In this paper, an extended version of the method of minimizing an energy gap functional for determining the optimal source points in the method of fundamental solutions (MFS) is applied to the 3D Laplace operator subject to the Dirichlet and Neumann boundary conditions. As we know, the MFS is a more popular meshless method for solving boundary or initial-boundary value problems due to its simplicity and high accuracy. However, the accuracy of the MFS depends strongly on the distribution of the source points. Finally, some of the numerical experiments are carried out to express the simplicity and effectiveness of the presented method.

中文翻译：

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通过最小化3D Laplace算子的能隙函数来确定MFS中的最佳源点

在本文中，在Dirichlet和Neumann边界条件下，将基本方法（MFS）中用于确定最佳源点的能隙函数最小化方法的扩展版本应用于3D Laplace算子。众所周知，MFS由于其简单性和高精度而成为解决边界或初始边界值问题的一种更为流行的无网格方法。但是，MFS的准确性在很大程度上取决于源点的分布。最后，进行了一些数值实验，以表达该方法的简单性和有效性。