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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 <jats:italic>\u03b5<\/jats:italic>. The results obtained in this work are compared with other simulations performed by the software of finite elements method, Flux 2<jats:italic>D<\/jats:italic>.<\/jats:p>","DOI":"10.1155\/2010\/742039","type":"journal-article","created":{"date-parts":[[2011,2,16]],"date-time":"2011-02-16T00:15:49Z","timestamp":1297815349000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Electromagnetic Problems Solving by  Conformal Mapping: A Mathematical Operator  for Optimization"],"prefix":"10.1155","volume":"2010","author":[{"given":"Wesley Pacheco","family":"Calixto","sequence":"first","affiliation":[]},{"given":"Bernardo","family":"Alvarenga","sequence":"additional","affiliation":[]},{"given":"Jesus Carlos","family":"da Mota","sequence":"additional","affiliation":[]},{"given":"Leonardo da Cunha","family":"Brito","sequence":"additional","affiliation":[]},{"given":"Marcel","family":"Wu","sequence":"additional","affiliation":[]},{"given":"Aylton Jos\u00e9","family":"Alves","sequence":"additional","affiliation":[]},{"given":"Luciano Martins","family":"Neto","sequence":"additional","affiliation":[]},{"given":"Carlos F. 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