We introduce the Quantization Monte Carlo method to solve thermal radiative transport equations with possibly several collision regimes, ranging from few collisions to massive number of collisions per time unit. For each particle in a given simulation cell, the proposed method advances the time by replacing many collisions with sampling directly from the escape distribution of the particle. In order to perform the sampling, for each triplet of parameters (opacity, remaining time, initial position in the cell) on a parameter grid, the escape distribution is precomputed offline and only the quantiles are retained. The online computation samples only from this quantized (i.e., discrete) version by choosing a parameter triplet on the grid (close to actual particle’s parameters) and returning at random one quantile from the precomputed set of quantiles for that parameter. We first check numerically that the escape laws depend smoothly on the parameters and then implement the procedure on a benchmark with good results.

中文翻译：

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用于求解辐射输运方程的量子化 Monte Carlo 方法


我们引入了量化蒙特卡洛方法来求解热辐射输运方程，该方程可能具有多种碰撞状态，范围从少量碰撞到每个时间单位的大量碰撞。对于给定模拟单元中的每个粒子，所提出的方法通过直接从粒子的逃逸分布中采样来代替许多碰撞来提前时间。为了执行采样，对于参数网格上的每个参数三元组（不透明度、剩余时间、单元格中的初始位置），转义分布是离线预计算的，并且只保留分位数。在线计算仅从此量化（即离散）版本中采样，方法是在网格上选择一个参数三元组（接近实际粒子的参数），然后从该参数的预计算分位数集中随机返回一个分位数。我们首先用数值检查逃逸定律是否平滑地依赖于参数，然后在基准上实施该程序并取得良好的结果。