Convergence Analysis of a Fourier-Based Solution Method of the Laplace Equation for a Model of Magnetic Recording | Zendy

John L. Fleming | Zendy

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Convergence Analysis of a Fourier-Based Solution Method of the Laplace Equation for a Model of Magnetic Recording

Author(s) -

John L. Fleming

Publication year - 2008

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2008/154352

Subject(s) - truncation (statistics) , laplace transform , fourier series , convergence (economics) , laplace's equation , fourier transform , mathematical analysis , mathematics , series (stratigraphy) , computer science , partial differential equation , paleontology , statistics , economics , biology , economic growth

When engineers model the magnetostatic fields applied to recordingheads of computer hard drives due to a magnetic recording medium,the solution of Laplace's equation must be found. A popular solutionmethod is based on Fourier analysis. However, due to the geometry ofthe read head model, an interesting mathematical problem arises. Thecoefficients for the Fourier series solution of the desired magneticpotential satisfy an infinite system of linear equations. Inpractice, the infinite system is truncated to a finite system withlittle consideration for the effect this truncation has on thesolution. The paper will provide a proper understanding of theunderlying problem and a formal analysis of the effect oftruncation

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