Publications

Papers with Peer Review

  1. N. Lamsahel, C. Manni, A. Ratnani, S. Serra-Capizzano, and H. Speleers. Outlier-free isogeometric discretizations for Laplace eigenvalue problems: Closed-form eigenvalue and eigenvector expressions. Numerische Mathematik, in press.
  2. S. Eddargani, C. Manni, and H. Speleers. Quadrature rules for splines of high smoothness on uniformly refined triangles. Mathematics of Computation, in press.
  3. T. Lyche, J-L. Merrien, and H. Speleers. A C1 simplex-spline basis for the Alfeld split in ℝs. Computer Aided Geometric Design 117, art. 102412, pp. 1–16, 2025.
  4. G. Barbarino, M. Claesson, S-E. Ekström, C. Garoni, D. Meadon, and H. Speleers. Matrix-less spectral approximation for large structured matrices. BIT Numerical Mathematics 65, art. 2, pp. 1–35, 2025.
  5. C. Garoni, C. Manni, F. Pelosi, and H. Speleers. Study and use of spectral symbol properties for isogeometric matrices on trimmed geometries. Numerical Linear Algebra with Applications 32(1), art. e2601, pp. 1–15, 2025.
  6. T. Lyche, C. Manni, and H. Speleers. A parsimonious approach to C2 cubic splines on arbitrary triangulations: Reduced macro-elements on the cubic Wang-Shi split. In: M. Lanini et al. (eds.) Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology, Springer INdAM Series 60, pp. 265–287, 2024.
  7. J. Grošelj and H. Speleers. Using geometric symmetries to achieve super-smoothness for cubic Powell-Sabin splines. In: M. Lanini et al. (eds.) Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology, Springer INdAM Series 60, pp. 205–229, 2024.
  8. S. Eddargani, T. Lyche, C. Manni, and H. Speleers. Quadrature rules for C1 quadratic spline finite elements on the Powell-Sabin 12-split. Computer Methods in Applied Mechanics and Engineering 430, art. 117196, pp. 1–32, 2024.
  9. K. Raval, C. Manni, and H. Speleers. Adaptive isogeometric analysis based on locally refined Tchebycheffian B-splines. Computer Methods in Applied Mechanics and Engineering 430, art. 117186, pp. 1–27, 2024.
  10. M. Marsala, C. Manni, and H. Speleers. Maximally smooth cubic spline quasi-interpolants on arbitrary triangulations. Computer Aided Geometric Design 112, art. 102348, pp. 1–22, 2024.
  11. T. Lyche, C. Manni, and H. Speleers. A local simplex spline basis for C3 quartic splines on arbitrary triangulations. Applied Mathematics and Computation 462, art. 128330, pp. 1–27, 2024.
  12. C. Manni, E. Sande, and H. Speleers. Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems. Computer Methods in Applied Mechanics and Engineering 417(B), art. 116314, pp. 1–33, 2023.
  13. M. Donatelli, C. Manni, M. Mazza, and H. Speleers. Spectral analysis of matrices in B-spline Galerkin methods for Riesz fractional equations. In: A. Cardone et al. (eds.) Fractional Differential Equations, Springer INdAM Series 50, pp. 53–73, 2023.
  14. J. Grošelj and H. Speleers. Extraction and application of super-smooth cubic B-splines over triangulations. Computer Aided Geometric Design 103, art. 102194, pp. 1–15, 2023.
  15. K. Raval, C. Manni, and H. Speleers. Tchebycheffian B-splines in isogeometric Galerkin methods. Computer Methods in Applied Mechanics and Engineering 403(A), art. 115648, pp. 1–31, 2023.
  16. M. Mazza, M. Donatelli, C. Manni, and H. Speleers. On the matrices in B-spline collocation methods for Riesz fractional equations and their spectral properties. Numerical Linear Algebra with Applications 30(1), art. e2462, pp. 1–23, 2023.
  17. C. Garoni, C. Manni, F. Pelosi, and H. Speleers. Spectral analysis of matrices resulting from isogeometric immersed methods and trimmed geometries. Computer Methods in Applied Mechanics and Engineering 400, art. 115551, pp. 1–30, 2022.
