不规则区域上Poisson方程的蒙特卡洛马尔科夫链方法求解

The Method of Monte Carlo Markov Chain for Solving the Poisson Equation on Irregular Domain

摘要: 本文研究了不规则区域上泊松方程的蒙特卡洛马尔科夫链方法数值求解。在不规则区域上，微分方程的数值计算通常是困难的。基于有限差分的思想，本文构造了可吸收马尔科夫链来求解不规则区域上的微分方程。不规则区域的数值实验结果表明了该方法的可行性和有效性。该方法为求解不规则区域上的泊松方程提供了一种新的计算思路，并保持了空间方向上二阶收敛阶。

Abstract: In this paper, the Monte Carlo Markov chain method for solving Poisson equation in irregular do-main is studied. In irregular domain, the numerical calculation of differential equations is usually difficult. Based on the idea of finite difference, an absorbable Markov chain is constructed to solve differential equations in irregular domain. The numerical experiments in irregular domain show that the method is feasible and effective. This method provides a new idea for solving Poisson’s equation in irregular region and keeps the second order convergence order.