Numerical methods for multiscale control problems and applications

Starting date
February 5, 2018
Duration (months)
12
Departments
Computer Science
Managers or local contacts
Albi Giacomo

Several phenomena in modern science and technology can be described by means of non-linear differential equations such as hyperbolic system with source term, kinetic equations and advection reaction diffusion models. These models play a fundamental role in classical physics, and in industrial applications, for example in plasma physics, granular gases, semiconductor design, or metheorolgy and geophysical problems. More recently these tools of mathematical science have been extended to interacting particle systems in order to describe soft-science problems such as: financial markets, opinon dynamics, traffic flow, crowd evacuation, cancer cells growth, biological newtwork formation.
In each of these contexts one of the fundamental aspect is to determine the conditions, and the forcing terms which highly influence the dynamics, and can be controlled.

Our project wants to analyze these themes by developing efficient numerical methods for control problems where the constrains are described by the evolution of kinetic, and hyperbolic models.

The research outlines we will develop are:


1) Control of kinetic models
(G. Albi, G. Dimarco, L. Pareschi, G. Puppo, M. Semplice, G. Visconti, M. Zanella).

2) Hamilton-Jacobi equation and applications to optimal control
(S. Cacace, E. Carlini, M. Falcone, R. Ferretti, G. Paolucci, L. Saluzzi).

3) IMEX method for differential equations
(G. Albi, G. Dimarco, L. Pareschi, S. Boscarino, G. Russo).


4) High-Order schemes for conservation and balance laws
(E. Abbate, S. Boscarino, G. Russo, G. Puppo, M. Semplice, A. Thomman, G. Visconti).


5) Mean-field optimal control and mean-field games, and uncertainty quantification
(G. Albi, S. Cacace, E. Carlini, G. Dimarco, L. Pareschi, M. Zanella).

Sponsors:

INdAM
Funds: assigned and managed by an external body

Project participants

Giacomo Albi
Temporary Assistant Professor

Collaboratori esterni

Sebastiano Boscarino
Università di Catania
Elisabetta Carlini
Università degli Studi di Roma "La Sapienza"
Giacomo DiMarco
Università di Ferrara
Maurizio Falcone
Università degli Studi di Roma
Roberto Ferretti
Università Roma Tre
Lorenzo Pareschi
Università di Ferrara
Gabriella Puppo
Politecnico di Torino
Giovanni Russo
Università di Catania
Matteo Semplice
Università di Torino
Simone Cacace
Università Roma Tre
Luca Saluzzi
Università di Roma "La Sapienza"
Giulio Paolucci
Università di Roma "La Sapienza"
Andrea Thomann
Università degli studi dell'Insubria
Giuseppe Visconti
Università di Torino
Mattia Zanella
Politecnico di Torino
Research areas involved in the project
Matematica - applicazioni e modelli
Numerical analysis

Activities

Research facilities