This paper presents a novel procedure for the fast numerical integration of magnetic field produced by arc-shaped conductors, characterized by rectangular cross section. Available procedures are based on the analytical integration of Biot-Savart’s law but most of them exploit the analytical integration along one coordinate, and then perform a two-dimensional numerical integration. In the proposed procedure, the analytical integration was performed along two coordinates, obtaining a one-dimensional integrand (thus avoiding the use of Elliptic Integrals), very easy to process using a state-of-the-art numerical quadrature library. The result is very satisfactory in terms of high speed and precision, particularly on conductor surface, and when its cross dimensions are very uneven.
Algorithm for the Fast Calculation of Magnetic Fields Generated by Arc-Shaped Conductors with Rectangular Cross Section
NERVI, MARIO;MOLFINO, PAOLO
2014-01-01
Abstract
This paper presents a novel procedure for the fast numerical integration of magnetic field produced by arc-shaped conductors, characterized by rectangular cross section. Available procedures are based on the analytical integration of Biot-Savart’s law but most of them exploit the analytical integration along one coordinate, and then perform a two-dimensional numerical integration. In the proposed procedure, the analytical integration was performed along two coordinates, obtaining a one-dimensional integrand (thus avoiding the use of Elliptic Integrals), very easy to process using a state-of-the-art numerical quadrature library. The result is very satisfactory in terms of high speed and precision, particularly on conductor surface, and when its cross dimensions are very uneven.
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