Journal Papers

• 2024

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

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

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

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

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

  6. 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.

  7. 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.

  8. 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. 

  9. 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.

  10. 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, submitted. 

• 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.