Cluster Computing for Transient Simulations of the Linear Boltzmann Equation on Irregular Three-Dimensional Domains

Abstract

Processes used to manufacture integrated circuits take place at a range of pressures and their models are of interest across a wide range of length scales. We present a kinetic transport and reaction model given by a system of linear Boltzmann equations that is applicable to several important processes that involve contacting in-process wafers with reactive gases. The model is valid for a range of pressures and for length scales from micrometers to centimeters, making it suitable for multiscale models. Since a kinetic model in three dimensions involves discretizations of the three-dimensional position as well as of the three-dimensional velocity space, millions of unknowns result. To efficiently perform transient simulations with many time steps, the size of the problem motivates the use of parallel computing. We present simulation results on an irregular three-dimensional domain that highlights the capabilities of the model and its implementation, as well as parallel performance studies on a distributed-memory cluster show that the computation time scales well with the number of processes.