Convergence analysis of a Fourier-based solution method of the Laplace equation for a model of magnetic recording. (English) Zbl 1152.78001

Summary: 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.


78A30 Electro- and magnetostatics
58E50 Applications of variational problems in infinite-dimensional spaces to the sciences
78M30 Variational methods applied to problems in optics and electromagnetic theory
65T50 Numerical methods for discrete and fast Fourier transforms
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