A Deterministic Dynamical Low-rank Approach for Charged Particle Transport

TL;DR

This paper introduces a low-rank dynamical approach for charged particle transport that significantly reduces computational costs while maintaining accuracy, by splitting the problem into collided and uncollided components and adapting the rank dynamically.

Contribution

It presents a hybrid dynamical low-rank method with a collided-uncollided split and rank adaptation, enabling efficient high-resolution simulations of charged particle transport.

Findings

Reproduces full-rank results at lower computational cost

Achieves accuracy comparable to TOPAS Monte Carlo simulations

Reduces memory footprint and runtime significantly

Abstract

Deterministically solving charged particle transport problems at a sufficient spatial and angular resolution is often prohibitively expensive, especially due to their highly forward peaked scattering. We propose a model order reduction approach which evolves the solution on a low-rank manifold in time, making computations feasible at much higher resolutions and reducing the overall run-time and memory footprint. For this, we use a hybrid dynamical low-rank approach based on a collided-uncollided split, i.e., the transport equation is split through a collision source method. Uncollided particles are described using a ray tracer, facilitating the inclusion of boundary conditions and straggling, whereas collided particles are represented using a moment method combined with the dynamical low-rank approximation. Here the energy is treated as a pseudo-time and a rank adaptive integrator is chosen to dynamically adapt the rank in energy. We can reproduce the results of a full-rank reference code at a much lower rank and thus computational cost and memory usage. The solution further achieves comparable accuracy with respect to TOPAS MC as previous deterministic approaches.