# Fast Kinetic Scheme : efficient MPI parallelization strategy for 3D Boltzmann equation

## TL;DR

This paper introduces an MPI parallelization strategy for the Fast Kinetic Scheme to efficiently solve the 3D Boltzmann equation, demonstrating near-ideal scalability on large-scale systems.

## Contribution

It extends the Fast Kinetic Scheme to the full Boltzmann equation and develops an efficient parallelization approach for high-dimensional kinetic simulations.

## Key findings

- Achieves close to ideal scalability on tera- and peta-scale systems.
- Successfully extends the scheme from BGK approximation to full Boltzmann equation.
- Demonstrates efficient parallelization for high-dimensional kinetic equations.

## Abstract

In this paper we present a parallelization strategy on distributed memory systems for the Fast Kinetic Scheme --- a semi-Lagrangian scheme developed in [J. Comput. Phys., Vol. 255, 2013, pp 680-698] for solving kinetic equations. The original algorithm was proposed for the BGK approximation of the collision kernel. In this work we deal with its extension to the full Boltzmann equation in six dimensions, where the collision operator is resolved by means of fast spectral method. We present close to ideal scalability of the proposed algorithm on tera- and peta-scale systems.