J. Hu, M. Zanella
- Purdue Univ., Politecnico di Torino
lunedì 26 novembre 2018
Efficient Numerical Methods for Kinetic equations
by Jingwei Hu (Purdue University)
In multiscale modeling hierarchy, the Boltzmann and related kinetic equations serve as a building block that bridges microscopic Newtonian mechanics and macroscopic continuum mechanics. In this short course, I will start with a brief introduction of basic kinetic equations, and then discuss various numerical aspects of efficiently solving these equations, including fast algorithms for collision operators, asymptotic-preserving schemes for multiscale problems. I will also cover some recent development on uncertainty quantification for kinetic equations.
26/11, 14:30-16:00, Aula B, Ca' Vignal 1.
28/11, 11:00-12:30, SPC, Polo S. Marta.
29/11, 9:00-10:30, SPC, Polo S. Marta.
Uncertainty quantification for kinetic equations of collective behaviors
by Mattia Zanella (Politecnico di Torino)
In this seminar we concentrate on collocation and stochastic Galerkin methods for the uncertainty quantification of Vlasov--Fokker--Planck (VFP) equations with nonlocal flux. In particular, we develop methods that preserve their structural properties and that are spectrally accurate in the random space. In contrast to a direct application of classical uncertainty quantification methods, which are typically lead to the loss of positivity and of entropy properties, the proposed schemes are capable to achieve high accuracy in the random space without losing non-negativity of the solution, which dissipates the entropy under suitable assumptions. Applications of the developed methods will be presented in the context of social and traffic dynamics.
29/11, 14:00-15:00, SPC, Polo S. Marta.
30/11, 11:00-12:00, Aula Alfa, Ca' Vignal 2.
Each mini-course is self-contained, and does not require Part A, and Part B.