# A discontinuous Galerkin fast spectral method for multi-species full Boltzmann on streaming multi-processors

## TL;DR

This paper introduces a fast spectral discontinuous Galerkin method for solving the multi-species full Boltzmann equation efficiently on GPUs, significantly outperforming traditional stochastic methods in speed.

## Contribution

The paper presents a novel GPU-accelerated DGFS implementation for the full Boltzmann equation, achieving high parallel efficiency and speedup over existing stochastic approaches.

## Key findings

- Solves the Boltzmann equation in minutes, two orders faster than DSMC.
- Achieves parallel efficiency of 0.96--0.99 on 36 GPUs.
- Demonstrates effective weak/strong scaling performance.

## Abstract

When the molecules of a gaseous system are far apart, say in microscale gas flows where the surface to volume ratio is high and hence the surface forces dominant, the molecule-surface interactions lead to the formation of a local thermodynamically non-equilibrium region extending few mean free paths from the surface. The dynamics of such systems is accurately described by Boltzmann equation. However, the multi-dimensional nature of Boltzmann equation presents a huge computational challenge. With the recent mathematical developments and the advent of petascale, the dynamics of full Boltzmann equation is now tractable. We present an implementation of the recently introduced multi-species discontinuous Galerkin fast spectral (DGFS) method for solving full Boltzmann on streaming multi-processors. The present implementation solves the inhomogeneous Boltzmann equation in span of few minutes, making it at least two order-of-magnitude faster than the present state-of-art stochastic method---direct simulation Monte Carlo---widely used for solving Boltzmann equation. Various performance metrics, such as weak/strong scaling have been presented. A parallel efficiency of 0.96--0.99 is demonstrated on 36 Nvidia Tesla-P100 GPUs.