  18. T. Lyche, C. Manni, and H. Speleers. Construction of C2 cubic splines on arbitrary triangulations. Foundations of Computational Mathematics 22(5), pp. 1309–1350, 2022.
  19. D. Fakhoury, E. Fakhoury, and H. Speleers. ExSpliNet: An interpretable and expressive spline-based neural network. Neural Networks 152, pp. 332–346, 2022.
  20. C. Hofreither, L. Mitter, and H. Speleers. Local multigrid solvers for adaptive isogeometric analysis in hierarchical spline spaces. IMA Journal of Numerical Analysis 42(3), pp. 2429–2458, 2022.
  21. E. Sande, C. Manni, and H. Speleers. Ritz-type projectors with boundary interpolation properties and explicit spline error estimates. Numerische Mathematik 151(2), pp. 475–494, 2022.
  22. H. Speleers. Algorithm 1020: Computation of multi-degree Tchebycheffian B-splines. ACM Transactions on Mathematical Software 48(1), art. 12, pp. 1–31, 2022. [Matlab toolbox]
  23. C. Manni, E. Sande, and H. Speleers. Application of optimal spline subspaces for the removal of spurious outliers in isogeometric discretizations. Computer Methods in Applied Mechanics and Engineering 389, art. 114260, pp. 1–38, 2022.
  24. M.L. Cardinali, C. Garoni, C. Manni, and H. Speleers. Isogeometric discretizations with generalized B-splines: Symbol-based spectral analysis. Applied Numerical Mathematics 166, pp. 288–312, 2021.
  25. J. Grošelj and H. Speleers. Super-smooth cubic Powell-Sabin splines on three-directional triangulations: B-spline representation and subdivision. Journal of Computational and Applied Mathematics 386, art. 113245, pp. 1–23, 2021.
  26. M.S. Floater, C. Manni, E. Sande, and H. Speleers. Best low-rank approximations and Kolmogorov n-widths. SIAM Journal on Matrix Analysis and Applications 42(1), pp. 330–350, 2021.
  27. H. Speleers and D. Toshniwal. A general class of C1 smooth rational splines: Application to construction of exact ellipses and ellipsoids. Computer-Aided Design 132, art. 102982, pp. 1–14, 2021.
  28. C. Garoni, C. Manni, S. Serra-Capizzano, and H. Speleers. NURBS in isogeometric discretization methods: A spectral analysis. Numerical Linear Algebra with Applications 27(6), art. e2318, pp. 1–34, 2020.
  29. M. Mazza, C. Manni, and H. Speleers. Spectral analysis of isogeometric discretizations of 2D curl-div problems with general geometry. In: S.J. Sherwin et al. (eds.) Spectral and High Order Methods for Partial Differential Equations: ICOSAHOM 2018, Lecture Notes in Computational Science and Engineering 134, 251–262, 2020.
  30. F. Patrizi, C. Manni, F. Pelosi, and H. Speleers. Adaptive refinement with locally linearly independent LR B-splines: Theory and applications. Computer Methods in Applied Mechanics and Engineering 369, art. 113230, pp. 1–20, 2020.
  31. R.R. Hiemstra, T.J.R. Hughes, C. Manni, H. Speleers, and D. Toshniwal. A Tchebycheffian extension of multidegree B-splines: Algorithmic computation and properties. SIAM Journal on Numerical Analysis 58(2), pp. 1138–1163, 2020.
  32. E. Sande, C. Manni, and H. Speleers. Explicit error estimates for spline approximation of arbitrary smoothness in isogeometric analysis. Numerische Mathematik 144(4), pp. 889–929, 2020.
  33. D. Toshniwal, H. Speleers, R.R. Hiemstra, C. Manni, and T.J.R. Hughes. Multi-degree B-splines: Algorithmic computation and properties. Computer Aided Geometric Design 76, art. 101792, pp. 1–16, 2020.
