Accelerated Solvers for Neutral Particle Dynamics in Plasma Simulation

TL;DR

This paper introduces hierarchical matrix techniques to accelerate the solution of kinetic models for neutral particles in plasma boundary simulations, significantly reducing computational costs and enabling higher resolution modeling.

Contribution

The work applies hierarchical matrix approximations to improve the efficiency of solving dense linear systems in plasma boundary simulations, a novel approach in this context.

Findings

Over 90% reduction in computation time and memory usage.

Enabled higher spatial resolution in neutral particle simulations.

Successfully integrated into the GBS simulation code.

Abstract

The simulation of turbulence in the boundary region of a tokamak is crucial for understanding and optimizing the performance of fusion reactors. In this work, the use of low-rank linear algebra techniques is shown to enhance the efficiency of boundary simulations, specifically by accelerating the solution of a kinetic model for the neutral particles. Solving the kinetic model deterministically using the method of characteristics requires the solution of integral equations, which typically result in dense linear systems upon discretization. We employ hierarchical matrix approximations to significantly reduce the computational cost of assembling and solving the linear systems, leading to substantial savings in both time and memory. The hierarchical matrix method is implemented and tested within the GBS simulation code for boundary simulations, achieving over 90\% reduction in computation time and memory, and enabling simulations with unprecedented spatial resolution for neutral particles.