Analysis of meshless weak and strong formulations for boundary value problems. (July 2017)

• Record Type: Journal Article
• Authors: Khan, Wajid; Siraj-ul-Islam, ; Ullah, Baseer
• Is Part Of: Engineering analysis with boundary elements. Volume 80(2017)
• Page Start: 1
• Page End: 17
• Publication Date: 2017-07
• Subjects: Meshless methods -- Element-free Galerkin method -- Numerical integration -- Local Radial Basis Functions -- Moving least squares approximation -- Haar wavelets -- Gaussian quadrature -- Elliptic Boundary Value Problems; 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.2017.03.010
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: This paper introduces a weak meshless procedure combined with a multi-resolution numerical integration and its comparison with a strong local meshless formulation for approximating displacement and strain modeled in the form of Elliptic Boundary Value Problems (EBVPs) in one- and two-dimensional spaces. Assets and losses of both strong and weak meshless approaches are considered in detail. The meshless weak formulation considered in the current paper is the well-known Element Free Galerkin (EFG) method whereas the Local Radial Basis Functions Collocation Method (LRBFCM) is taken as a strong formulation. First aspect of the current work is implementation of the new numerical integration techniques introduced in Siraj-ul-Islam et al. (2010) and Aziz et al. (2011) [1, 2] in the EFG method and its comparison with numerical integration based on standard Gaussian quadrature, adaptive integration and stabilized nodal integration techniques used in the context of EFG and other allied weak meshless formulations. Second aspect of the current work is analysis of comparative performance of the localized versions of strong and weak meshless formulations. Standard numerical tests are conducted to validate performance of both the approaches.