Integration methods for the calculation of the magnetostatic field due to coils
نویسنده
چکیده
Integration methods for the calculation of the magnetostatic field due to coils Marzia Fontana Abstract Analytical and numerical integration methods of the Biot-Savart law are presented for the three-dimensional computation of the magnetic eld generated by stationary currents. For complex-shaped conductors a nite volume approximation is proposed, based on a composite Gauss-Legendre quadrature on tetrahedral subdo-mains of the conductors. For circular coils with rectangular cross section, a modiied semi-analytical Urankar's method is considered, expressed in terms of elementary functions, Jacobian elliptic functions and complete/incomplete elliptic integrals of the rst, second and third kind. As alternative, numerical integration can be applied to sequences of one-dimensional non-singular integrals in azimuthal coordinate. For massive computation on a large number of eld points, an optimized integration scheme for coils is suggested, by combining the modiied Urankar's method with one-dimensional numerical integration. Numerical examples are reported on signiicant test cases for a comparison among the several integration methods proposed.
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