Calixto, Wesley Pacheco; da Mota, Jesus Carlos; Pinheiro de Alvarenga, Bernardo Methodology for the reduction of parameters in the inverse transformation of Schwarz-Christoffel applied to electromagnetic devices with axial geometry. (English) Zbl 1245.78010 Int. J. Numer. Model. 24, No. 6, 568-582 (2011). Summary: This paper presents a method for calculating the parameters of the Schwarz-Christoffel inverse transformation using a genetic algorithm. It is shown that for problems involving a polygonal geometry with axial symmetry, the number of estimated parameters is reduced by half. Simulations are performed with polygonal figures with several different geometries and with up to 27 sides. A four-sided polygon is inversely mapped in order to verify the accuracy of the method. The method is also applied for calculating the induction lines and the flux lines in the region of a doubly slotted airgap of an electrical machine. Finally, based on the length of the midline of induction in the airgap, a new and very simple formula to calculate the Carter factor of an electrical machine is presented, which takes into account the actual geometry of the airgap. MSC: 78A55 Technical applications of optics and electromagnetic theory 68T05 Learning and adaptive systems in artificial intelligence 90C15 Stochastic programming 30C30 Schwarz-Christoffel-type mappings 65E05 General theory of numerical methods in complex analysis (potential theory, etc.) Keywords:Schwarz-Christoffel transformation; genetic algorithm; simulation; conformal mapping Software:SC Toolbox; Schwarz-Christoffel PDFBibTeX XMLCite \textit{W. P. Calixto} et al., Int. J. Numer. Model. 24, No. 6, 568--582 (2011; Zbl 1245.78010) Full Text: DOI References: [1] Henrici, Applied and Computational Complex Analysis (1986) · Zbl 0578.30001 [2] Spiegel, Complex Variable (1967) [3] Nehari, Conformal Mapping (1952) [4] Cohn, Conformal Mapping on Riemann Surfaces (1967) · Zbl 0175.08202 [5] Gibbs, Conformal Transformations in Electrical Engineering (1958) · Zbl 0084.07006 [6] Wen, Conformal Mapping and Boundary Value Problems (1992) [7] Trefethen, Numerical computation of the Schwar-Christoffel transformation, SIAM Journal on Scientific Computing 1 (1) pp 82– (1980) · Zbl 0451.30004 [8] Driscoll, Numerical conformal mapping using cross-ratios and Delaunay triangulation, SIAM Journal on Scientific Computing 19 (6) pp 1783– (1998) · Zbl 0915.30006 [9] Costamagna, On the numerical inversion of the Schwarz-Christoffel conformal transformation, IEEE Transactions on Microwave Theory and Technique 35 pp 35– (1987) [10] Driscoll, Schwarz-Christoffel Mapping. Cambridge Monographs on Applied and Computational Mathematics (2002) · Zbl 1003.30005 [11] Howell, A modified Schwarz-Christoffel transformation for elongated regions, SIAM Journal on Scientific Computing 11 (5) pp 928– (1990) · Zbl 0703.30006 [12] Abramowitz, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables (1968) [13] Milne, Infinite Families of Exact Sums of Squares Formulas, Jacobi Elliptic Functions, Continued Fractions, and Schur Functions (2002) · Zbl 1125.11315 [14] Jog, Parallel genetic algorithms applied to the traveling salesman problem, SIAM Journal on Optimization 1 (4) pp 515– (1991) · Zbl 0754.90061 [15] Michalewicz, How to Solve it: Modern Heuristics (1999) · Zbl 1058.68105 [16] Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence (1975) · Zbl 0317.68006 [17] Calixto WP Application of conformal mapping to the calculus of Carter’s factor. Masters Degree Dissertation (In Portuguese) 2008 [18] Herrera F Lozano M Verdegay JL Crossover Operators and Offspring Selection for Real Coded Genetic Algorithms Technical Report 1994 [19] Carter, Air-gap induction, Journal IEE 38 pp 925– (1901) [20] Walker, The Schwarz-Christoffel Transformation and its Applications: A Simple Exposition (1964) · Zbl 0115.06402 [21] Carter, The magnetic field of the dynamo-electric machine, Journal IEE 64 pp 1115– (1926) [22] Calixto, A new methodology to calculate Carter factor using genetic algorithms, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields (2010) · Zbl 1220.78075 [23] Langsdorf, Principles of Direct Current Machines (1959) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.