82 citations · 753 across the 71 of their papers we have counts for
18 papers · 1 filter
Reduced variance random batch methods for nonlocal PDEs
Lorenzo Pareschi, Mattia Zanella
Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-line…
Uncertainty Quantification for the Homogeneous Landau-Fokker-Planck Equation via Deterministic Particle Galerkin methods
Rafael Bailo, José Antonio Carrillo, Andrea Medaglia +1
We design a deterministic particle method for the solution of the spatially homogeneous Landau equation with uncertainty. The deterministic particle approximation is based on the r…
Particle simulation methods for the Landau-Fokker-Planck equation with uncertain data
Andrea Medaglia, Lorenzo Pareschi, Mattia Zanella
The design of particle simulation methods for collisional plasma physics has always represented a challenge due to the unbounded total collisional cross section, which prevents a n…
Stochastic Galerkin particle methods for kinetic equations of plasmas with uncertainties
Andrea Medaglia, Lorenzo Pareschi, Mattia Zanella
The study of uncertainty propagation is of fundamental importance in plasma physics simulations. To this end, in the present work we propose a novel stochastic Galerkin (sG) partic…
Micro-macro stochastic Galerkin methods for nonlinear Fokker-Plank equations with random inputs
Giacomo Dimarco, Lorenzo Pareschi, Mattia Zanella
Nonlinear Fokker-Planck equations play a major role in modeling large systems of interacting particles with a proved effectiveness in describing real world phenomena ranging from c…
Monte Carlo stochastic Galerkin methods for non-Maxwellian kinetic models of multiagent systems with uncertainties
Andrea Medaglia, Andrea Tosin, Mattia Zanella
In this paper, we focus on the construction of a hybrid scheme for the approximation of non-Maxwellian kinetic models with uncertainties. In the context of multiagent systems, the…
Mean-field control variate methods for kinetic equations with uncertainties and applications to socio-economic sciences
Lorenzo Pareschi, Torsten Trimborn, Mattia Zanella
In this paper, we extend a recently introduced multi-fidelity control variate for the uncertainty quantification of the Boltzmann equation to the case of kinetic models arising in…
Monte Carlo stochastic Galerkin methods for the Boltzmann equation with uncertainties: space-homogeneous case
Lorenzo Pareschi, Mattia Zanella
In this paper we propose a novel numerical approach for the Boltzmann equation with uncertainties. The method combines the efficiency of classical direct simulation Monte Carlo (DS…
Structure preserving schemes for Fokker-Planck equations with nonconstant diffusion matrices
N. Loy, M. Zanella
In this work we consider an extension of a recently proposed structure preserving numerical scheme for nonlinear Fokker-Planck-type equations to the case of nonconstant full diffus…
Monte Carlo gPC methods for diffusive kinetic flocking models with uncertainties
Jose Antonio Carrillo, Mattia Zanella
In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantiti…
Structure preserving stochastic Galerkin methods for Fokker-Planck equations with background interactions
Mattia Zanella
This paper is devoted to the construction of structure preserving stochastic Galerkin schemes for Fokker-Planck type equations with uncertainties and interacting with an external d…
Particle based gPC methods for mean-field models of swarming with uncertainty
J. A. Carrillo, L. Pareschi, M. Zanella
In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The metho…
Hybrid stochastic kinetic description of two-dimensional traffic dynamics
Michael Herty, Andrea Tosin, Giuseppe Visconti +1
In this work we present a two-dimensional kinetic traffic model which takes into account speed changes both when vehicles interact along the road lanes and when they change lane. A…
Uncertainty quantification for kinetic models in socio-economic and life sciences
Giacomo Dimarco, Lorenzo Pareschi, Mattia Zanella
Kinetic equations play a major rule in modeling large systems of interacting particles. Recently the legacy of classical kinetic theory found novel applications in socio-economic a…
Structure preserving schemes for mean-field equations of collective behavior
Lorenzo Pareschi, Mattia Zanella
In this paper we consider the development of numerical schemes for mean-field equations describing the collective behavior of a large group of interacting agents. The schemes are b…
Structure preserving schemes for nonlinear Fokker-Planck equations and applications
Lorenzo Pareschi, Mattia Zanella
In this paper we focus on the construction of numerical schemes for nonlinear Fokker-Planck equations that preserve the structural properties, like non negativity of the solution,…
Opinion dynamics over complex networks: kinetic modeling and numerical methods
Giacomo Albi, Lorenzo Pareschi, Mattia Zanella
In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents' distribution over the evolving network is…
Uncertainty Quantification in Control Problems for Flocking Models
Giacomo Albi, Lorenzo Pareschi, Mattia Zanella
In this paper the optimal control of flocking models with random inputs is investigated from a numerical point of view. The effect of uncertainty in the interaction parameters is s…