LJKDeterministic Models and Algorithms: EDPMOISEMGMI Seminar

On Thursday March 12 2015 at 11h00 in Salle 1  Tour IRMA

Seminary of Mr Minh Binh TRAN (Basque Center for Applied Mathematics, Bilbao)

Nonlinear approximation theory for the homogeneous Boltzmann equation

Summary

A challenging problem in solving the Boltzmann equation numerically is that the velocity space is approximated by a finite region. Therefore, most methods are based on a truncation technique and the computational cost is then very high if the velocity domain is large. Moreover, sometimes, nonphysical conditions have to be imposed on the equation in order to keep the velocity domain bounded. In this talk, we introduce the first nonlinear approximation theory for the Boltzmann equation. Our nonlinear wavelet approximation is nontruncated and based on a nonlinear, adaptive spectral method associated with a new wavelet filtering technique and a new formulation of the equation. The approximation is proved to converge and perfectly preserve most of the properties of the homogeneous Boltzmann equation. It could also be considered as a general framework for approximating kinetic integral equations.
