Persona: Salete Casino, Eduardo
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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/0000-0003-0533-3464We 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.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/0000-0001-5201-4277The 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.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, MiguelA 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.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, LuisSince 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.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, LuisSeismic 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.Publicación Numerical modeling of cracked arch dams. Effect of open joints during the construction phase(MDPI, 2024-03-24) Conde, André; Salete Casino, Eduardo; Toledo, Miguel Á.Running a numerical model for a cracked arch dam that takes into account all the particularities of the materials and dam with a high level of detail has a great computational cost involved. For this reason, it is usual to simplify such a model in search of a simpler solution while preserving the characteristic of being representative, with all the particularities that the model of an arch dam has. A common simplification lies in not considering open transverse joints in the construction phase of a cracked dam. An aim of this study is to propose a methodology that combines open joints and cracking, something on which, to the authors’ knowledge, no studies have been published. An additional goal is a study of the need and adequacy of different approaches on performance (computational time) and its consequences for model accuracy. For this purpose, an accurate methodology for a stationary finite element method numerical simulation of deformations in cracked arch dams is presented. Using a tetrahedron mesh of a real dam, different simplifications commonly used in numerical models are compared. It is concluded that some of the standard simplifications produce a significant effect on the computation time and accuracy of the results.Publicación Cracks in Arch Dams: an overview of documented instances(MDPI, 2024-08-27) Conde, André; Toledo, Miguel Á.; Salete Casino, EduardoIt is essential to understand how failure mechanisms work in arch dams and, in particular, their most common manifestation: cracking. In this paper, the different types of cracking are explained in terms of their causes and consequences. Then, an exhaustive literature review is carried out that results in a detailed compilation of the characteristics of 38 cracked arch dams from all over the world, including crack characteristics (zone, position, dimensions and probable cause). This review is restricted to only those dams for which information on the position of the cracks or dam displacements is publicly available. As part of the review, a brief summary of key data for each dam is included, as well as a compilation of published crack diagrams. The positions of the cracks of all the dams are classified using diagrams in relation to the type of dam and the origin of the crack. Finally, the distribution of some dam parameters and crack features is analyzed by studying the relationships between them.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, FranciscoIn 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.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, MiguelThis 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.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, FranciscoIn 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.