Two-domain analysis of field-producing bodies, using fictitious poles

An unconventional numerical method is presented for analysing the behaviour of a field-producing body, e.g. a bar magnet. The body shape is restricted to axisymmetry and to mirror-image symmetry about a central plane, but is otherwise general. The body internal features are likewise general, and may include mixed materials having non-linear properties. The basic principle is always to have a specified surface potential distribution upon trial. It is shown that the external and internal analyses may then proceed independently. Externally, Laplace’s equation is solved using a sparse set of fictitious internal poles. The solution is self-validating, and provides a direct transformation from surface potential to internal body flux distribution, taking account of any applied external field. Internally, flux is then converted using simple circuit technique to a new surface potential distribution. This closure enables the correct distributions to be found by iteration. For uniformly permeable body material, an alternative internal procedure makes iteration unnecessary. An unconventional composite magnet is analysed, and the traditional problem of a uniformly permeable cylinder in an applied field solved. CYBER 76 computer times are single seconds only. The method is compared with established pole-type methods and found advantageous. Extension to non-axisymmetry should be possible.