Motivated by a heat radiative transport equation, we consider a particle undergoing collisions in a space-time domain and propose a method to sample its escape time, space and direction from the domain. The first step of the procedure is an estimation of how many elementary collisions is safe to take before chances of exiting the domain are too high; then these collisions are aggregated into a single movement. The method does not use any model nor any particular regime of parameters. We give theoretical results both under the normal approximation and without it and test the method on some benchmarks from the literature. The results confirm the theoretical predictions and show that the proposal is an efficient method to sample the escape distribution of the particle.

翻译：摘要：受热辐射传输方程的启发，我们考虑在时空域中发生碰撞的粒子，并提出一种方法以采样其从该域中逃逸的时间、空间和方向。该过程的第一步是估计在逃逸概率过高前可安全进行的初级碰撞次数；随后将这些碰撞聚合为单一运动。该方法不依赖于任何模型或特定参数工况。我们在正态近似及无近似条件下给出理论结果，并在文献中的若干基准问题上对该方法进行了测试。结果证实了理论预测，表明该方案是采样粒子逃逸分布的一种高效方法。