Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 742039, 19 pages
doi:10.1155/2010/742039
Research Article

Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization

Wesley Pacheco Calixto,1,2,3 Bernardo Alvarenga,1,3 Jesus Carlos da Mota,4 Leonardo da Cunha Brito,1 Marcel Wu,3 Aylton José Alves,3 Luciano Martins Neto,3 and Carlos F. R. Lemos Antunes2,3

1Electrical & Computer Engineering School, Federal University of Goias (UFG), Avenda Universitaria, 1488 Qd. 86 Bl., 74605-010 Goiania, GO, Brazil
2Electrical Engineering and Computers Department of the Faculty of Sciences and Technology, University of Coimbra, 3030-290 Coimbra, Portugal
3Electromagnetism and Electric Grounding Systems Nucleus Research and Development, Department Electrical Engineering, Federal University of Uberlandia, 38400-902 Uberlandia, MG, Brazil
4Institute of Mathematics & Statistics (IME), Federal University of Goias, Campus II, 74001-970 Goiania, GO, Brazil

Received 22 September 2010; Accepted 10 December 2010

Academic Editor: Piermarco Cannarsa

Copyright © 2010 Wesley Pacheco Calixto et al. 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

Having the property to modify only the geometry of a polygonal structure, preserving its physical magnitudes, the Conformal Mapping is an exceptional tool to solve electromagnetism problems with known boundary conditions. This work aims to introduce a new developed mathematical operator, based on polynomial extrapolation. This operator has the capacity to accelerate an optimization method applied in conformal mappings, to determinate the equipotential lines, the field lines, the capacitance, and the permeance of some polygonal geometry electrical devices with an inner dielectric of permittivity 𝜖 . The results obtained in this work are compared with other simulations performed by the software of finite elements method, Flux 2 𝐷 .