Solving Eikonal equation in 2D and 3D by Generalized Finite Difference Method

In this paper we propose an implementation, for irregular cloud of points, of the meshless method called Generalized Finite Di erence Method to solve the fully nonlinear Eikonal equation in 2D and 3D. We obtain the explicit formulae for derivatives and solve the system of nonlinear equations using t...

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Detalles Bibliográficos
Autores: Salete Casino, Eduardo, Flores, Jesús, García, Ángel, Negreanu, Mihaela, Vargas Ureña, Antonio Manuel, Ureña, Francisco
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:inglés
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/25121
Acceso en línea:https://hdl.handle.net/20.500.14468/25121
Access Level:acceso abierto
Palabra clave:33 Ciencias Tecnológicas::3310 Tecnología industrial
Generalized finite difference method
nonlinear Eikonal equation
Meshless methods
PDEs
Descripción
Sumario:In this paper we propose an implementation, for irregular cloud of points, of the meshless method called Generalized Finite Di erence Method to solve the fully nonlinear Eikonal equation in 2D and 3D. We obtain the explicit formulae for derivatives and solve the system of nonlinear equations using the Newton-Raphson method to obtain the approximate numerical values of the function for the discretization of the domain. It is also shown that the approximation of the scheme used is of second order. Finally, we provide several examples of its application over irregular domains in order to test accuracy of the scheme, as well as comparison with order numerical methods.