An iterative method to obtain non-uniform field distribution in magnetic substrates

An iterative method to find the non-uniform field distribution for arbitrary shapes is studied. In this method, when a magnetic material is placed in an applied field H_a produced by an external source, interaction occurs between the applied field and the magnetic material. Initially, with no demagnetizing field, the internal field equals the applied field until the material becomes saturated in the direction of the local applied field when the field is sufficiently strong. The main iteration loop starts with this initial value for the magnetization M. The material produces a contribution, a demagnetizing field H_d, to the magnetic field in which when added to the applied magnetic field, results in the total internal field H_i. The magnetic material now responds to this new total field and the magnetization redistributes itself in the new direction of the local total field. The iteration continues with this new magnetization, producing new demagnetizing and total internal fields. Results show that after further iterations the field becomes more parallel and the distribution of H_i is found to be symmetric with respect to the corners. The flux originates in the upper half and ends in the lower half following the general direction of H_a.