论文标题
拉普拉斯·格林（Laplace Green）的功能，用于无限的地面平面
Laplace Green's Functions for Infinite Ground Planes with Local Roughness
论文作者
论文摘要
引入并构造了带有圆形孔的无限平面上侧的Dirichlet和Neumann边界条件的Laplace方程的绿色功能。这些功能可以解决孔在任何表面封闭的域中的边界值问题的解决方案。这种方法可以考虑感兴趣域内的任意正面和负面的地面高度，通常，使用常规图像方法无法实现。这些问题出现在静电学中，但是，开发的方法适用于拉普拉斯或泊松方程控制的其他领域。提供了绿色功能的积分和系列表示。开发了基于具有快速多层加速度的边界元素方法的有效计算技术。提出了一些基准问题的数值研究。
The Green's functions for the Laplace equation respectively satisfying the Dirichlet and Neumann boundary conditions on the upper side of an infinite plane with a circular hole are introduced and constructed. These functions enables solution of the boundary value problems in domains where the hole is closed by any surface. This approach enables accounting for arbitrary positive and negative ground elevations inside the domain of interest, which, generally, is not possible to achieve using the regular method of images. Such problems appear in electrostatics, however, the methods developed apply to other domains where the Laplace or Poisson equations govern. Integral and series representations of the Green's functions are provided. An efficient computational technique based on the boundary element method with fast multipole acceleration is developed. A numerical study of some benchmark problems is presented.
