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Salete Casino, Eduardo

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Salete Casino
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2021 - 20234
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Autor: Flores, Jesús × search.filters.applied.f.itemDepartamento: Ingeniería de Construcción y Fabricación ×

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Mostrando 1 - 4 de 4
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    Solving Eikonal equation in 2D and 3D by Generalized Finite Difference Method
    (Wiley, 2021-09-17) Salete Casino, Eduardo; Flores, Jesús; García, Ángel; Negreanu, Mihaela; Vargas Ureña, Antonio Manuel; Ureña, Francisco
    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.
  • Miniatura
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    Numerical Solutions to Wave Propagation and Heat Transfer Non-Linear PDEs by Using a Meshless Method
    (MDPI, 2022-01-21) Flores, Jesús; García, Ángel; Negreanu, Mihaela; Salete Casino, Eduardo; Ureña, Francisco; Vargas Ureña, Antonio Manuel
    The applications of the Eikonal and stationary heat transfer equations in broad fields of science and engineering are the motivation to present an implementation, not only valid for structured domains but also for completely irregular domains, of the meshless Generalized Finite Difference Method (GFDM). In this paper, the fully non-linear Eikonal equation and the stationary heat transfer equation with variable thermal conductivity and source term are solved in 2D. The explicit formulae for derivatives are developed and applied to the equations in order to obtain the numerical schemes to be used. Moreover, the numerical values that approximate the functions for the considered domain are obtained. Numerous examples for both equations on irregular 2D domains are exposed to underline the effectiveness and practicality of the method.
  • Miniatura
    Publicación
    Generalized finite difference method applied to solve seismic wave propagation problems. Examples of 3D simulations
    (Wiley, 2023) Flores, Jesús; Salete Casino, Eduardo; Benito Muñoz, Juan J.; Vargas Ureña, Antonio Manuel; Conde, Eduardo R.; https://orcid.org/0000-0001-5201-4277
    The simulation of seismic wave propagation generally requires dealing with complex tridimensional geometries that are irregular in shape 11 and have non-uniform properties, features that make interesting the application of the generalized finite difference method in this field. 12 This work continues the extensive developments by the research team focused on the simulation of seismic wave propagation in two-13 dimensional domains. In this new contribution, the general formulation and the treatment of free surface boundary conditions are 14 extended for the three-dimensional case and the results obtained from different examples are analyzed.
  • Miniatura
    Publicación
    A spatio-temporal fully meshless method for hyperbolic PDEs
    (ELSEVIER, 2023) Flores, Jesús; García, Ángel; Negreanu, M.; Salete Casino, Eduardo; Ureña, Francisco; A.M. Vargas; https://orcid.org/0000-0003-0533-3464
    We introduce a meshless method derived by considering the time variable as a spatial variable without the need to extend further conditions to the solution of linear and non-linear hyperbolic PDEs. The method is based on the moving least squares method, more precisely in the Generalized Finite Difference Method which allows us to select well-conditioned stars. Several 2D and 3D examples including the time variable are shown for both regular and irregular node distributions. The results are compared with explicit GFDM both in terms of errors and execution time.