Marco Vianello: work on Interpolation and Integration Methods for PDEs

online publications and preprints (downloadable pdf)

1. Unisolvence of randomized MultiQuadric Kansa collocation for convection-diffusion with mixed boundary conditions
   arXiv: 2503.00963, with M. Mohammadi and A. Sommariva
   
   
2. Unisolvence of unsymmetric random Kansa collocation by Gaussians and other analytic RBF vanishing at infinity
   arXiv: 2405.18550, with A. Sommariva
   J. Comput. Appl. Math., to appear
   
   
3. Cheap and stable quadrature on polyhedral elements
   arXiv: 2502.03446, with A. Sommariva
   Finite Elem. Anal. Des., to appear
   
   
4. Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers
   with M. Mohammadi and A. Sommariva
   Appl. Math. Lett. 168 (2025), 109571
   
   
5. Nonsingularity of unsymmetric Kansa matrices: random collocation by MultiQuadrics and Inverse MultiQuadrics
   with R. Cavoretto, A. De Rossi, F. Dell'Accio and A. Sommariva
   Math. Comput. Simul. 234 (2025), 390--395
   
   
6. 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
   
   
7. Unisolvence of random Kansa collocation by Thin-Plate Splines for the Poisson equation
   preprint, with F. Dell'Accio and A. Sommariva
   Eng. Anal. Bound. Elem. 165 (2024), 105773
   
   
8. TetraFreeQ: tetrahedra-free quadrature on polyhedral elements
   preprint, with A. Sommariva
   Appl. Numer. Math. 200 (2024), 389--398
   
   
9. Low-cardinality Positive Interior cubature on NURBS-shaped domains
   preprint, with A. Sommariva
   BIT Numer. Math. 63, 22 (2023)
   
   
10. Algebraic cubature on polygonal elements with a circular edge
    preprint, with E. Artioli and A. Sommariva
    Comput. Math. Appl. 79 (2020), 2057--2066
    
    
11. 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
    
    
12. On the generation of symmetric Lebesgue-like points in the triangle
    preprint, with F. Rapetti and A. Sommariva
    J. Comput. Appl. Math. 236 (2012), 4925--4932
    
    
13. A massively parallel exponential integrator for advection-diffusion models
    preprint, with L. Bergamaschi, M. Caliari and A. Martinez
    J. Comput. Appl. Math. 231 (2009), 82--91
    
    
14. The LEM exponential integrator for advection-diffusion-reaction equations
    preprint, with L. Bergamaschi and M. Caliari
    J. Comput. Appl. Math. 210 (2007), 56--63
    
    
15. A parallel exponential integrator for large-scale discretizations of advection-diffusion models
    preprint, with L. Bergamaschi, M. Caliari and A. Martinez
    Springer LNCS vol. 3666, 2005 (Proc. of Euro PVM MPI 2005, Sorrento, Italy), 483--492
    
    
16. The ReLPM exponential integrator for FE discretizations of advection-diffusion equations
    preprint, with L. Bergamaschi and M. Caliari
    Springer LNCS vol. 3039, part IV, 2004 (Proc. of ICCS 2004, Krakow, Poland), 434--442
    
    
17. Interpolating discrete advection-diffusion propagators at Leja sequences
    preprint, with L. Bergamaschi and M. Caliari
    J. Comput. Appl. Math. 172 (2004), no. 1, 79--99