  34. H. Speleers. Algorithm 999: Computation of multi-degree B-splines. ACM Transactions on Mathematical Software 45(4), art. 43, pp. 1–15, 2019. [Matlab toolbox]
  35. C. Garoni, H. Speleers, S-E. Ekström, A. Reali, S. Serra-Capizzano, and T.J.R. Hughes. Symbol-based analysis of finite element and isogeometric B-spline discretizations of eigenvalue problems: Exposition and review. Archives of Computational Methods in Engineering 26(5), pp. 1639–1690, 2019.
  36. T. Lyche, C. Manni, and H. Speleers. Tchebycheffian B-splines revisited: An introductory exposition. In: C. Giannelli and H. Speleers (eds.) Advanced Methods for Geometric Modeling and Numerical Simulation, Springer INdAM Series 35, pp. 179–216, 2019.
  37. E. Sande, C. Manni, and H. Speleers. Sharp error estimates for spline approximation: Explicit constants, n-widths, and eigenfunction convergence. Mathematical Models and Methods in Applied Sciences 29(6), pp. 1175–1205, 2019.
  38. C. Giannelli, T. Kanduč, F. Pelosi, and H. Speleers. An immersed-isogeometric model: Application to linear elasticity and implementation with THBox-splines. Journal of Computational and Applied Mathematics 349, pp. 410–423, 2019.
  39. C. Bracco, T. Lyche, C. Manni, and H. Speleers. Tchebycheffian spline spaces over planar T-meshes: Dimension bounds and dimension instabilities. Journal of Computational and Applied Mathematics 349, pp. 265–278, 2019.
  40. M. Mazza, C. Manni, A. Ratnani, S. Serra-Capizzano, and H. Speleers. Isogeometric analysis for 2D and 3D curl-div problems: Spectral symbols and fast iterative solvers. Computer Methods in Applied Mechanics and Engineering 344, pp. 970–997, 2019.
  41. C. Manni and H. Speleers. Dimension of Tchebycheffian spline spaces over planar T-meshes: The conformality method. Rendiconti del Seminario Matematico dell'Università e del Politecnico di Torino 76(2), pp. 135–145, 2018.
  42. J. Grošelj and H. Speleers. Three recipes for quasi-interpolation with cubic Powell-Sabin splines. Computer Aided Geometric Design 67, pp. 47–70, 2018.
  43. X. Wei, Y.J. Zhang, D. Toshniwal, H. Speleers, X. Li, C. Manni, J.A. Evans, and T.J.R. Hughes. Blended B-spline construction on unstructured quadrilateral and hexahedral meshes with optimal convergence rates in isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 341, pp. 609–639, 2018.
  44. S-E. Ekström, I. Furci, C. Garoni, C. Manni, S. Serra-Capizzano, and H. Speleers. Are the eigenvalues of the B-spline isogeometric analysis approximation of -Δu=λu known in almost closed form? Numerical Linear Algebra with Applications 25(5), art. e2198, pp. 1–34, 2018.
  45. D. Toshniwal, H. Speleers, and T.J.R. Hughes. Smooth cubic spline spaces on unstructured quadrilateral meshes with particular emphasis on extraordinary points: Geometric design and isogeometric analysis considerations. Computer Methods in Applied Mechanics and Engineering 327, pp. 411–458, 2017.
  46. J. Grošelj and H. Speleers. Construction and analysis of cubic Powell-Sabin B-splines. Computer Aided Geometric Design 57, pp. 1–22, 2017.
  47. C. Manni, F. Roman, and H. Speleers. Generalized B-splines in isogeometric analysis. In: G.E. Fasshauer and L.L. Schumaker (eds.) Approximation Theory XV: San Antonio 2016, Springer Proceedings in Mathematics & Statistics 201, pp. 239–267, 2017.
  48. F. Roman, C. Manni, and H. Speleers. Numerical approximation of GB-splines by a convolutional approach. Applied Numerical Mathematics 116, pp. 273–285, 2017.
  49. C. Garoni, C. Manni, S. Serra-Capizzano, D. Sesana, and H. Speleers. Spectral analysis and spectral symbol of matrices in isogeometric Galerkin methods. Mathematics of Computation 86(305), pp. 1343–1373, 2017.
