Journal Papers

• 2026

  1. FVD, Set-Valued Analysis of Generalized Barycentric Coordinates and Their Geometric Properties, https://arxiv.org/abs/2306.00710.

  2. FVD, V. Kungurtsev, J. Marecek, Stochastic Langevin and Hamiltonian Differential Inclusions with Applications to Machine Learning, https://arxiv.org/abs/2206.11533

  3. R. D'Ambrosio, FVD, L. Dieci, An IVP solver for Filippov systems on co-dimension 2 manifolds and approximation of periodic orbits, in progress.

  4. R. D'Ambrosio, FVD, Asymptotic preserving time integration of the stochastic KdV equation with multiplicative noise, under review.

  5. FVD, M. Roubalik, J. Marecek, Predictability and Fairness in Load Aggregation with Deadband, under review https://arxiv.org/abs/2305.17725

  6. D. Fiedler, FVD, J. Mrkos, Optimal Chaining of Vehicle Plans with Time Windows, under review https://arxiv.org/abs/2401.02873

  7. FVD, P. Przybylowicz, Y. Wu, X. Xie, A Randomized Runge-Kutta Method for time-irregular delay differential equations, under review https://arxiv.org/abs/2401.11658

• 2025

  1. R. D'Ambrosio, FVD, Structure-Preserving Physics-Informed Neural Networks with Chebyshev-Type Loss Functions, under review.

  2. V. Bohaienko, F. Diele, FVD, C. Marangi, A. Martiradonna, A. Provenzale, Vertical modeling of carbon sequestration in coastal wetlands using fractional-order derivatives and moisture dynamics, Mathematics and Computers in Simulation, Volume 233, 2025, Pages 369-388 https://doi.org/10.1016/j.matcom.2025.02.005

  3. FVD, L. Lopez, S.F. Pellegrino, Physics Informed Neural Networks for Learning the Horizon in Bond-Based Peridynamic Models, Computer Methods in Applied Mechanics and Engineering, Volume 436, 1 March 2025, 117727  https://doi.org/10.1016/j.cma.2024.117727

  4. M. Berardi, FVD, M. Icardi, Inverse Physics-Informed Neural Networks for transport models in porous materials, Computer Methods in Applied Mechanics and Engineering, Volume 435, 2025, 117628 https://doi.org/10.1016/j.cma.2024.117628

• 2024

  1. FVD. S.F. Pellegrino, Convergence Analysis of a Spectral Numerical Method for a Peridynamic Formulation of Richards' Equation, Mathematics and Computers in Simulation, 2024, 223: 219-228  https://doi.org/10.1016/j.matcom.2024.04.007

  2. FVD, L. Lopez, S.F. Pellegrino, Physics Informed Neural Networks for an Inverse Problem in Peridynamic Models, Engineering with Computers, 2024 https://doi.org/10.1007/s00366-024-01957-5

  3. L. Dieci, FVD, N. Sukumar, Nonnegative moment coordinates on convex and nonconvex finite elements, Mathematics in Engineering, 2024, 6(1): 81-99 https://www.aimspress.com/article/doi/10.3934/mine.2024004

  4. FVD, P. Przybylowicz, Y. Wu, Existence, uniqueness and approximation of solutions to Carathéodory delay differential equations, Journal of Computational and Applied Mathematics, Volume 436, 2024, 115411 https://doi.org/10.1016/j.cam.2023.115411

• 2023

  1. M. Berardi, FVD, R. Guglielmi, A preliminary model for optimal control of moisture content in unsaturated soils, Computational Geosciences, 27, 1133–1144 (2023) https://doi.org/10.1007/s10596-023-10250-1 

  2. FVD, F. Di Lena, Numerical Modeling of Peridynamic Richards’ Equation with Piecewise Smooth Initial Conditions Using Spectral Methods. Symmetry 2023, 15, 960 https://doi.org/10.3390/sym15050960

  3. M. Berardi, FVD, S.F. Pellegrino, A Numerical Method for a Nonlocal Form of Richards' Equation Based on Peridynamic Theory, Computers & Mathematics with Applications, Volume 143, 2023, pp. 23-32, https://doi.org/10.1016/j.camwa.2023.04.032

