Distinguished Seminar in Computational Science and Engineering
October 24, 2024, 12-1PM
Numerical methods for Boltzmann equation and related models
Giacomo Dimarco
Full Professor
Department of Mathematics and Computer Science,
University of Ferrara, Italy
Abstract:
In this talk, we will provide an overview of the state-of-the-art numerical methods for kinetic partial differential equations, with a particular focus on the widely studied Boltzmann equation. Kinetic models represent a powerful mathematical tool commonly used to describe the behaviors and the interactions of large particle systems. These equations are fundamental across various fields, including mathematics, physics, engineering and chemistry, while also finding broad applications in biology, medicine, economics and social sciences. Due to the high number of dimensions and their intrinsic physical properties, the construction of numerical methods represents a challenge and requires a careful balance between accuracy and computational complexity. Throughout the talk, we will discuss the derivation of fast algorithms, the concept of asymptotic preserving methods, Monte Carlo techniques, and the development of hybrid schemes.
Bio:
Giacomo Dimarco is Full Professor of Applied Mathematics since December 2021, Head of the Department of Mathematics and Computer Science and Director of the Center for Modeling and Scientific Computing of the University of Ferrara, Italy. He obtained his M.S. in Aerospace Engineering from the University of Pisa in 2004 and completed his PhD in Applied Mathematics at the University of Ferrara in 2008. From 2009 to 2013, he was an Assistant Professor at the University of Toulouse III in France, before returning to Italy, where he held the position of Associate Professor in Numerical Analysis from 2013 to 2021. He is Associate Editor for the Journal of Computational Physics and for Networks and Heterogeneous Media. His research interests encompass applied and computational mathematics, including kinetic equations, computational fluid dynamics, plasma physics, multiscale modeling, numerical methods for partial differential equations, collective dynamics, Monte Carlo methods, control, and uncertainty quantification.
Numerical methods for Boltzmann equation and related models
Giacomo Dimarco
University of Ferrara, Italy