1 citations · 1 across the 10 of their papers we have counts for
11 papers
Physics Informed Neural Networks for Learning the Horizon Size in Bond-Based Peridynamic Models
Fabio V. Difonzo, Luciano Lopez, Sabrina F. Pellegrino
This paper broaches the peridynamic inverse problem of determining the horizon size of the kernel function in a one-dimensional model of a linear microelastic material. We explore…
A spectral method for dispersive solutions of the nonlocal Sine-Gordon equation
A. Coclite, L. Lopez, S. F. Pellegrino
Moved by the need for rigorous and reliable numerical tools for the analysis of peridynamic materials, the authors propose a model able to capture the dispersive features of nonloc…
Convergence Analysis of a Spectral Numerical Method for a Peridynamic Formulation of Richards' Equation
Fabio V. Difonzo, Sabrina F. Pellegrino
We study the implementation of a Chebyshev spectral method with forward Euler integrator to investigate a peridynamic nonlocal formulation of Richards' equation. We prove the conve…
Physics Informed Neural Networks for an Inverse Problem in Peridynamic Models
Fabio Vito Difonzo, Luciano Lopez, Sabrina Francesca Pellegrino
Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by…
A filtered Chebyshev spectral method for conservation laws on network
Sabrina Francesca Pellegrino
We propose a spectral method based on the implementation of Chebyshev polynomials to study a model of conservation laws on network. We avoid the Gibbs phenomenon near shock discont…
A Numerical Method for a Nonlocal Form of Richards' Equation Based on Peridynamic Theory
M. Berardi, F. V. Difonzo, S. F. Pellegrino
Forecasting water content dynamics in heterogeneous porous media has significant interest in hydrological applications; in particular, the treatment of infiltration when in presenc…
A fast-convolution based space-time Chebyshev spectral method for peridynamic models
Luciano Lopez, Sabrina Francesca Pellegrino
Peridynamics is a nonlocal generalization of continuum mechanics theory which adresses discontinuous problems without using partial derivatives and replacing its by an integral ope…
Computation of Eigenvalues for Nonlocal Models by Spectral Methods
Luciano Lopez, Sabrina Francesca Pellegrino
The purpose of this work is to study spectral methods to approximate the eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain is an interval, it is very c…
A space-time discretization of a nonlinear peridynamic model on a 2D lamina
Luciano Lopez, Sabrina Francesca Pellegrino
Peridynamics is a nonlocal theory for dynamic fracture analysis consisting in a second order in time partial integro-differential equation. In this paper, we consider a nonlinear m…
On the implementation of a finite volumes scheme with monotone transmission conditions for scalar conservation laws on a star-shaped network
Sabrina Francesca Pellegrino
In this paper we validate the implementation of the numerical scheme proposed in [3]. The validation is made by comparison with an explicit solution here obtained, and the solution…
Numerical Methods for the Nonlocal Wave Equation of the Peridynamics
Giuseppe Maria Coclite, Alessandro Fanizzi, Luciano Lopez +2
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently rec…