Mathematical Analysis and Numerical Simulation in Magnetic Recording

Abstract

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.

Keywords:

• finite element method
• nonlinear differential equation
• numerical method

AMS Subject Classification:

• 34B99
• 34B60
• 74F17