论文标题
多级渐近保护蒙特卡洛用于粒子模拟
Multilevel Asymptotic-Preserving Monte Carlo for Particle Simulations
论文作者
论文摘要
我们开发了一种新型的多层次渐近造型蒙特卡洛法，称为多级动力学扩散蒙特卡洛（ML-KDMC），用于使用Bhatnagar-gross-krook（bgk）碰撞操作员模拟动力学玻尔兹曼族传输方程。例如，在核融合反应器等离子体边缘的中性颗粒的数学模型中发生了该方程。在这种情况下，已知动力学扩散蒙特卡洛方法在低碰撞和高胶卷极限中保持准确性，而后者却没有爆炸的模拟成本。我们表明，通过将此方法置于多级蒙特卡洛（MLMC）框架中，使用较大时间步尺寸的层次结构，仿真成本甚至进一步降低。我们的ML-KDMC方法中的不同级别通过新的和改进的配方将粒子轨迹与不同的时间步长相关联的配方连接。此外，提出了一种新的，更一般的选择策略。我们通过将其应用于具有非均匀和各向异性等离子体背景的一维测试案例来说明我们的ML-KDMC方法的效率。与单级KDMC方案相比，我们的方法在低碰撞和高碰撞状态下产生了显着的加速。在高胶卷的情况下，我们的ML-KDMC通过几个数量级优于单级KDMC方法。
We develop a novel multilevel asymptotic-preserving Monte Carlo method, called Multilevel Kinetic-Diffusion Monte Carlo (ML-KDMC), for simulating the kinetic Boltzmann transport equation with a Bhatnagar-Gross-Krook (BGK) collision operator. This equation occurs, for instance, in mathematical models of the neutral particles in the plasma edge of nuclear fusion reactors. In this context, the Kinetic-Diffusion Monte Carlo method is known to maintain accuracy both in the low-collisional and the high-collisional limit, without an exploding simulation cost in the latter. We show that, by situating this method within a Multilevel Monte Carlo (MLMC) framework, using a hierarchy of larger time step sizes, the simulation cost is reduced even further. The different levels in our ML-KDMC method are connected via a new and improved recipe for correlating particle trajectories with different time step sizes. Furthermore, a new and more general level selection strategy is presented. We illustrate the efficiency of our ML-KDMC method by applying it to a one-dimensional test case with nonhomogeneous and anisotropic plasma background. Our method yields significant speedups compared to the single-level KDMC scheme, both in the low and high collisional regime. In the high-collisional case, our ML-KDMC outperforms the single-level KDMC method by several orders of magnitude.
