Examinando por Autor "Gavete, Luis"

Mostrando 1 - 7 de 7
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    Publicación
    Application of generalised finite differences method to reflection and transmission problems in seismic SH waves propagation
    (Wiley, 2017-01-09) Ureña, Miguel; Benito Muñoz, Juan J. ; Ureña, Francisco; Salete Casino, Eduardo; Gavete, Luis; Muelas Rodríguez, Ángel
    A matrix formulation of the generalised finite difference method is introduced. A necessary and sufficient condition for the uniqueness of the solution is demonstrated, and important practical consequences are obtained. A generalised finite differences scheme for SH wave is obtained, the stability of the scheme is analysed and the formula for the velocity of the wave due to the scheme is obtained in order to deal with the numerical dispersion. The method is applied to seismic waves propagation problems, specifically to the problem of reflection and transmission of plane waves in heterogeneous media. A heterogeneous approach without nodes at the interface is chosen to solve the problem in heterogeneous media.
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    Publicación
    The Application of the Generalized Finite Difference Method (GFDM) for Modelling Geophysical Test
    (Wiley, 2019-04-10) Muelas Rodríguez, Ángel; Salete Casino, Eduardo; Benito Muñoz, Juan J.; Ureña, Francisco; Gavete, Luis; Ureña, Miguel
    A matrix formulation of the generalised finite difference method is introduced. A necessary and sufficient condition for the uniqueness of the solution is demonstrated, and important practical consequences are obtained. A generalised finite differences scheme for SH wave is obtained, the stability of the scheme is analysed and the formula for the velocity of the wave due to the scheme is obtained in order to deal with the numerical dispersion. The method is applied to seismic waves propagation problems, specifically to the problem of reflection and transmission of plane waves in heterogeneous media. A heterogeneous approach without nodes at the interface is chosen to solve the problem in heterogeneous media.
  • Miniatura
    Publicación
    A new meshless approach to deal with interfaces in seismic problems
    (Elsevier, 2018-06) Benito Muñoz, Juan J.; Ureña, Francisco; Ureña, Miguel; Salete Casino, Eduardo; Gavete, Luis
    Since methods based on finite differences are the dominant methods for seismic wave propagation, the generalized finite differences method may join with them to offer its main advantage, the possibility of using an irregular cloud of nodes. We analyze the problem of a plane wave in a heterogeneous medium. We obtain heterogeneous schemes for P-SV and SH waves, considering the elastic parameters and the density as linear functions. With the aim of analyzing the accuracy of these schemes we compare the obtained amplitudes with the theoretical amplitudes for reflected and transmitted waves and we verify that the convergence order is preserved.
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    Publicación
    On the numerical solution to a parabolic-elliptic system with chemotactic and periodic terms using Generalized Finite Differences
    (Elsevier, 2020-04) Benito Muñoz, Juan J.; García, Ángel; Gavete, Luis; Negreanu, Mihaela; Ureña, Francisco; Vargas Ureña, Antonio Manuel
    In the present paper we propose the Generalized Finite Difference Method (GFDM) for numerical solution of a cross-diffusion system with chemotactic terms. We derive the discretization of the system using a GFD scheme in order to prove and illustrate that the uniform stability behavior/ convergence of the continuous model is also preserved for the discrete model. We prove the convergence of the explicit method and give the conditions of convergence. Extensive numerical experiments are presented to illustrate the accuracy, efficiency and robustness of the GFDM.
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    Publicación
    Schemes in generalized finite differences for seismic wave propagation in Kelvin–Voight viscoelastic media
    (Elsevier, 2018-10) Benito Muñoz, Juan J.; Ureña, Francisco; Ureña, Miguel; Salete Casino, Eduardo; Gavete, Luis
    Seismic wave propagation in homogeneous and isotropic Kelvin–Voight viscoelastic media is dealt with the meshless generalized finite difference method. The schemes in generalized finite differences for the decoupled system P-SV and SH are obtained. For each scheme, a stability limit is achieved and the star dispersion is calculated. Some cases are shown using irregular discretizations.
  • Miniatura
    Publicación
    Solving a fully parabolic chemotaxis system with periodic asymptotic behavior using Generalized Finite Difference Method
    (Elsevier, 2020-11) Benito Muñoz, Juan J.; García, Ángel; Gavete, Luis; Negreanu, Mihaela; Ureña, Francisco; Vargas Ureña, Antonio Manuel
    This work studies a parabolic-parabolic chemotactic PDE's system which describes the evolution of a biological population “U” and a chemical substance “V”, using a Generalized Finite Difference Method, in a two dimensional bounded domain with regular boundary. In a previous paper [12], the authors asserted global classical solvability and periodic asymptotic behavior for the continuous system in 2D. In this continuous work, a rigorous proof of the global classical solvability to the discretization of the model proposed in [12] is presented in two dimensional space. Numerical experiments concerning the convergence in space and in time, and long-time simulations are presented in order to illustrate the accuracy, efficiency and robustness of the developed numerical algorithms.
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    Publicación
    Solving a reaction-di usion system with chemotaxis and non-local terms using Generalized Finite Di erence Method. Study of the convergence
    (Elsevier, 2021-06) Benito Muñoz, Juan J.; García, Ángel; Gavete, Luis; Negreanu, Mihaela; Ureña, Francisco; Vargas Ureña, Antonio Manuel
    In this paper a parabolic–parabolic chemotaxis system of PDEs that describes the evolution of a population with non-local terms is studied. We derive the discretization of the system using the meshless method called Generalized Finite Difference Method. We prove the conditional convergence of the solution obtained from the numerical method to the analytical solution in the two-dimensional case. Several examples of the application are given to illustrate the accuracy and efficiency of the numerical method. We also present two examples of a parabolic–elliptic model, as generalized by the parabolic–parabolic system addressed in this paper, to show the validity of the discretization of the non-local terms.