A modified formulation of the volume integral equations method for 3D magnetostatics

A magnetization-based formulation of the volume integral equations method for 3-D magnetostatics is discussed. The magnetization of each element is related, via the constitutive law of the material, to the average magnetic flux density within the element rather than to the value at the center as is usually done. This assumption leads to more accurate distribution of magnetization and allows a faster convergence of the solution. Moreover, it leads to more symmetric matrix of the coefficients and reduces the numerical instability due to looping patterns of magnetization, which is inherent to integral methods. The formulation is made effective by the use of a hybrid numerical and analytical approach, which allows for the fast and accurate calculation of the coefficients. The proposed model is validated and compared with the usual model both for saturable and linear material with high susceptibility.