High performance multidimensional polynomial handling through expression templates for the Boltzmann equation - Dongol, Keynesh (Nanyang Technological University, 2023)
This thesis is dedicated to the development of a numerical solver for the Boltzmann Collision Operator. Non-equilibrium phenomenons are prevalent everywhere, from semi-conductor technologies to solar cells[1]. It is recently that the field of ultrafast physics has taken over the world by storm and hence ushered in a new field of strongly out-of-equilibrium dynamics with the promising potential to further drive technological advances. For an accurate depiction of strongly out-of-equilibrium dynamics, it is necessary that we are able to simulate complicated interplay of scattering events in a crystal. Recently, a novel approach using The Time Dependent Boltzmann Equation (TDBE) has been shown to feasibly treat the full complexity of strongly out- of-equilibrium dynamics, while conserving momentum, energy, and particle density. Though the TDBE’s approach is a lot cheaper than a full quan- tum mechanical treatment, the reality is TDBE faces an uphill battle due to the presence of its scattering integral which has an impractical scaling with precision. One such approximation used to minimise the numerical complexity was to limit the order of the terms in the integral (either to linear or quadratic). In this thesis, I will introduce a major modification to this solver by extending the formulation of the solver to include higher or- der basis functions to further describe the above dynamics more accurately. Whilst the complexity of the solver increases, it is possible to reduce the overall operations to accurately describe strongly out-of-equilibrium dynam- ics. Such a task requires an understanding of the theoretical model behind the TDBE and hardware utilization of our solver to able to able contribute to the solver.