【摘要】：已證實(shí)傳統(tǒng)定時(shí)間步長(zhǎng)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(shí),總產(chǎn)生非零的偏度。為進(jìn)一步提高精度,設(shè)計(jì)了具有5個(gè)轉(zhuǎn)移概率的新LMC有偏擴(kuò)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(kuò)散率,有效網(wǎng)格和時(shí)間步長(zhǎng)的范圍就能夠數(shù)值計(jì)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(gè)特殊的網(wǎng)格步長(zhǎng),能讓算法仿真的首步誤差是最大誤差。在該網(wǎng)格步長(zhǎng)下,也能發(fā)現(xiàn)最優(yōu)時(shí)間步長(zhǎng),使得最大誤差達(dá)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(guó)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(hào)】：TP391.9
，

本文編號(hào)：2214172