Marco Vianello: work on Quadrature, Cubature and Summation

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

1. Homogenization of composite materials reinforced with unidirectional fibres with complex curvilinear cross section: a virtual element approach
   preprint, with E. Artioli, G. Elefante and A. Sommariva
   AIMS Math. Eng. 6 (2024), 510--535
   
   
2. Qsurf: compressed QMC integration on parametric surfaces
   preprint, with G. Elefante and A. Sommariva
   JAS - J. Approx. Software 1, 1 (2024)
   
   
3. Tchakaloff-like compression of QMC volume and surface integration on the union of balls
   preprint, with G. Elefante and A. Sommariva
   Calcolo 61, 46 (2024)
   
   
4. Numerical cubature on scattered data by adaptive interpolation
   preprint, with R. Cavoretto, A. De Rossi, F. Dell'Accio, F. Di Tommaso, N. Siar and A. Sommariva
   J. Comput. Appl. Math. 444 (2024), 115793
   
   
5. TetraFreeQ: tetrahedra-free quadrature on polyhedral elements
   preprint, with A. Sommariva
   Appl. Numer. Math. 200 (2024), 389--398
   
   
6. Low-cardinality Positive Interior cubature on NURBS-shaped domains
   preprint, with A. Sommariva
   BIT Numer. Math. 63, 22 (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