I. Introduction
For devices with a huge volume free space compared to the active structure or high ratio between the object geometries, the finite element method leads to problems of accuracy and convergence to the solution [1]. In such case, integral methods can be attractive alternatives [2], [3]. Integral formulations of the magnetostatic field problems are particularly advantageous for the numerical solution of open-boundary problems which include ferromagnetic materials since only the active regions containing these materials need to be discretized. This paper gives in the first part a magnetostatic formulation in the framework of the integral volume methods in which the collocation and Galerkin methods are used to solve the magnetostatic equations. The computation of the source potential and of the integrals to built the interaction matrix are so presented in this part. The second part proposes the Newton-Raphson and modified fixed point method to solve the nonlinear formulation. The last one presents the results obtained for different applications.