Ghost-point based radial basis function collocation methods with variable shape parameters
Journal
Engineering Analysis with Boundary Elements
Journal Volume
130
Pages
40-48
Date Issued
2021
Author(s)
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. ? 2021 Elsevier Ltd
Subjects
Franke's formula; Ghost point method; Kansa method; Multiquadrics; Radial basis functions; Shape parameter
Type
journal article