Marco Vianello: work on Cubature rules for polytopal FEM & VEM

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

1. Effective numerical integration on complex shaped elements by discrete signed measures
   with L. Rinaldi and A. Sommariva
   arXiv:2510.23069
   
   
2. Cheap and stable quadrature on polyhedral elements
   with A. Sommariva
   Finite Elem. Anal. Des. 251 (2025), 104409
   
   
3. 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
   
   
4. TetraFreeQ: tetrahedra-free quadrature on polyhedral elements
   preprint, with A. Sommariva
   Appl. Numer. Math. 200 (2024), 389--398
   
   
5. Low-cardinality Positive Interior cubature on NURBS-shaped domains
   preprint, with A. Sommariva
   BIT Numer. Math. 63, 22 (2023)
   
   
6. Computing Tchakaloff-like cubature rules on spline curvilinear polygons
   preprint, with A. Sommariva
   Dolomites Res. Notes Approx. DRNA 14 (2021), 1--11
   
   
7. Algebraic cubature on polygonal elements with a circular edge
   preprint, with E. Artioli and A. Sommariva
   Comput. Math. Appl. 79 (2020), 2057--2066
   
   
8. 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
   
   
9. 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)
   
   
10. 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