  50. H. Speleers. Hierarchical spline spaces: Quasi-interpolants and local approximation estimates. Advances in Computational Mathematics 43(2), pp. 235–255, 2017.
  51. D. Toshniwal, H. Speleers, R.R. Hiemstra, and T.J.R. Hughes. Multi-degree smooth polar splines: A framework for geometric modeling and isogeometric analysis. Computer Methods in Applied Mechanics and Engineering 316, pp. 1005–1061, 2017.
  52. T. Kanduč, C. Giannelli, F. Pelosi, and H. Speleers. Adaptive isogeometric analysis with hierarchical box splines. Computer Methods in Applied Mechanics and Engineering 316, pp. 817–838, 2017.
  53. C. Garoni, C. Manni, S. Serra-Capizzano, D. Sesana, and H. Speleers. Lusin theorem, GLT sequences and matrix computations: An application to the spectral analysis of PDE discretization matrices. Journal of Mathematical Analysis and Applications 446(1), pp. 365–382, 2017.
  54. M. Donatelli, C. Garoni, C. Manni, S. Serra-Capizzano, and H. Speleers. Symbol-based multigrid methods for Galerkin B-spline isogeometric analysis. SIAM Journal on Numerical Analysis 55(1), pp. 31–62, 2017.
  55. F. Roman, C. Manni, and H. Speleers. Spectral analysis of matrices in Galerkin methods based on generalized B-splines with high smoothness. Numerische Mathematik 135(1), pp. 169–216, 2017.
  56. F. Pelosi, C. Giannelli, C. Manni, M.L. Sampoli, and H. Speleers. Splines over regular triangulations in numerical simulation. Computer-Aided Design 82, pp. 100–111, 2017.
  57. C. Bracco, T. Lyche, C. Manni, F. Roman, and H. Speleers. On the dimension of Tchebycheffian spline spaces over planar T-meshes. Computer Aided Geometric Design 45, pp. 151–173, 2016.
  58. M. Donatelli, C. Garoni, C. Manni, S. Serra-Capizzano, and H. Speleers. Spectral analysis and spectral symbol of matrices in isogeometric collocation methods. Mathematics of Computation 85(300), pp. 1639–1680, 2016.
  59. H. Speleers and C. Manni. Effortless quasi-interpolation in hierarchical spaces. Numerische Mathematik 132(1), pp. 155–184, 2016.
  60. C. Bracco, T. Lyche, C. Manni, F. Roman, and H. Speleers. Generalized spline spaces over T-meshes: Dimension formula and locally refined generalized B-splines. Applied Mathematics and Computation 272(1), pp. 187–198, 2016.
  61. H. Speleers and C. Manni. Optimizing domain parameterization in isogeometric analysis based on Powell-Sabin splines. Journal of Computational and Applied Mathematics 289, pp. 68–86, 2015.
  62. C. Manni, A. Reali, and H. Speleers. Isogeometric collocation methods with generalized B-splines. Computers & Mathematics with Applications 70(7), pp. 1659–1675, 2015.
  63. D. Lettieri, C. Manni, F. Pelosi, and H. Speleers. Shape preserving HC2 interpolatory subdivision. BIT Numerical Mathematics 55, pp. 751–779, 2015.
  64. H. Speleers. A new B-spline representation for cubic splines over Powell-Sabin triangulations. Computer Aided Geometric Design 37, pp. 42–56, 2015.
  65. L. Beirão da Veiga, T.J.R. Hughes, J. Kiendl, C. Lovadina, J. Niiranen, A. Reali, and H. Speleers. A locking-free model for Reissner-Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS. Mathematical Models and Methods in Applied Sciences 25(8), pp. 1519–1551, 2015.
  66. M. Donatelli, C. Garoni, C. Manni, S. Serra-Capizzano, and H. Speleers. Two-grid optimality for Galerkin linear systems based on B-splines. Computing and Visualization in Science 17(3), pp. 119–133, 2015.
  67. H. Speleers. Inner products of box splines and their derivatives. BIT Numerical Mathematics 55(2), pp. 559–567, 2015.
