The random walk on the boundary method for calculating capacitance
The random walk on the boundary method for calculating capacitance
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DOI：
10.1016/j.jcp.2003.10.005
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发表时间：
2004-04
影响因子：
4.1
通讯作者：
M. Mascagni;N. Simonov
中科院分区：
文献类型：
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作者：
M. Mascagni;N. Simonov
在本文中，我们提出了“边界上的随机行走”方法的快速解决方案的积分方程中出现的静电和相关领域。该方法是基于马尔可夫链的构造的蒙特卡罗方法，马尔可夫链容易被解释为沿着积分方程中的积分的边界的随机行走。为了说明这种技术的有用性，我们将其应用到单位立方体的电容的计算。获得立方体的电容通常需要计算电荷密度，并且该问题已被该领域的许多人用作此类算法的基准。在这里，“边界随机游走”方法不需要电荷密度计算，并在2.7×10 - 7的统计误差内获得立方体的电容，这是迄今为止最准确的估计。
In this paper we present the “random walk on the boundary” method for the rapid solution of integral equations that arise in electrostatics and related areas. This method is a Monte Carlo method based on the construction of a Markov chain that is readily interpreted as a random walk along the boundary over which integration in the integral equation is taken. To illustrate the usefulness of this technique, we apply it to the computation of the capacitance of the unit cube. Obtaining the capacitance of the cube usually requires computing the charge density, and this problem has been used as a benchmark by many in the field for algorithms of this kind. Here, the “random walk on the boundary” method does not require charge density computation, and obtains the capacitance of the cube within a statistical error of 2.7×10−7, the most accurate estimate to date.