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Regularized meshless method for multiply-connected-domain Laplace problems

机译:多重连通域拉普拉斯问题的正则化无网格方法

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摘要

In this paper, the regularized meshless method (RMM) is developed to solve two-dimensional Laplace problem with multiply-connected domain. The solution is represented by using the double-layer potential. The source points can be located on the physical boundary by using the proposed technique to regularize the singularity and hypersingularity of the kernel functions. The troublesome singularity in the traditional methods is avoided and the diagonal terms of influence matrices are easily determined. The accuracy and stability of the RMM are verified in numerical experiments of the Dirichlet, Neumann, and mixed-type problems under a domain having multiple holes. The method is found to perform pretty well in comparison with the boundary element method.
机译:本文提出了正则化无网格方法(RMM)来解决具有多重连通域的二维拉普拉斯问题。该解决方案通过使用双层电势来表示。通过使用所提出的技术来规范核函数的奇异性和超奇异性,可以将源点定位在物理边界上。避免了传统方法中麻烦的奇点,并且易于确定影响矩阵的对角项。在具有多个孔的区域下,通过Dirichlet,Neumann和混合型问题的数值实验验证了RMM的准确性和稳定性。与边界元方法相比,该方法的性能很好。

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