标题： 一种确定性动力低秩方法用于带电粒子输运 显示英文标题

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

摘要： 在足够空间和角度分辨率下确定性地求解带电粒子输运问题通常计算成本过高，尤其是由于它们的高度前向散射特性。我们提出一种模型降阶方法，该方法在时间上沿低秩流形演化解，使在更高分辨率下的计算变得可行，并减少了整体运行时间和内存占用。为此，我们使用基于碰撞-未碰撞分裂的混合动力低秩方法，即通过碰撞源方法将输运方程进行分裂。未碰撞粒子使用光线追踪器进行描述，便于包含边界条件和能量分散，而碰撞粒子则使用矩方法结合动力低秩近似进行表示。在此，能量被当作伪时间处理，并选择一个自适应秩的积分器以在能量方向动态调整秩。我们可以在较低的秩下重现全秩参考代码的结果，从而降低计算成本和内存使用。该解与TOPAS蒙特卡罗方法相比，精度相当，与以往的确定性方法相当。 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.