【摘要】：已證實傳統(tǒng)定時間步長LMC算法,能準(zhǔn)確復(fù)現(xiàn)粒子分布的均值和方差。而存在漂移時,總產(chǎn)生非零的偏度。為進一步提高精度,設(shè)計了具有5個轉(zhuǎn)移概率的新LMC有偏擴散模型算法,且新算法能準(zhǔn)確地復(fù)現(xiàn)分布的前三階矩。一旦給定漂移速度和擴散率,有效網(wǎng)格和時間步長的范圍就能夠數(shù)值計算出來。引入了一種新的度量方法來研究新算法的精度特性。從而發(fā)現(xiàn)了一個特殊的網(wǎng)格步長,能讓算法仿真的首步誤差是最大誤差。在該網(wǎng)格步長下,也能發(fā)現(xiàn)最優(yōu)時間步長,使得最大誤差達到最小。
[Abstract]:It has been proved that the traditional fixed time step size LMC algorithm can accurately reproduce the mean and variance of particle distribution. And when there is drift, there is always a non-zero bias. In order to further improve the accuracy, a new LMC biased diffusion model algorithm with five transition probabilities is designed, and the first three moments of the distribution can be accurately reproduced by the new algorithm. Once the drift velocity and diffusivity are given, the range of effective mesh and time step can be calculated numerically. A new measurement method is introduced to study the accuracy of the new algorithm. Thus, a special mesh step size is found, and the first step error of the algorithm simulation is the maximum error. Under the grid step, the optimal time step can also be found and the maximum error is minimized.
【作者單位】： 國防科學(xué)技術(shù)大學(xué)信息系統(tǒng)與管理學(xué)院;
【基金】：National Natural Science Foundation of China(61673388)
【分類號】：TP391.9
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本文編號：2214172