  68. H. Speleers. A family of smooth quasi-interpolants defined over Powell-Sabin triangulations. Constructive Approximation 41(2), pp. 297–324, 2015.
  69. C. Manni, F. Mazzia, A. Sestini, and H. Speleers. BS2 methods for semi-linear second order boundary value problems. Applied Mathematics and Computation 255, pp. 147–156, 2015.
  70. M. Donatelli, C. Garoni, C. Manni, S. Serra-Capizzano, and H. Speleers. Robust and optimal multi-iterative techniques for IgA collocation linear systems. Computer Methods in Applied Mechanics and Engineering 284, pp. 1120–1146, 2015.
  71. M. Donatelli, C. Garoni, C. Manni, S. Serra-Capizzano, and H. Speleers. Robust and optimal multi-iterative techniques for IgA Galerkin linear systems. Computer Methods in Applied Mechanics and Engineering 284, pp. 230–264, 2015.
  72. D. Lettieri, C. Manni, and H. Speleers. Piecewise rational quintic shape-preserving interpolation with high smoothness. Jaen Journal on Approximation 6(2), pp. 233–260, 2014.
  73. C. Garoni, C. Manni, F. Pelosi, S. Serra-Capizzano, and H. Speleers. On the spectrum of stiffness matrices arising from isogeometric analysis. Numerische Mathematik 127(4), pp. 751–799, 2014.
  74. C. Manni, F. Pelosi, and H. Speleers. Local hierarchical h-refinements in IgA based on generalized B-splines. In: M.S. Floater et al. (eds.) Mathematical Methods for Curves and Surfaces, Lecture Notes in Computer Science 8177, pp. 341–363, 2014.
  75. C. Giannelli, B. Jüttler, and H. Speleers. Strongly stable bases for adaptively refined multilevel spline spaces. Advances in Computational Mathematics 40(2), pp. 459–490, 2014.
  76. L.L. Schumaker and H. Speleers. Convexity preserving C0 splines. Advances in Computational Mathematics 40(1), pp. 117–135, 2014.
  77. H. Speleers, C. Manni, and F. Pelosi. From NURBS to NURPS geometries. Computer Methods in Applied Mechanics and Engineering 255, pp. 238–254, 2013.
  78. H. Speleers. Construction of normalized B-splines for a family of smooth spline spaces over Powell-Sabin triangulations. Constructive Approximation 37(1), pp. 41–72, 2013.
  79. H. Speleers. Multivariate normalized Powell-Sabin B-splines and quasi-interpolants. Computer Aided Geometric Design 30(1), pp. 2–19, 2013.
  80. C. Giannelli, B. Jüttler, and H. Speleers. THB-splines: The truncated basis for hierarchical splines. Computer Aided Geometric Design 29(7), pp. 485–498, 2012.
  81. H. Speleers. Interpolation with quintic Powell-Sabin splines. Applied Numerical Mathematics 62(5), pp. 620–635, 2012.
  82. H. Speleers, C. Manni, F. Pelosi, and M.L. Sampoli. Isogeometric analysis with Powell-Sabin splines for advection-diffusion-reaction problems. Computer Methods in Applied Mechanics and Engineering 221–222, pp. 132–148, 2012.
  83. H. Speleers. On multivariate polynomials in Bernstein-Bézier form and tensor algebra. Journal of Computational and Applied Mathematics 236(4), pp. 589–599, 2011.
  84. L.L. Schumaker and H. Speleers. Convexity preserving splines over triangulations. Computer Aided Geometric Design 28(4), pp. 270–284, 2011.
  85. H. Speleers. A normalized basis for reduced Clough-Tocher splines. Computer Aided Geometric Design 27(9), pp. 700–712, 2010.
  86. H. Speleers. A normalized basis for quintic Powell-Sabin splines. Computer Aided Geometric Design 27(6), pp. 438–457, 2010.
  87. L.L. Schumaker and H. Speleers. Nonnegativity preserving macro-element interpolation of scattered data. Computer Aided Geometric Design 27(3), pp. 245–261, 2010.
