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Dipoles formulation for the method of fundamental solutions applied to potential problems

机译：用于解决潜在问题的基本解法的偶极子公式

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摘要

This paper generalizes and extends the traditional source formulation within the method of fundamental solutions (MFS) to use dipoles (or even series of multi-poles). In this paper, two-dimensional potential problems are considered. The present formulation is formulated by taking the limiting case of two adjacent sources. The necessary kernels are derived in explicit forms. Some numerical examples, covering different cases of boundary conditions and geometry, are solved. Several parametric studies are presented to demonstrate different configurations for placement of sources (monopoles or dipoles). The accuracy of the presented new formulation is verified by comparing its results to those obtained from other numerical and analytical methods. The main advantage of the present formulation lies in decreasing the oscillation in the sources intensity and reducing the number of sources required which is useful especially in concave and narrow geometries.
机译：本文在基本解决方案（MFS）的方法中概括并扩展了传统的源公式，以使用偶极子（或什至一系列多极子）。本文考虑了二维潜在问题。通过考虑两个相邻源的极限情况来制定本配方。必要的内核以显式形式导出。解决了一些数值示例，涵盖了边界条件和几何的不同情况。提出了几项参数研究，以证明源（单极或偶极子）放置的不同配置。通过将其结果与从其他数值和分析方法获得的结果进行比较，可以验证所提出的新制剂的准确性。本配方的主要优点在于减少了光源强度的振荡并减少了所需光源的数量，这在凹形和窄几何形状中特别有用。

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