Accelerated Neutral Solvers for Plasma Simulation

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. When the kinetic model is solved deterministically using the method of characteristics, it leads to 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. Given the number of unknowns N, the computational cost of the method is numerically observed to scale as linear-logarithmically as opposed to the quadratic scaling with N of the dense version. This improvement enables the modeling of larger physical domains at higher resolution, facilitating a better understanding of turbulence and supporting the development of synthetic diagnostics.

This work is based on joint work with Daniel Kressner, Davide Mancini and Paolo Ricci.