|
|
Calendario degli incontri a.a. 2024-2025
|
|
|
Martedì 15 ottobre 2024, ore 15.00, Sala di Consiglio
Adriano Festa
Politecnico di Torino
A network model for urban planning
Abstract:
In this seminar we present a mathematical model to describe the evolution of a city, which is determined by the interaction of two large populations of agents, workers and firms. The map of the city is described by a network with the edges representing at the same time residential areas and communication routes. The two populations compete for space while interacting through the labour market. The resulting model is described by a two population Mean-Field Game system coupled with an Optimal Transport problem. We prove existence and uniqueness of the solution and we provide some numerical tools to develop several numerical simulations. This is a joint work with Fabio Camilli (Sapienza Roma) and Luciano Marzufero (Libera Università di Bolzano).
Giovedì 05 settembre 2024, ore 14.00, Sala di Consiglio
Andreas Meister
University of Kassel
Modified Patankar-Runge-Kutta Methods: Introduction, Analysis and Numerical Applications
Abstract:
Modified Patankar-Runge-Kutta (MPRK) schemes are numerical methods for the solution of positive and conservative production-destruction systems. They adapt explicit Runge-Kutta schemes in a way to ensure positivity and conservation irrespective of the time step size. We introduce a general definition of MPRK schemes and present a thorough investigation of necessary as well as sufficient conditions to derive first, second and third order accurate MPRK schemes. The theoretical results will be confirmed by numerical experiments in which MPRK schemes are applied to solve non-stiff and stiff systems of ordinary differential equations. Furthermore, we present an investigation of MPRK schemes in the context of convection-diffusion-reaction equations with source terms of production-destruction type.
|