  88. H. Speleers, P. Dierckx, and S. Vandewalle. On the local approximation power of quasi-hierarchical Powell-Sabin splines. In: M. Dæhlen et al. (eds.) Mathematical Methods for Curves and Surfaces, Lecture Notes in Computer Science 5862, pp. 419–433, 2010.
  89. H. Speleers, P. Dierckx, and S. Vandewalle. Quasi-hierarchical Powell-Sabin B-splines. Computer Aided Geometric Design 26(2), pp. 174–191, 2009.
  90. H. Speleers, P. Dierckx, and S. Vandewalle. On the Lp-stability of quasi-hierarchical Powell-Sabin B-splines. In: M. Neamtu and L.L. Schumaker (eds.) Approximation Theory XII, Nashboro Press, pp. 398–413, 2008.
  91. H. Speleers, P. Dierckx, and S. Vandewalle. Multigrid methods with Powell-Sabin splines. IMA Journal of Numerical Analysis 28(4), pp. 888–908, 2008.
  92. H. Speleers, P. Dierckx, and S. Vandewalle. Powell-Sabin splines with boundary conditions for polygonal and non-polygonal domains. Journal of Computational and Applied Mathematics 206(1), pp. 55–72, 2007.
  93. H. Speleers, P. Dierckx, and S. Vandewalle. Weight control for modelling with NURPS surfaces. Computer Aided Geometric Design 24(3), pp. 179–186, 2007.
  94. H. Speleers, P. Dierckx, and S. Vandewalle. Local subdivision of Powell-Sabin splines. Computer Aided Geometric Design 23(5), pp. 446–462, 2006.
  95. H. Speleers, P. Dierckx, and S. Vandewalle. Numerical solution of partial differential equations with Powell-Sabin splines. Journal of Computational and Applied Mathematics 189(1–2), pp. 643–659, 2006.

Book Chapters

  1. T. Lyche, C. Manni, and H. Speleers. Foundations of spline theory: B-splines, spline approximation, and hierarchical refinement. In: T. Lyche, C. Manni, and H. Speleers (eds.) Splines and PDEs: From Approximation Theory to Numerical Linear Algebra, Lecture Notes in Mathematics 2219, Springer Cham, pp. 1–76, 2018.
  2. C. Manni and H. Speleers. Standard and non-standard CAGD tools for isogeometric analysis: A tutorial. In: A. Buffa and G. Sangalli (eds.) IsoGeometric Analysis: A New Paradigm in the Numerical Approximation of PDEs, Lecture Notes in Mathematics 2161, Springer Cham, pp. 1–69, 2016.
  3. H. Speleers, P. Dierckx, and S. Vandewalle. Computer aided geometric design with Powell-Sabin splines. In: J.S. Wright and L.M. Hughes (eds.) Computer Animation, Nova Science Publishers, pp. 177–208, 2011.
  4. H. Speleers, P. Dierckx, and S. Vandewalle. Computer aided geometric design with Powell-Sabin splines. In: C.M. De Smet and J.A. Peeters (eds.) Computer-Aided Design and Other Computing Research Developments, Nova Science Publishers, pp. 319–350, 2009.

Books

  1. C. Manni and H. Speleers (eds.). Geometric Challenges in Isogeometric Analysis. Springer INdAM Series 49, Springer Cham, 2022.
  2. C. Giannelli and H. Speleers (eds.). Advanced Methods for Geometric Modeling and Numerical Simulation. Springer INdAM Series 35, Springer Cham, 2019.
  3. T. Lyche, C. Manni, and H. Speleers (eds.). Splines and PDEs: From Approximation Theory to Numerical Linear Algebra. Lecture Notes in Mathematics 2219, Springer Cham, 2018.

Other Publications

  1. H. Speleers. Construction, analysis and application of Powell-Sabin spline finite elements. Ph.D. Thesis, Dept. of Computer Science, University of Leuven, 2008.
  2. H. Speleers. Numerical simulation using Powell-Sabin splines. M.Sc. Thesis, Dept. of Computer Science, University of Leuven, 2004. (in Dutch)

This page is maintained by Hendrik Speleers
URL: https://www.mat.uniroma2.it/~speleers/research/publications.html