Localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for nonlocal diffusion problems. (1st March 2018)

• Record Type: Journal Article
• Authors: Zhao, Wei; Hon, Yiu-chung; Stoll, Martin
• Is Part Of: Computers & mathematics with applications. Volume 75:issue 5(2018)
• Page Start: 1685
• Page End: 1704
• Publication Date: 2018-03-01
• Subjects: Spectral/pseudo-spectral methods -- Radial basis functions -- Cardinal function -- Nonlocal diffusion equations -- Discontinuity; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2017.11.030
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: Spectral/pseudo-spectral methods based on high order polynomials have been successfully used for solving partial differential and integral equations. In this paper, we will present the use of a localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for solving 2D nonlocal problems with radial nonlocal kernels. The basic idea of the LRBF-PSM is to construct a set of orthogonal functions by RBFs on each overlapping sub-domain from which the global solution can be obtained by extending the approximation on each sub-domain to the entire domain. Numerical implementation indicates that the proposed LRBF-PSM is simple to use, efficient and robust to solve various nonlocal problems.