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Marco Vianello: work on Quadrature, Cubature and Summation

online publications and preprints (downloadable pdf), with some conference posters
see also the software section


  1. Tchakaloff-like compression of QMC volume and surface integration on union of balls
    preprint, with G. Elefante and A. Sommariva

  2. Homogenization of composite materials reinforced with unidirectional fibres with complex curvilinear cross section: a virtual element approach
    AIMS Math. Eng., to appear, with E. Artioli, G. Elefante and A. Sommariva

  3. Numerical cubature on scattered data by adaptive interpolation
    with R. Cavoretto, A. De Rossi, F. Dell'Accio, F. Di Tommaso, N. Siar and A. Sommariva
    J. Comput. Appl. Math., published online 24 January 2024

  4. Qsurf: compressed QMC integration on parametric surfaces
    arXiv:2304.08090, with G. Elefante and A. Sommariva
    J. Approx. Software, to appear

  5. TetraFreeQ: tetrahedra-free quadrature on polyhedral elements
    preprint, with A. Sommariva
    Appl. Numer. Math., published online 11 July 2023

  6. Low-cardinality Positive Interior cubature on NURBS-shaped domains
    preprint, with A. Sommariva
    BIT Numer. Math. 63 (2023)

  7. Cubature rules with positive weights on union of disks
    preprint, with A. Sommariva
    Dolomites Res. Notes Approx. DRNA 15 (2022) (Special Issue for the 60th of S. De Marchi, 73--81)

  8. CQMC: an improved code for low-dimensional Compressed Quasi-MonteCarlo cubature
    with G. Elefante and A. Sommariva
    Dolomites Res. Notes Approx. DRNA 15 (2022) (Special Issue "Software for Approximation 2022", 92--100)

  9. RBFCUB: a numerical package for near-optimal meshless cubature on general polygons
    preprint, with R. Cavoretto, A. De Rossi and A. Sommariva
    Appl. Math. Lett. 125 (2022)

  10. RBF moment computation and meshless cubature on general polygonal regions
    preprint, with A. Sommariva
    Appl. Math. Comput. 409 (2021)

  11. Near-algebraic Tchakaloff-like quadrature on spherical triangles
    preprint, with A. Sommariva
    Appl. Math. Lett. 120 (2021)

  12. Computing Tchakaloff-like cubature rules on spline curvilinear polygons
    preprint, with A. Sommariva
    Dolomites Res. Notes Approx. DRNA 14 (2021), 1--11

  13. Quadrature-based polynomial optimization
    preprint, with A. Martinez, F. Piazzon and A. Sommariva
    Optim. Lett. 14 (2020), 1027--1036
    co-winner of the OPTL Best Paper Awards for 2020

  14. Compressed cubature over polygons with applications to optical design
    preprint, with B. Bauman (LLNL, USA) and A. Sommariva
    J. Comput. Appl. Math. 370 (2020)

  15. Algebraic cubature on polygonal elements with a circular edge
    preprint, with E. Artioli and A. Sommariva
    Comput. Math. Appl. 79 (2020), 2057--2066

  16. Tchakaloff polynomial meshes
    preprint, with L. Bos
    Ann. Polon. Math. 122 (2019), 221--231

  17. Numerical quadrature on the intersection of planar disks
    preprint, with A. Sommariva
    FILOMAT 31:13 (2017), 4105--4115

  18. Subperiodic trigonometric subsampling: a numerical approach
    preprint, with A. Sommariva
    Appl. Anal. Discrete Math. 11 (2017), 470--483

  19. On the use of compressed polyhedral quadrature formulas in embedded interface methods
    preprint, with Y. Sudhakar, A. Sommariva and W.A. Wall
    SIAM J. Sci. Comput. 39 (2017), B571-B587
    such formulas have been used within the parallel multiphysics finite-element research code BACI
    developed at the Institute for Computational Mechanics, TUM Muenchen


