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A method of fundamental solutions without fictitious boundary

机译：无虚拟边界的基本解法

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This paper proposes a novel meshless boundary method called the singular boundary method (SBM). This method is mathematically simple, easy-to-program. and truly meshless. Like the method of fundamental solutions (MFS), the SBM employs the singular fundamental solution of the governing equation of interest as the interpolation basis function. However, unlike the MFS, the source and collocation points of the SBM coincide on the physical boundary without the requirement of introducing fictitious boundary. In order to avoid the singularity at the origin, this method proposes an inverse interpolation technique to evaluate the singular diagonal elements of the MFS coefficient matrix. The SBM is successfully tested on a benchmark problems, which shows that the method has a rapid convergence rate and is numerically stable.
机译：本文提出了一种新颖的无网格边界方法，称为奇异边界方法（SBM）。这种方法在数学上很简单，易于编程。真正的无网格像基本解法（MFS）一样，SBM将感兴趣的控制方程的奇异基本解用作插值基函数。但是，与MFS不同，SBM的源点和配置点在物理边界上重合，而无需引入虚拟边界。为了避免原点的奇异性，此方法提出了一种逆插值技术来评估MFS系数矩阵的奇异对角线元素。在基准问题上成功地测试了SBM，这表明该方法具有快速的收敛速度并且在数值上稳定。

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