The generalized finite difference method with third- and fourth-order approximations and treatment of ill-conditioned stars. (1st June 2021)

• Record Type: Journal Article
• Authors: Albuquerque-Ferreira, A.C.; Ureña, Miguel; Higinio Ramos,
• Is Part Of: Engineering analysis with boundary elements. Volume 127(2021)
• Page Start: 29
• Page End: 39
• Publication Date: 2021-06-01
• Subjects: Generalized finite difference method -- Higher-order approximations -- Ill-conditioned stars -- Parallel processing; 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.2021.03.005
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this paper, we solve 2D and 3D second-order partial differential equations considering the Generalized Finite Difference Method with third- and fourth-order approximations. We analyze the influence of the number of points per star and establish some values as references. We propose a new strategy to deal with ill-conditioned stars, which are frequent in higher-order approximations. This strategy uses a few points per star and presents excellent results both for detecting ill-conditioned stars and for increasing the accuracy of the numerical approximation. We apply parallel processing to the formation of stars and derivatives, and show the speedup achieved.