Gwangju Institute of Science and Technology, Physics Track, Gwangju Metropolitan City, 61005, South Korea.
Gwangju Institute of Science and Technology, Electrical Engineering and Computer Science Track, Gwangju Metropolitan City, 61005, South Korea.
Sci Rep. 2023 Jan 20;13(1):1143. doi: 10.1038/s41598-023-28361-1.
Due to the isomorphism between an electrostatic problem and the corresponding Brownian diffusion one, the induced charge density on a conducting surface by a charge is isomorphic to the first-passage probability of the diffusion initiated at the location of the charge. Based on the isomorphism, many diffusion algorithms such as "Walk-on-Spheres" (WOS), "Walk-on-Planes" and so on have been developed. Among them, for fast diffusion simulations WOS algorithm is generally applied with an [Formula: see text]-layer, which is used for diffusion convergence on the boundary but induces another error from the [Formula: see text]-layer in addition to the intrinsic Monte Carlo error. However, for a finite flat boundary it is possible to terminate a diffusion process via "Walk-on-Hemispheres" (WOH) algorithm without the [Formula: see text]-layer. In this paper, we implement and demonstrate this algorithm for the induced charge density distribution on parallel infinite planes when a unit charge is between the plates. In addition, we apply it to the mutual capacitance of two circular parallel plates. In both simulations, WOH algorithm shows much better performance than the previous WOS algorithm.
由于静电问题与相应的布朗扩散问题之间存在同构性，因此电荷在导体表面上产生的感应电荷密度与从电荷位置引发的扩散的首次通过概率同构。基于这种同构性，已经开发出了许多扩散算法，例如“Walk-on-Spheres”（WOS）、“Walk-on-Planes”等。其中，对于快速扩散模拟，通常应用 WOS 算法的 [Formula: see text]-层，该层用于在边界上进行扩散收敛，但除了固有蒙特卡罗误差外，还会从 [Formula: see text]-层引入另一个误差。然而，对于有限的平坦边界，可以通过“Walk-on-Hemispheres”（WOH）算法终止扩散过程，而无需 [Formula: see text]-层。在本文中，我们针对平板之间存在单位电荷时平行无限平板上的感应电荷密度分布实现并演示了该算法。此外，我们还将其应用于两个圆形平行板之间的互电容。在这两种情况下，WOH 算法的性能均明显优于先前的 WOS 算法。
