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Salete Casino, Eduardo

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0000-0003-1863-9972
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Salete Casino
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Eduardo
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2020 - 20235
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Autor: García, Ángel × Fecha de finalización: 2024 ×

Resultados de la búsqueda

Mostrando 1 - 5 de 5
  • Miniatura
    Publicación
    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
    Publicación
    An effective numeric method for different formulations of the elastic wave propagation problem in isotropic medium
    (Elsevier, 2021-08) Salete Casino, Eduardo; Vargas Ureña, Antonio Manuel; García, Ángel; Benito Muñoz, Juan J.; Ureña, Francisco; Ureña, Miguel
    This paper shows how the Generalized Finite Difference Method allows the same schemes in differences to be used for different formulations of the wave propagation problem. These formulations present pros and cons, depending on the type of boundary and initial conditions at our disposal and also the variables we want to compute, while keeping additional calculations to a minimum. We obtain the explicit schemes of this meshless method for different possible formulations in finite differences of the problem. Criteria for stability and convergence of the schemes are given for each case. The study of the dispersion of the phase and group velocities presented in previuos paper of the authors is also completed here. We show the application of the propounded schemes to the wave propagation problem and the comparison of the efficiency, convenience and accuracy of the different formulations.
  • Miniatura
    Publicación
    Complex Ginzburg–Landau Equation with Generalized Finite Differences
    (MDPI, 2020-12-20) Salete Casino, Eduardo; Vargas Ureña, Antonio Manuel; García, Ángel; Negreanu, Mihaela; Benito Muñoz, Juan J.; Ureña, Francisco
    In this paper we obtain a novel implementation for irregular clouds of nodes of the meshless method called Generalized Finite Difference Method for solving the complex Ginzburg–Landau equation. We derive the explicit formulae for the spatial derivative and an explicit scheme by splitting the equation into a system of two parabolic PDEs. We prove the conditional convergence of the numerical scheme towards the continuous solution under certain assumptions. We obtain a second order approximation as it is clear from the numerical results. Finally, we provide several examples of its application over irregular domains in order to test the accuracy of the explicit scheme, as well as comparison with other numerical methods.
  • Miniatura
    Publicación
    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
    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.