineering 2008, 197:2732-2762.
19. Cottrell J.A., Hughes T.J.R., Reali A. Studies of refinement and continuity in isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 2007, 196:4160-4183.
20. Cottrell J.A., Reali A., Bazilevs Y., Hughes T.J.R. Isogeometric analysis of structural vibrations. Computer Methods in Applied Mechanics and Engineering 2006, 195:5257-5296.
21. Scott M.A., Simpson R.N., Evans J.A., Lipton S., Bordas S.P.A., Hughes T.J.R., Sederberg T.W. Isogeometric boundary element analysis using unstructured T-splines. Computer Methods in Applied Mechanics and Engineering 2013, 254:197-221.
22. Benson D.J., Bazilevs Y., Hsu M.C., Hughes T.J.R. Isogeometric shell analysis: the Reissner-Mindlin shell. Computer Methods in Applied Mechanics and Engineering 2010, 199(5-8):276-289.
23. Benson D.J., Bazilevs Y., Hsu M.C., Hughes T.J.R. A large deformation, rotation-free, isogeometric shell. International Journal for Numerical Methods in Engineering 2011, 200:1367-1378.
24. Benson D.J., Bazilevs Y., De Luycker E., Hsu M.C., Scott M.A., Hughes T.J.R., Belytschko T. A generalized finite element formulation for arbitrary basis functions: from isogeometric analysis to XFEM. International Journal for Numerical Methods in Engineering 2010, 83:765-785.
25. Echter R., Bischoff M. Numerical efficiency, locking and unlocking of NURBS finite elements. Computer Methods in Applied Mechanics and Engineering 2010, 199(5-8):374-382.
26. Kiendl J., Bazilevs Y., Hsu M.C., Wuechner R., Bletzinger K.U. The bending strip method for isogeometric analysis of Kirchhoff-Love shell structures comprised of multiple patches. Computer Methods in Applied Mechanics and Engineering 2010, 199(37-40):2403-2416.
27. Verhoosel C.V., Scott M.A., Hughes T.J.R., de Borst R. An isogeometric analysis approach to gradient damage models. International Journal for Numerical Methods in Engineering 2011, 86:115-134.
28. Verhoosel C.V., Scott M.A., de Borst R., Hughes T.J.R. An isogeometric approach to cohesive zone modeling. International Journal for Numerical Methods in Engineering 2011, 87:336-360.
29. Borden M.J., Scott M.A., Verhoosel C.V., Landis C.M., Hughes T.J.R. A phase-field description of dynamic brittle fracture. Computer Methods in Applied Mechanics and Engineering 2012, 217:77-95.
30. Gomez H., Calo V.M., Bazilevs Y., Hughes T.J.R. Isogeometric analysis of the Cahn-Hilliard phase-field model. Computer Methods in Applied Mechanics and Engineering 2008, 197:4333-4352.
31. Gomez H., Hughes T.J.R., Nogueira X., Calo V.M. Isogeometric analysis of the isothermal Navier-Stokes-Korteweg equations. Computer Methods in Applied Mechanics and Engineering 2010, 199(25-28):1828-1840.
32. Lipton S., Evans J.A., Bazilevs Y., Elguedj T., Hughes T.J.R. Robustness of isogeometric structural discretizations under severe mesh distortion. Computer Methods in Applied Mechanics and Engineering 2010, 199(5-8):357-373.
33. Wall W.A., Frenzel M.A., Cyron C. Isogeometric structural shape optimization. Computer Methods in Applied Mechanics and Engineering 2008, 197:2976-2988.
34. Qian X. Full analytical sensitivities in NURBS based isogeometric shape optimization. Computer Methods in Applied Mechanics and Engineering 2010, 199(29-32):2059-2071.
35. Nagy A.P., Abdalla M.M., Gurdal Z. Isogeometric sizing and shape optimization of beam structures. Computer Methods in Applied Mechanics and Engineering 2010, 199(17-20):1216-1230.
