Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 154352, 11 pages
doi:10.1155/2008/154352
Research Article
Convergence Analysis of a Fourier-Based Solution Method
of the Laplace Equation for a Model of Magnetic Recording
Department of Mathematics and Computer Science, Duquesne University, 600 Forbes Avenue, Pittsburgh 15282, PA, USA
Received 1 April 2007; Accepted 25 November 2007
Academic Editor: F. E. Udwadia
Copyright © 2008 John L. Fleming. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
When engineers model the magnetostatic fields applied to recording
heads of computer hard drives due to a magnetic recording medium,
the solution of Laplace's equation must be found. A popular solution
method is based on Fourier analysis. However, due to the geometry of
the read head model, an interesting mathematical problem arises. The
coefficients for the Fourier series solution of the desired magnetic
potential satisfy an infinite system of linear equations. In
practice, the infinite system is truncated to a finite system with
little consideration for the effect this truncation has on the
solution. The paper will provide a proper understanding of the
underlying problem and a formal analysis of the effect of
truncation.