Examinando por Materia "Finite difference method"

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    Analysis of the stability and dispersion for a Riemannian acoustic wave equation
    (ELSEVIER SCIENCE INC, 2019-01-15) Quiceno, H. R.; Arias, C.; Quiceno, H. R.; Arias, C.; Universidad EAFIT. Departamento de Ciencias; Matemáticas y Aplicaciones
    The construction of images of the Earth's interior using methods as reverse time migration (RTM) or full wave inversion (FWI) strongly depends on the numerical solution of the wave equation. A mathematical expression of the numerical stability and dispersion for a particular wave equation used must be known in order to avoid unbounded numbers of amplitudes. In case of the acoustic wave equation, the Courant–Friedrich–Lewy (CFL) condition is a necessary but is not a sufficient condition for convergence. Thus, we need to search other types of expression for stability condition. In seismic wave problems, the generalized Riemannian wave equation is used to model their propagation in domains with curved meshes which is suitable for zones with rugged topography. However, only a heuristic version of stability condition was reported in the literature for this equation. We derived an expression for stability condition and numerical dispersion analysis for the Riemannian acoustic wave equation in a two-dimensional medium and analyzed its implications in terms of computational cost. © 2018 Elsevier Inc.
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    Error estimation and h-adaptive refinement in the analysis of natural frequencies
    (ELSEVIER SCIENCE BV, 2001-12-01) Fuenmayor, FJ; Restrepo, JL; Tarancon, JE; Baeza, L; Universidad EAFIT. Departamento de Ingeniería Mecánica; Estudios en Mantenimiento (GEMI)
    This paper deals with the estimation of the discretization error and the definition of an optimum h-adaptive process in the finite element analysis of natural frequencies and modes. Consistent and lumped mass matrices are considered. In the first case, the discretization error essentially proceeds from the stiffness modelization, so it is possible to apply the same error estimators than those considered in static problems. On the other hand, the error associated with the modelization of the inertial properties must be taken into account if lumped mass matrices are used. As far as h-adaptivity is concerned, it is usually interesting to obtain meshes with a specified error for each mode. However, traditional criteria for static problems consider only one load case. Defining the optimum mesh as the one that gets the desired error with the minimum number of elements, a method is proposed for the h-adaptive process taking into account a set of natural modes simultaneously. The proposed methods have been validated by applying them to bi-dimensional test problems. © 2001 Elsevier Science B.V. All rights reserved.