A duality method for the compressible Reynolds equation. Application to simulation of read/write processes in magnetic storage devices

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

doi:10.1016/j.cam.2004.06.009

Cited by 8 publications

(3 citation statements)

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“…Next, taking into account the dominating convection feature in (3.1), following [2] we propose to adapt a characteristics technique for steady state problems. This method introduces an artificial dependence on a time variable, t, so that:P (x, t) = P (x)H(x, t) = H(x).…”

Section: Methodsmentioning

confidence: 99%

“…In [7], the complexity and limitations of using a Newton technique for the nonlinear diffusive term are pointed out and a combination with a continuation method is applied. More recently, in [2] we have introduced a new numerical method to solve a 1-d nonlinear compressible Reynolds equation which mainly takes advantage of writing the problem in terms of an appropriate maximal monotone operator, preventing from the use of general purpose Newton methods and the complexity and limitations associated to them. In all previous papers the convergence of the involved numerical methods is not mathematically analyzed.…”

Section: Introductionmentioning

confidence: 99%

“…Secondly, a new version of a duality method is proposed to deal with the nonlinear diffusive term appearing in Reynolds equation. In [2] a classical constant parameter version of this duality method has been applied. In the present paper, both the constant and functional parameter versions of the method are applied in the head-tape elastohydrodynamic setting.…”

Section: Introductionmentioning

confidence: 99%

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

Arregui¹,

Cendán²,

Parés

et al. 2008

ESAIM: M2AN

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Abstract. In this work we present new numerical methods to simulate the mechanics of head-tape magnetic storage devices. The elastohydrodynamic problem is formulated in terms of a coupled system which is governed by a nonlinear compressible Reynolds equation for the air pressure over the head, and a rod model for the tape displacement. A fixed point algorithm between the solutions of the elastic and hydrodynamic problems is proposed. For the nonlinear Reynolds equation, a characteristics method and a duality algorithm are developed to cope with the convection dominating and nonlinear diffusion features, respectively. Furthermore, in the duality method the convergence and optimal choice of the parameters are analyzed. At each fixed point iteration, in the elastic model a complementarity formulation is required and appropriate numerical techniques are used. For the spatial discretization different finite element spaces are chosen. Finally, numerical test examples illustrate the theoretical results, as well as the good performance in the simulation of real devices.Mathematics Subject Classification. 76A20, 76D08, 35J60, 65J15, 65N60.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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