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Mathematical Problems in Engineering
Volume 2008, Article ID 154352, 11 pages
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.


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.