Marco Vianello: work on Interpolation and Integration Methods for PDEs

online publications and preprints (downloadable pdf)

1. Unisolvence of Kansa collocation for elliptic equations by polyharmonic splines with random fictitious centers
   arXiv: 2410.03279, 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
   
   
3. Nonsingularity of unsymmetric Kansa matrices: random collocation by MultiQuadrics and Inverse MultiQuadrics
   arXiv: 2403.18017, with R. Cavoretto, A. De Rossi, F. Dell'Accio and A. Sommariva
   Math. Comput. Simul., minor revision
   
   
4. 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
   
   
5. 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
   
   
6. TetraFreeQ: tetrahedra-free quadrature on polyhedral elements
   preprint, with A. Sommariva
   Appl. Numer. Math. 200 (2024), 389--398
   
   
7. Low-cardinality Positive Interior cubature on NURBS-shaped domains
   preprint, with A. Sommariva
   BIT Numer. Math. 63, 22 (2023)
   
   
8. Algebraic cubature on polygonal elements with a circular edge
   preprint, with E. Artioli and A. Sommariva
   Comput. Math. Appl. 79 (2020), 2057--2066
   
   
9. 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
   
   
10. 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
    
    
11. 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
    
    
12. The LEM exponential integrator for advection-diffusion-reaction equations
    preprint, with L. Bergamaschi and M. Caliari
    J. Comput. Appl. Math. 210 (2007), 56--63
    
    
13. 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
    
    
14. 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
    
    
15. 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