求解抛物型方程的并行Monte Carlo区域分解算法  

Parallel Monte Carlo Domain Decomposition Algorithm for Solving Parabolic Functions

作　　者：刘芳芳[1] 刘播[2] 

机构地区：[1]中国科学院软件研究所,北京100083 [2]吉林大学数学研究所,长春130012

出　　处：《吉林大学学报（理学版）》2007年第2期173-178,共6页Journal of Jilin University:Science Edition

摘　　要：介绍了用Monte Carlo方法求解抛物型方程的3种游动模型,给出了相应的证明及误差的概率估计式;将Monte Carlo方法和区域分解算法相结合提出一种可并行计算抛物型方程的方法,针对形式一般的方程给出了具体算法,并指出算法适用的条件;分别对二维、三维抛物型方程进行数值实验,实验结果表明该算法通过合理的安排,几乎不需要数据传递,在并行机上可以节省大量的计算时间.This paper introduces three random walk models on computating parabolic equations solved by Monte Carlo method, the corresponding prove and the error estimation are given; then a method on computating parabolic functions parallel is proposed based on the combination of Monte Carlo method with domain decomposition algorithm, the algorithm for one-dimension functions is expounded. The condition suitable to the algorithm is given. Some numerical experiments were carried out for 2D- and 3D-parabolic functions. The results show that the method can well handle parabolic functions parallel and can save lots of time.

关 键 词：MONTE CARLO方法 区域分解 并行计算 抛物型方程 

分 类 号：O242.1[理学—计算数学]