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Mathematical Problems in Engineering
Volume 2010, Article ID 742039, 19 pages
Research Article

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

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.

Linked References

  1. P. Henrici, Applied and Computational Complex Analysis, vol. 3 of Pure and Applied Mathematics, John Wiley & Sons, New York, NY, USA, 1986. View at Zentralblatt MATH
  2. M. R. Spiegel, Complex Variable, McGraw-Hill, New York, NY, USA, 1967.
  3. J. D. Kraus and K. R. Carver, Electromagnetics, McGraw-Hill, New York, NY, USA, 1973.
  4. W. P. Calixto, E. G. Marra, L. C. Brito, and B. P. Alvarenga, “A new methodology to calculate carter factor using geneticalgorithms,” International Journal of Numerical Modelling: Electronic Networks, Devices and Fields. In press. View at Publisher · View at Google Scholar
  5. Z. Nehari, Conformal Mapping, McGraw-Hill, New York, NY, USA, 1952. View at Zentralblatt MATH
  6. H. Cohn, Conformal Mapping on Riemann Surfaces, Dover, New York, NY, USA, 1967. View at Zentralblatt MATH
  7. W. J. Gibbs, Conformal Transformations in Electrical Engineering, Chapman and Hall, London, UK, 1958.
  8. G. C. Wen, Conformal Mappings and Boundary Value Problems, vol. 106 of Translations of Mathematical Monographs, American Mathematical Society, Providence, RI, USA, 1992. View at Zentralblatt MATH
  9. L. N. Trefethen, “Numerical computation of the Schwarz-Christoffel transformation,” Society for Industrial and Applied Mathematics, vol. 1, no. 1, pp. 82–102, 1980. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. T. A. Driscoll and S. A. Vavasis, “Numerical conformal mapping using cross-ratios and Delaunay triangulation,” SIAM Journal on Scientific Computing, vol. 19, no. 6, pp. 1783–1803, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. E. Costamagna, “On the numerical inversion of the schwarz-christoffel conformal transformation,” IEEE Transactions on Microwave Theory and Techniques, vol. 35, no. 1, pp. 35–40, 1987. View at Google Scholar
  12. T. A. Driscoll and L. N. Trefethen, Schwarz-Christoffel Mapping, vol. 8 of Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, UK, 2002. View at Publisher · View at Google Scholar
  13. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables, Dover, New York, NY, USA, 1968.
  14. S. C. Milne, Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, and Schur Functions, vol. 5 of Developments in Mathematics, Kluwer Academic Publishers, Boston, Mass, USA, 2002.
  15. W. P. Calixto, Application of conformal mapping to the calculus of Carter's factor, M.S. thesis, Electrical & Computer Engineering School, Federal University of Goias, Goiania, Brazil, 2008.
  16. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, Artificial Intelligence, Springer, Berlin, Germany, 1992.
  17. Z. Michalewicz and D. B. Fogel, How to Solve it: Modern Heuristics, Springer, Berlin, Germany, 2000.
  18. J. H. Holland, Adaptation in Natural and Artificial Systems: an Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, University of Michigan Press, Ann Arbor, Mich, USA, 1975.
  19. F. Herrera, M. Lozano, and J. L. Verdegay, “Crossover operators and offspring selection for real coded genetic algorithms,” Tech. Rep., Department of Intelligence of the Computation and Artificial intelligence, University of Granada, Granada, Spain, 1994. View at Google Scholar
  20. Cedrat, Flux 2D User's Guide, Cedrat, Grenoble, France, 2000.
  21. R. E. Collins, Mathematical Methods for Physicists and Engineers, Dover, New York, NY, USA, 2nd edition, 1999.