Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices

Arregui, Iñigo; Cendán, J. Jesús; Parés, Carlos; Vázquez, Carlos

doi:10.1051/m2an:2008021

Cited by 9 publications

(8 citation statements)

References 24 publications

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“…16.31 202 [2] 13.51 364 [4] 11.59 526 [6] 10.23 688 [8] 9.63 850 [10] 8.76 Table 1: Relative pressure errors for a variety of coarse space dimensions for coefficient with channels and inclusions.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Note that this condition allows to prove the convergence of the fixed point iteration in [10] for a variational inequality problem. Also, for an elastohydrodynamic problem in magnetic storage devices the convergence is theoretically proved under the same condition in [4]. We also mention that the number of fixed point iteration where chosen to be a constant number independently of of the time step iteration.…”

Section: A Duality Methods For Nonlinear Termsmentioning

confidence: 92%

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Numerical upscaling of the free boundary dam problem in multiscale high-contrast media

Galvis

Contreras

Vázquez

2020

Journal of Computational and Applied Mathematics

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In this paper, we address the numerical homogenization approximation of a free-boundary dam problem posed in a heterogeneous media. More precisely, we propose a generalized multiscale finite element (GMsFEM) method for the heterogeneous dam problem. The motivation of using the GMsFEM approach comes from the multiscale nature of the porous media due to its high-contrast permeability. Thus, although we can classically formulate the free-boundary dam problem as in the homogeneous case, a very high resolution will be needed by a standard finite element approximation in order to obtain realistic results that recover the multiscale nature. First, we introduce a fictitious time variable which motivates a suitable time discretization that can be understood as a fixed point iteration to the steady state solution, and we use a duality method to deal with the involved multivalued nonlinear terms. Next, we compute efficient approximations of the pressure and the saturation by using the GMfsFEM method and we can identify the free boundary. More precisely, the GMsGEM method provides numerical * results that capture the behavior of the solution due to the variations of the coefficient at the fine-resolution, by just solving linear systems with size proportional to the number of coarse blocks of a coarse-grid (that does not need to be adapted to the variations of the coefficient). Finally, we present illustrative numerical results to validate the proposed methodology.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: A Duality Methods For Nonlinear Termsmentioning

confidence: 92%

Numerical upscaling of the free boundary dam problem in multiscale high-contrast media

Galvis

Contreras

Vázquez

2020

Journal of Computational and Applied Mathematics

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“…The tape deflection u is given by a fourth order linear equation of Euler-Bernoulli Beam equation type (see [4], [9,Chap. 6] and [1]). The position of the tape "u" is given by the beam equation, (see [4], [9,Chap.6] for details).…”

Section: Modellingmentioning

confidence: 99%

“…In order to compute the solution we reformulate the problem in terms of an obstacle one relative to the unknown h = u − δ, so that we can guarantee that h > 0, that is to say, the tape keeps above the head. We shall follow the ideas of [1,2], and apply a finite element method together with a duality algorithm handling Yosida approximation tools for maximal monotone operators. These techniques have already been successfully used for example in [7] and [8].…”

Section: Numerical Resolutionmentioning

confidence: 99%

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Mathematical Analysis and Numerical Simulation in Magnetic Recording

Muñoz

Tello

2014

Mathematical Modelling and Analysis

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The head-tape interaction in magnetic recording is described in the literature by a coupled system of partial differential equations. In this paper we study the limit case of the system which reduces the problem to a second order nonlocal equation on a one-dimensional domain. We describe the numerical method of resolution of the problem, which is reformulated as an obstacle one to prevent head-tape contact. A finite element method and a duality algorithm handling Yosida approximation tools for maximal monotone operators are used in order to solve numerically the obstacle problem. Numerical simulations are introduced to describe some qualitative properties of the solution. Finally some conclusions are drawn.

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Mechanical Behaviour in DC Alloys Casting Processes

Barral

Quintela

Sánchez

2014

Arch Computat Methods Eng

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The aim of this work is to give a review of algorithms computationally efficient to simulate the thermo-mechanical behaviour in casting processes; in particular, the butt curl deformation and the contraction of the lateral sides of the slab. The main aim is to give an overview of the most used methods to deal with the nonlinearities due to the thermo-elastic-viscoplastic laws of the involved materials and to the contact condition with the bottom block. To evaluate the efficiency of the proposed methods, some academic tests adapted to the difficulties arising in casting processes are presented. Applications of the techniques proposed to aluminium casting processes are discussed and numerical results are given.

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Numerical solution of a 1-d elastohydrodynamic problem in magnetic storage devices

Cited by 9 publications

References 24 publications

Numerical upscaling of the free boundary dam problem in multiscale high-contrast media

Numerical upscaling of the free boundary dam problem in multiscale high-contrast media

Mathematical Analysis and Numerical Simulation in Magnetic Recording

Mechanical Behaviour in DC Alloys Casting Processes

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