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

Author

Listed:
  • Wesley Pacheco Calixto
  • Bernardo Alvarenga
  • Jesus Carlos da Mota
  • Leonardo da Cunha Brito
  • Marcel Wu
  • Aylton José Alves
  • Luciano Martins Neto
  • Carlos F. R. Lemos Antunes

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 . The results obtained in this work are compared with other simulations performed by the software of finite elements method, Flux .

Suggested Citation

  • Wesley Pacheco Calixto & Bernardo Alvarenga & Jesus Carlos da Mota & Leonardo da Cunha Brito & Marcel Wu & Aylton José Alves & Luciano Martins Neto & Carlos F. R. Lemos Antunes, 2010. "Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-19, February.
    • Handle: RePEc:hin:jnlmpe:742039
    DOI: 10.1155/2010/742039
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