The meshless local collocation method for solving multi-dimensional Cahn-Hilliard, Swift-Hohenberg and phase field crystal equations. (May 2017)

• Record Type: Journal Article
• Authors: Dehghan, Mehdi; Abbaszadeh, Mostafa
• Is Part Of: Engineering analysis with boundary elements. Volume 78(2017)
• Page Start: 49
• Page End: 64
• Publication Date: 2017-05
• Subjects: Meshless methods -- Local radial basis functions collocation method -- Local strong form -- Cahn-Hilliard equation -- Swift-Hohenberg equation -- Phase field crystal equation; 65M60 -- 65L60 -- 65M20; 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.2017.02.005
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: The collocation technique based on the radial basis functions (RBFs) method is simple and efficient for solving a wide area of problems. But the mentioned technique is poor for solving problems that have shock (advection problems) or the discontinuous initial condition. The local RBFs collocation technique is a meshless method based on the strong form. The use of local collocation RBFs method overcomes the mentioned important issue. In the current paper, based on the proposed idea in Wang (2015) [54], we consider a linear combination of shape functions of local radial basis functions collocation method and moving Kriging interpolation technique. For showing the efficiency of new technique, some multi-dimensional problems such as Cahn-Hilliard, Swift-Hohenberg and phase field crystal equations have been chosen. Moreover, several test problems are given that show the acceptable accuracy and efficiency of the proposed scheme.