36. Nagy A.P., Abdalla M.M., Gurdal Z. On the variational formulation of stress constraints in isogeometric design. Computer Methods in Applied Mechanics and Engineering 2010, 199(41-44):2687-2696.
37. R.N. Simpson, M.A. Scott, M. Taus, D. Thomas, H. Lian, Acoustic isogeometric boudary element analysis, Computer Methods in Applied Mechanics and Engineering (in press).
38. Buffa A., Sangalli G., Vázquez R. Isogeometric analysis in electromagnetics: B-splines approximation. Computer Methods in Applied Mechanics and Engineering 2010, 199(17-20):1143-1152.
39. Cohen E., Martin T., Kirby R.M., Lyche T., Riesenfeld R.F. Analysis-aware modeling: understanding quality considerations in modeling for isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 2010, 199(5-8):334-356.
40. Lu J. Circular element: isogeometric elements of smooth boundary. Computer Methods in Applied Mechanics and Engineering 2009, 198(30-32):2391-2402.
41. Kim H., Seo Y., Youn S. Isogeometric analysis for trimmed CAD surfaces. Computer Methods in Applied Mechanics and Engineering 2009, 198(37-40):2982-2995.
42. Costantini P., Manni C., Pelosi F., Sampoli M.L. Quasi-interpolation in isogeometric analysis based on generalized B-splines. Computer Aided Geometric Design 2010, 27(8):656-668.
43. Aigner M., Heinrich C., Juettler B., Pilgerstorfer E., Simeon B., Vuong A.V. Swept volume parameterization for isogeometric analysis. Lecture Notes in Computer Science 2009, vol. 5654:19-44. E.R. Hancock, R.R. Martin, M.A. Sabin (Eds.).
44. Martin T., Cohen E., Kirby R.M. Volumetric parameterization and trivariate B-spline fitting using harmonic functions. Computer Aided Geometric Design 2009, 26(6):648-664.
45. Wang W., Zhang Y. Wavelets-based NURBS simplification and fairing. Computer Methods in Applied Mechanics and Engineering 2010, 199(5-8):290-300.
46. Wang W., Zhang Y., Scott M.A., Hughes T.J.R. Converting an unstructured quadrilateral mesh to a standard T-spline surface. Computational Mechanics 2011, 48:477-498.
47. Burstedde C., Wilcox L.C., Ghattas O. p4est: Scalable algorithms for parallel adaptive mesh refinement on forests of octrees. SIAM Journal on Scientific Computing 2011, 33(3):1103-1133.
48. Bangerth W., Burstedde C., Heister T., Kronbichler M. Algorithms and data structures for massively parallel generic adaptive finite element codes. ACM Transactions on Mathematical Software 2011, 38(2):14:1-14:28.
49. Sederberg T.W., Zheng J., Bakenov A., Nasri A. T-splines and T-NURCCs. ACM Transactions on Graphics 2003, 22:477-484.
50. Scott M.A., Li X., Sederberg T.W., Hughes T.J.R. Local refinement of analysis-suitable T-splines. Computer Methods in Applied Mechanics and Engineering 2012, 213:206-222.
51. da Veiga L.B., Buffa A., Sangalli G., Vázquez R. Analysis-suitable T-splines of arbitrary degree: definition, linear independence, and approximation properties. Mathematical Models and Methods in Applied Sciences 2013, 23(11). in press.
52. X. Li, M.A. Scott, Analysis-suitable T-splines: characterization, refineability, and approximation, Mathematical Models and Methods in Applied Science (in press).
53. Beirao da Veiga L., Buffa A., Cho D., Sangalli G. Analysis-suitable T-splines are dual-compatible. Computer Methods in Applied Mechanics and Engineering 2012, 249-252:42-51.
54. Li X., Zheng J., Sederberg T.W., Hughes T.J.R., Scott M.A. On linear independence of T-spline blending functions. Computer Aided Geometric Design 2012, 29:63-76.
