Solving Monge-Ampère equation in 2D and 3D by Generalized Finite Difference Method. (1st March 2021)

• Record Type: Journal Article
• Authors: Benito, J.J.; García, A.; Gavete, L.; Negreanu, M.; Ureña, F.; Vargas, A.M.
• Is Part Of: Engineering analysis with boundary elements. Volume 124(2021)
• Page Start: 52
• Page End: 63
• Publication Date: 2021-03-01
• Subjects: Generalized Finite Difference Method -- Monge-Ampère equation -- Iterative algorithm; 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.2020.12.007
• Languages: English
• ISSNs: 0955-7997

Abstract

Abstract: In this paper we derive the discretization of the nonlinear Monge-Ampère equation by means of the explicit formulae of the meshless Generalized Finite Difference Method (GFDM) in both two and three dimensional settings (2D and 3D). To do so we implement the Cascadic iterative algorithm. We provide a rigorous proof of the consistency of the GFDM for this elliptic equation and present several examples in 2D and 3D, where the method shows its potential and accuracy. We provide a discussion on the number of total nodes in the domain and the number of local supporting nodes. Also, we give an example with physical meaning where we find a surface whose Gaussian curvature is given.