Sergio Barrera Cabodevila

Speeding up the numerical solution of the Boltzmann Equation in Diffusion Approximation

Supervisor: Sergio Barrera Cabodevila 

The Kinetic Theory framework is a state-of-the-art weak-coupling tool to explore the thermalization in heavy-ion collisions. The Boltzmann Equation in Diffusion Approximation (BEDA) is one particular implementation of a kinetic theory for which a GPU-based code has been recently developed. This code has an important issue of instabilities that significantly decreases its efficiency related to the numerical integration of the diffusion terms with the finite volume method. In this stay, we propose that the student modify this integration with a Crank-Nicolson method that does not suffer from these instabilities. The student will familiarize with the kinetic theory framework, very close to the kinetic description in statistical mechanics, as well as novel computational tools such as GPU programming. It is strongly recommended to have previous knowledge of basic computational techniques to solve partial differential equations. Prior C++ knowledge is also advisable.