• 2022

  1. M. Berardi, FVD, A quadrature-based scheme for numerical solutions to Kirchhoff transformed Richards' equation, Journal of Computational Dynamics 2022 9(2): 69-84, https://doi.org/10.3934/jcd.2022001

  2. FVD, Isochronous attainable manifolds for piecewise smooth dynamical systems, Qualitative Theory of Dynamical Systems 21, 6 (2022), https://doi.org/10.1007/s12346-021-00536-z

• 2021

  1. FVD, C. Masciopinto, M. Vurro, M. Berardi, Shooting the numerical solution of moisture flow equation with root water uptake models: a Python tool, Water Resources Management 35, 2553–2567 (2021), https://doi.org/10.1007/s11269-021-02850-2

• 2020

  1. FVD, A note on attractivity for the intersection of two discontinuity manifolds, Opuscula Mathematica 40, no. 6 (2020), 685-702, https://doi.org/10.7494/OpMath.2020.40.6.685.

  2. M. Berardi, FVD, L. Lopez, A mixed MoL-TMoL for solving 2D Richards' equation in layered soils, Computers & Mathematics with Applications, 2020, 79(7), pp. 1990-2001, https://doi.org/10.1016/j.camwa.2019.07.026

  3. M. Berardi, FVD, Strong solutions for Richards' equation with Cauchy conditions and constant pressure gradient, Environmental Fluid Mechanics,  2020, 20(1), 165-174, https://doi.org/10.1007/s10652-019-09705-w

• 2019

  1. M. Berardi, FVD, F. Notarnicola, M. Vurro, A transversal method of lines for the numerical modeling of vertical infiltration into the vadose zone, Applied Numerical Mathematics, 2019,  135, 264–275, https://doi.org/10.1016/j.apnum.2018.08.013

• 2018

  1. M. Berardi, FVD, M. Vurro, L. Lopez, The 1D Richards' equation in two layered soils: a Filippov approach to treat discontinuities, Advances in Water Resources, 2018, 115, 264-272, https://doi.org/10.1016/j.advwatres.2017.09.027

• 2017

  1. L. Dieci, FVD, On the inverse of some sign matrices and on the moments sliding vector field on the intersection of several manifolds: nodally attractive case, Journal of Dynamics and Differential Equations, 2017, 29(4), 1355-1381. https://doi.org/10.1007/s10884-016-9527-5

  2. L. Dieci, FVD, The moments sliding vector field on the intersection of two manifolds, Journal of Dynamics and Differential Equations, 2017, 29(1), 169-201. https://doi.org/10.1007/s10884-015-9439-9

• 2016

  1. L. Dieci, FVD, Minimum Variation Solutions for Sliding Vector Fields on  the Intersection of Two Surfaces in R³, Journal of Computational and Applied Mathematics, 2016, 292, 732-745. https://doi.org/10.1016/j.cam.2015.02.026

• 2015

  1. FVD, The Filippov moments solution on the intersection of two and three manifolds, PhD Thesis, Georgia Institute of Technology, December 2015.

• 2014

  1. L. Dieci, FVD, A comparison of Filippov sliding vector fields in co-dimension 2, Journal of Computational and Applied Mathematics, 2014, 262, 161–179. https://doi.org/10.1016/j.cam.2013.10.055. Corrigendum in Journal of Computational and Applied Mathematics, 2014, 272, 273-273. https://doi.org/10.1016/j.cam.2014.06.006

Conference Papers

• 2024

  1. FVD, R. Garrappa, An easy-to-use tool to solve differential equations with the fractional Laplacian, IFAC-PapersOnLine, Volume 58, Issue 12, 2024, Pages 312-317, ISSN 2405-8963, https://doi.org/10.1016/j.ifacol.2024.08.208

• 2021

  1. FVD, G. Girardi, On the shooting method applied to Richards' equation with a forcing term, Gervasi O. et al. (eds) Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science, vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_20

Book Chapters

• 2023

  1. FVD, R. Garrappa, A numerical procedure for fractional-time-space differential equations with the spectral fractional Laplacian. In: Cardone, A., Donatelli, M., Durastante, F., Garrappa, R., Mazza, M., Popolizio, M. (eds) Fractional Differential Equations. INDAM 2021. Springer INdAM Series, vol 50. Springer, Singapore. https://doi.org/10.1007/978-981-19-7716-9_3