标题： 确定性求解器用于单一单向质子束的线性玻尔兹曼模型 显示英文标题

标题： A deterministic solver for the linear Boltzmann model of a single mono-directional proton beam

摘要： 质子束的线性玻尔兹曼模型是一个六维偏微分方程（PDE）。我们基于散射分解和深度分裂方法提出了一种求解线性玻尔兹曼模型的确定性求解器。主要思想是首先将质子分为初级质子和散射质子，并利用源迭代法推导出它们的方程。然后我们将深度视为经典时演化问题中的时间变量，并应用深度分裂方法。在深度分裂方法中，整个算子被分解为三部分，每个子系统都易于并行化，这对于高效的模拟至关重要。由此产生的离散化在深度和能量变量上均表现出二阶收敛性。我们将求解器得到的剂量分布与蒙特卡罗模拟在各种材料和非均匀情况下的剂量分布进行了比较。 显示英文摘要

摘要： The linear Boltzmann model for proton beams is a six-dimensional partial differential equation (PDE). We propose a deterministic solver for the linear Boltzmann model based on scattering decomposition and depth-splitting methods. The main idea is to first divide the protons into primary protons and scattering protons, whose equations are derived using the source iteration method. We then treat depth as the time variable in classical time-evolutionary problems and apply the depth-splitting method. In the depth-splitting method, the full operator is decomposed into three parts, with each subsystem being easily parallelizable, which is crucial for efficient simulations. The resulting discretization exhibits second-order convergence in both the depth and energy variables. The dose distributions obtained from our solver are compared with those from Monte Carlo simulations for various materials and heterogeneous cases.