High Performance Computational Methods for the Boltzmann Equation

The Boltzmann equation is highly important in mathematical modeling of physical systems large and small, from galactic dynamics to electron transport. Its range of applicability exceeds that of well-known continuum models, such as the Navier-Stokes-Fourier equations.

In particular, the Boltzmann equation can accurately predict rarefied gas phenomena, which occur in a wide variety of high-tech 21st century applications, such as microelectronics, plasma physics, and high altitude flight.

While numerical methods for continuum models are well established, numerical methods that accurately and efficiently solve the Boltzmann equation are undeveloped.

The main objective of this research proposal is to enable three-dimensional numerical simulation of rarefied flows by developing accurate and efficient numerical solution procedures for ``the method of moments'' to numerically solve the Boltzmann equation.

The approach described herein is innovative and original as it is the first to exploit Kronecker structure and structural properties of the Boltzmann equation to improve efficiency.

The developed techniques will be consolidated into a high performance computing framework and applied, for the first time, to an industrial photolithography application.

The proposed research involves a private-public partnership between domain experts in ``the method of moments'' at the Technical University of Eindhoven (TU/e) and experts in ``photolithography'' at ASML.

If awarded, this proposal will allow me to lay the groundwork necessary to achieve a paradigm-shift in numerical simulation of rarefied gas flows.

It could emanate into a successful line of research for the coming decade, with academic as well as commercial interests aligned with my career goals.

I am highly motivated and uniquely positioned to carry out this research due to my specialistic expertise in efficient solution methodologies and my interdisciplinary training in mathematics, computational science and engineering.