Abstract
Mathematical modelling of air lubrication phenomena taking place during read/write processes in magnetic storage devices (hard-disks, for example) can be addressed by using a compressible Reynolds equation for the air pressure. In the present paper, we propose a duality algorithm with optimal functional parameters to numerically solve the nonlinear diffusive term. A theoretical result is stated and some numerical examples are presented to illustrate the performance of the method.
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Arregui, I., Cendán, J.J., Vázquez, C.: A duality method for the compressible Reynolds equation. Aplication to simulation of read/write processes in magnetic storage devices. J. Comput. Appl. Math., 175, 31–40 (2005)
Bermúdez, A.: Un método numérico para la resolución de ecuaciones con varios términos no lineales. Aplicación a un problema de flujo de gas en un conducto. Rev. Acad. Cienc. Exactas Fýs. Nat., 78, 89–96 (1981)
Bermúdez, A., Moreno, C.: Duality methods for solving variational inequalities. Comp. Math. with Appl., 7, 43–58 (1981)
Bhushan, B.: Tribology and Mechanics of Magnetic Storage Devices. Springer, New York (1996)
Burgdorfer, A.: The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings. ASME J. Basic Engrg., 81, 99–100 (1959)
Cendán, J.J.: Estudio matemático y numérico del modelo de Reynolds-Koiter y de los modelos tribológicos en lectura magnética. PhD Thesis, University of Vigo (2005)
Friedman, A.: Mathematics in Industrial Problems. 7. Springer, New York (1995)
Jai, M.: Homogenization and two-scale convergence of the compressible Reynolds lubrification equation modelling the .ying characteristics of a rough magnetic head over a rough rigid-disk surface. Math. Modelling Numer. Anal., 29, 199–233 (1995)
Parés, C., Macýas, J., Castro, M.: Duality methods with authomatic choice of parameters. Application to shallow water equations in conservative form. Numer. Math., 89, 161–189 (2001)
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Arregui, I., Cend án, J.J., Parés, C., Vázquez, C. (2006). Optimization of a Duality Method for the Compressible Reynolds Equation. In: de Castro, A.B., Gómez, D., Quintela, P., Salgado, P. (eds) Numerical Mathematics and Advanced Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34288-5_25
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DOI: https://doi.org/10.1007/978-3-540-34288-5_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34287-8
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