REGULARIZED MESHLESS METHOD FOR SOLVING LAPLACE PROBLEMS WITH HOLES

Abstract

In this paper, a regularized meshless method (RMM) is developed to solve the two-dimension Laplace problem with multiply-connected domain. The solution is represented by using the double layer potential. The source points can be located on the real boundary by using the proposed regularized technique to regularize the singularity and hypersingularity of the kernel functions. The difficulty of the coincidence of the source and collocation points is avoided and thereby the diagonal terms of influence matrices are easily determined. The numerical results demonstrate the accuracy of the solutions after comparing with those of exact solution and BEM for the Dirichlet, Neumann and mixed-type problems with multiple holes. Good agreements are observed.在本論文中，使用正規化無網格法求解二維多連通拉普拉斯問題，利用勢能理論的雙層勢能法疊加出場解。藉由本研究所提出的去奇異技術可將核函數的奇異性與超強奇異性正規化，使得場點與源點可以同時分佈在相同的邊界上，因此可解得影響係數矩陣的主對角線項上的有限值。在本文中舉了Dirichlt、Numann及mixed-type三種邊界條件的多洞問題來測試，由本法所獲得之結果將與解析解及邊界元素法結果做比較，可獲得令人滿意的結果。