55. Bazilevs Y., Calo V.M., Cottrell J.A., Evans J.A., Hughes T.J.R., Lipton S., Scott M.A., Sederberg T.W. Isogeometric analysis using T-splines. Computer Methods in Applied Mechanics and Engineering 2010, 199(5-8):229-263.
56. Scott M.A., Borden M.J., Verhoosel C.V., Sederberg T.W., Hughes T.J.R. Isogeometric finite element data structures based on Bézier extraction of T-splines. International Journal for Numerical Methods in Engineering 2011, 88:126-156.
57. Borden M.J., Scott M.A., Evans J.A., Hughes T.J.R. Isogeometric finite element data structures based on Bézier extraction of NURBS. International Journal for Numerical Methods in Engineering 2011, 87:15-47.
58. Farin G.E. NURBS Curves and Surfaces: from projective geometry to practical use 1999, A.K. Peters Ltd., Natick, MA.
59. Farin G.E. Curves and Surfaces for CAGD, A Practical Guide 1999, Morgan Kaufmann Publishers, San Francisco. fifth ed.
60. T.W. Sederberg, Computer Aided Geometric Design: Course Notes. , 2010. http://www.tsplines.com/educationportal.html.
61. Ramshaw L. Blossoms are polar forms. Computer Aided Geometric Design 1989, 6(4):323-358.
62. Giannelli C., Jüttler B. Bases and dimensions of bivariate hierarchical tensor-product splines. Journal of Computational and Applied Mathematics 2013, 239:162-178.
63. Hughes T.J.R. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis 2000, Dover Publications, Mineola, NY.
64. Brooks A.N., Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering 1982, 32:199-259.
65. Chung J., Hulbert G.M. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α method. Journal of Applied Mechanics 1993, 60:371-375.
66. Jansen K.E., Whiting C.H., Hulbert G.M. A generalized-α method for integrating the filtered Navier-Stokes equations with a stabilized finite element method. Computer Methods in Applied Mechanics and Engineering 1999, 190:305-319.
67. Hughes T.J.R. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Computer Methods in Applied Mechanics and Engineering 1995, 127:387-401.
68. Larson M.G., Målqvist A. Adaptive variational multiscale methods based on a posteriori error estimation: Duality techniques for elliptic problems. Lecture Notes in Computational Science and Engineering 2005, vol. 44:181-193. Springer, Berlin Heidelberg. B. Engquist, O. Runborg, P. Lötstedt (Eds.).
69. Hauke G., Doweidar M.H., Miana M. The multiscale approach to error estimation and adaptivity. Computer Methods in Applied Mechanics and Engineering 2006, 195(13-16):1573-1593.
70. Hauke G., Doweidar M.H., Fuentes S. Mesh adaptivity for the transport equation led by variational multiscale error estimators. International Journal for Numerical Methods in Fluids 2012, 69(12):1835-1850.
71. Saad Y., Schultz M. GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal of Scientific and Statistical Computing 1986, 7:856-869.
72. M. Heroux, R. Bartlett, V.H.R. Hoekstra, J. Hu, T. Kolda, R. Lehoucq, K. Long, R. Pawlowski, E. Phipps, A. Salinger, H. Thornquist, R. Tuminaro, J. Willenbring, A. Williams, An overview of trilinos, Tech. Rep. SAND2003-2927, Sandia National Laboratories, 2003.
73. Evans J.A., Bazilevs Y., Babuška I., Hughes T.J.R. n-Widths, sup-infs, and optimality ratios for the k-version of the isogeometric finite element method. Computer Methods in Applied Mechanics and Engineering 2009, 198(21-26):1726-1741.
74. H2 regularity properties of singular parameterizations in isogeometric analysis. Graphical models 2012, 74(6):361-372.
75. Takacs T., Jüttler B. Existence of stiffness matrix integrals for singularly parameterized domains in isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 2011, 200:3568-3582.
76. Autodesk, Autodesk T-Splines Plug-in for Rhino user manual, Autodesk, 2012.