标题： 确定性动力学低秩方法在带电粒子输运中的应用 显示英文标题

标题： A Deterministic Dynamical Low-rank Approach for Charged Particle Transport

摘要： 确定性地以足够的空间和角度分辨率求解带电粒子输运问题通常代价高昂，特别是由于其高度前向散射的特性。 我们提出了一种模型降阶方法，该方法在时间上使解在低秩流形上演化，从而在更高分辨率下实现计算可行性，减少整体运行时间和内存占用。 为此，我们采用了一种基于碰撞-未碰撞分裂的混合动态低秩方法，即通过碰撞源方法将输运方程分解。 未碰撞粒子使用光线追踪器描述，便于包含边界条件和漂移效应，而碰撞粒子则使用矩方法结合动态低秩近似来表示。 在这里，能量被视为伪时间，并选择了一个秩自适应积分器以在能量上动态调整秩。 我们可以用较低的秩重现全秩参考代码的结果，因此降低了计算成本和内存使用。 此外，该解相对于TOPAS MC的准确性与先前的确定性方法相当。 显示英文摘要

摘要： 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.