Determining the Optimal Source Points in MFS by Minimizing an Energy Gap Functional for 3D Laplace Operator. (21st December 2020)

• Record Type: Journal Article
• Authors: Sajjadmanesh, M.; Shakib Khanghah, S.; Aydi, H.
• Other Names: Nisar Kottakkaran Sooppy Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-12-21
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/6633908
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.