Ghost-point based radial basis function collocation methods with variable shape parameters. (1st September 2021)

• Record Type: Journal Article
• Authors: Lin, Shin-Ruei; Young, D.L.; Chen, Chuin-Shan
• Is Part Of: Engineering analysis with boundary elements. Volume 130(2021)
• Page Start: 40
• Page End: 48
• Publication Date: 2021-09-01
• Subjects: Radial basis functions -- Shape parameter -- Franke's formula -- Multiquadrics -- Ghost point method -- Kansa method; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2021.05.006
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this study, a strategy was proposed to determine the interval of the variable shape parameter for the ghost point method using radial basis functions. The determination of a suitable interval for the variable shape parameter remains a challenge. The modified Franke formula was used as an initial predictor of the center of the interval of the variable shape parameter in this study. After extensive tests, a numerical procedure was found for the determination of a suitable interval. The improvement from the imposition of the partial differential equation on the boundary points using the ghost point method was also investigated. To demonstrate the effectiveness of the proposed approach, four numerical examples are presented, including second and fourth order partial differential equations in 2D and 3D.