Augmented moving least squares approximation using fundamental solutions. (June 2020)

• Record Type: Journal Article
• Authors: Wang, Fajie; Qu, Wenzhen; Li, Xiaolin
• Is Part Of: Engineering analysis with boundary elements. Volume 115(2020)
• Page Start: 10
• Page End: 20
• Publication Date: 2020-06
• Subjects: Meshless method -- Moving least squares approximation -- Augmented moving least squares approximation -- Fundamental solution -- Shape function; 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.2020.03.003
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: An augmented moving least squares (AMLS) approximation is presented in this paper for constructing approximate functions in meshless methods. The basis functions in the AMLS approximation, differ from monomial basis functions in the classical moving least squares (MLS) approximation, involve fundamental solutions of the underlying differential equations, and thus enhance the performance of the MLS approximation. As the MLS approximation, the AMLS approximation can also be used for curve and surface fitting. Numerical examples involving 2D and 3D Laplace, Helmholtz and modified Helmholtz equations in complicated domains reveal that the accuracy of the AMLS approximation is about 10 4 ~ 10 6 times higher than that of the MLS approximation.