The Department is delighted to welcome Lorenzo Pareschi (Università di Ferrara) as a Nelder fellow in September-October 2015.

Background: Lorenzo's research activity focuses mainly on phenomena described by time dependent nonlinear partial differential equations, in particular by hyperbolic balance laws and kinetic models. Both classes of equations express fundamental laws of physics and are of great importance in many modern applications that range from gas dynamics, plasma and quantum physics to shallow water, traffic flows, economy and biology, to mention only a few relevant examples. If you are would like to meet him, please send an email to lorenzo.pareschi@unife.it.

Abstract: Lorenzo will deliver a minicourse on numerical methods for kinetic equations. The lectures will take place on Friday 2nd, Wednesday 7th and Friday 9th October. In this course the design and the mathematical analysis of numerical methods for kinetic partial differential equations will be considered. Kinetic equations represent a way of describing the time evolution of a system consisting of a large number of particles. Kinetic equations represent the bridge between a microscopic description and a macroscopic description of the physical reality. 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.

We review the basic numerical techniques for dealing with such equations, including the case of semi-Lagrangian methods, discrete velocity models and spectral methods. In addition we give an overview of the current state of the art of numerical methods for kinetic equations. This covers the derivation of fast algorithms, the notion of asymptotic preserving methods and the construction of hybrid schemes.

Friday 2 October, 15:00-17:00, Huxley 144

Lecture1:‌ Preliminaries on kinetic equations
Lecture 2: Semi-Lagrangian schemes

Wednesday 7 October, 16.00-18.00, Huxley 130

Lecture 3: Discrete-velocity and spectral methods
Lecture 4: Breaking complexity

Friday 9 October, 15.00-17.00, Huxley 340

Lecture 5: Asymptotic-preserving schemes
Lecture 6: Fluid-kinetic coupling and hybrid methods

 Follow the link to find out further information on Prof Pareschi's website