摘要
已证实传统定时间步长LMC算法,能准确复现粒子分布的均值和方差。而存在漂移时,总产生非零的偏度。为进一步提高精度,设计了具有5个转移概率的新LMC有偏扩散模型算法,且新算法能准确地复现分布的前三阶矩。一旦给定漂移速度和扩散率,有效网格和时间步长的范围就能够数值计算出来。引入了一种新的度量方法来研究新算法的精度特性。从而发现了一个特殊的网格步长,能让算法仿真的首步误差是最大误差。在该网格步长下,也能发现最优时间步长,使得最大误差达到最小。
It is already proved that the traditional fixed time step lattice Monte Carlo （LMC） algorithm can reproduce both the mean and the variance of the particle displacement exactly. However, there is always a non-zero skewness when there is a drift. To further improve the accuracy, a new LMC algorithm of biased diffusion model with five transition probabilities has been devised, which indeed reproduces the first three moments exactly. The valid scope of lattice step and time step can be determined numerically once the drift and the diffusivity are given. A new measurement is introduced to study the accuracy characteristics of the new algorithm. As a result, a particular lattice step can be discovered in which case the first step error is the maximum error in the simulation tests. Then, given the particular lattice step, the optimal time step can also be found to minimize the maximum error.
出处
《系统仿真学报》
CAS
CSCD
北大核心
2017年第10期2247-2253,共7页
Journal of System Simulation
基金
National Natural Science Foundation of China(61673388)
关键词
LMC算法
扩散模型
精度度量
精度特性
LMC algorithm
diffusion model
accuracy measurement
accuracy characteristic
