基于Monte Carlo方法的泊松方程求解  

The Solution of the Poisson Equation by Monte Carlo Method

作　　者：严嘉毅 陈豫眉 郑玉霞[1] Yan Jia-yi;Chen Yu-mei;Zheng Yu-xia(College of Mathematic and Information,Xihua Normal University,Nanchong 637009,China;College of Mathematics Education,Xihua Normal University,Nanchong 637009,China;College of Computing Method and Application Software,Xihua Normal University,Nanchong 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学公共数学学院,四川南充637009 [3]西华师范大学计算方法及应用软件研究所,四川南充637009

出　　处：《洛阳师范学院学报》2019年第5期15-18,共4页Journal of Luoyang Normal University

基　　金：四川省教育厅科研项目重点项目(15ZA0149);四川省科技厅项目(2017JY0186);西华师范大学英才基金项目(17YC371)

摘　　要：基于Monte Carlo方法的主要原理,求解泊松方程第一边值问题.通过构建随机游动模型,确定统计量,抽样产生随机样本,得到泊松方程解的估计值.并给出了详细的推导步骤和算法流程,证明了统计量均值是泊松方程第一边值问题的解,为该方法在复杂问题中提供一个简单的思路.The first boundary value problem of the Poisson equation is solved based on the principle of Monte Carlo method. By constructing the random walk model, determining statistics, random sampling, the estimated value of the solution of the Poisson equation is obtained. The detailed derivation steps and algorithm are given, and the statistical mean value is proved to be the solution of the first boundary value problem of the Poisson equation, which provides an idea of using this method in complex problems.

关 键 词：MONTE CARLO方法 随机游动模型 泊松方程 第一边值问题 

分 类 号：O242.2[理学—计算数学]