  20. Caratheodory-Tchakaloff Subsampling
    with F. Piazzon and A. Sommariva
    Dolomites Res. Notes Approx. DRNA 10 (2017), 5--14
    poster presented at the II Joint Meeting Spain-Brazil in Mathematics (Cadiz, December 11-14 2018)

  21. Polynomial approximation and quadrature on geographic rectangles
    preprint, with M. Gentile and A. Sommariva
    Appl. Math. Comput. 297 (2017), 159--179
    poster presented at SIAM GeoSciences 2013, Padova (Italy)

  22. Compression of multivariate discrete measures and applications
    preprint, with A. Sommariva
    Numer. Funct. Anal. Optim. 36 (2015), 1198--1223

  23. Product Gaussian quadrature on circular lunes
    preprint, with G. Da Fies
    Numer. Math. Theory Methods Appl. 7 (2014), 251--264

  24. Algebraic cubature by linear blending of elliptical arcs
    preprint, with G. Da Fies and A. Sommariva
    Appl. Numer. Math. 74 (2013), 49--61

  25. Algebraic cubature on planar lenses and bubbles
    preprint, with G. Da Fies
    Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12

  26. Trigonometric Gaussian quadrature on subintervals of the period
    preprint, with G. Da Fies
    Electron. Trans. Numer. Anal. 39 (2012), 102--112

  27. Subperiodic trigonometric interpolation and quadrature
    preprint, with L. Bos
    Appl. Math. Comput. 218 (2012), 10630--10638

  28. Polynomial interpolation and cubature over polygons
    preprint, with M. Gentile and A. Sommariva
    J. Comput. Appl. Math. 235 (2011), 5232--5239

  29. An algebraic cubature formula on curvilinear polygons
    preprint, with G. Santin and A. Sommariva
    Appl. Math. Comput. 217 (2011), 10003--10015

  30. Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave
    preprint, with M. Caliari, S. De Marchi and A. Sommariva
    Numer. Algorithms 56 (2011), 45--60

  31. Gauss-Green cubature and moment computation over arbitrary geometries
    preprint, with A. Sommariva
    J. Comput. Appl. Math. 231 (2009), 886--896
    the Matlab code has been used in the CFD package SADoRe: Highly Accurate Lagrangian
    Flux Calculation via Algebraic Quadratures on Spline-Approximated Donating Regions

    by Q. Zhang (see paper in SIAM Review 55, 2013)

  32. A numerical code for fast interpolation and cubature at the Padua points
    preprint, with M. Caliari, S. De Marchi and A. Sommariva
    Proceedings of the 9th CMMSE (2009), Vol. I, 218--228

  33. New cubature formulae and hyperinterpolation in three variables
    preprint, with S. De Marchi and Y. Xu
    BIT Numerical Mathematics 49 (2009), 55--73

  34. Nontensorial Clenshaw-Curtis cubature
    preprint, with A. Sommariva and R. Zanovello
    Numer. Algorithms 49 (2008), 409--427

  35. Meshless cubature over the disk by Thin-Plate Splines
    preprint, with A. Punzi and A. Sommariva
    J. Comput. Appl. Math. 221 (2008), 430--436

  36. Product Gauss cubature over polygons based on Green's integration formula
    preprint, with A. Sommariva
    BIT Numerical Mathematics 47 (2007), 441--453
    this algorithm has been cited/used in many works on numerical PDEs, see its GoogleScholar page

  37. Meshless cubature by Green's formula
    preprint, with A. Sommariva
    Appl. Math. Comput. 183 (2006), 1098--1107

  38. Numerical cubature on scattered data by radial basis functions
    preprint, with A. Sommariva
    Computing 76 (2006), 295--310

  39. Fast summation of power series with coefficients analytic at infinity
    with A. Sommariva and R. Zanovello
    Numer. Algorithms 27 (2001), 77--87

  40. A new summation method for power series with rational coefficients
    with S. Dassie`and R. Zanovello
    Math. Comp. 69 (2000), 749--756

  41. Asymptotic summation of power series
    preprint, with S. Dassie`and R. Zanovello
    Numer. Math. 80 (1998), 61--73