Numerical algorithm for the time dependent strongly-out-of-equilibrium Boltzmann equation: high dimensional Gauss integration

Abstract

This thesis focuses on substituting the current Monte Carlo method with Gauss integration, which adapts to the geometry of the problem, to solve the collision term of Boltzmann equation. The scattering integral is first derived from the time dependent Boltzmann equation for the study of electronic population in stronglyout- of-equilibrium solids. Next, Gauss points of the Cartesian product of simplexes are constructed using C++ to solve the scattering integral with Gauss integration. Comparing the new Gauss integration with the Monte Carlo method, it was found that Gauss integration can produce an accurate result in a shorter period of time, which is sufficient to replace the Monte Carlo method in solving the problem. Lastly, this new method was used in application to graphene to compute the thermalisation of electrons in scattering.