A greedy meshless local Petrov–Galerkin methodbased on radial basis functions. Issue 3 (21st December 2015)

• Record Type: Journal Article
• Authors: Mirzaei, Davoud
• Is Part Of: Numerical methods for partial differential equations. Volume 32:Issue 3(2016:May)
• Page Start: 847
• Page End: 861
• Publication Date: 2015-12-21
• Subjects: adaptive methods -- greedy algorithms -- newton basis -- meshless local Petrov–Galerkin -- meshless methods -- radial basis functions; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22031
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : The meshless local Petrov–Galerkin (MLPG) method with global radial basis functions (RBF) as trial approximation leads to a full final linear system and a large condition number. This makes MLPG less efficient when the number of data points is increased. We can overcome this drawback if we avoid using more points from the data site than absolutely necessary. In this article, we equip the MLPG method with the greedy sparse approximation technique of (Schaback, Numercail Algorithms 67 (2014), 531–547) and use it for numerical solution of partial differential equations. This scheme uses as few neighbor nodal values as possible and allows to control the consistency error by explicit calculation. Whatever the given RBF is, the final system is sparse and the algorithm is well‐conditioned. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 847–861, 2016