This paper is devoted to the practical computation of the
magnetic potential induced by a distribution of magnetization in
the theory of micromagnetics. The problem turns out to be a coupling of
an interior and an exterior problem. The aim of this work is to describe
a complete method that mixes the approaches of Ying [12] and Goldstein
[6] which consists in constructing a mesh for the exterior
domain composed of homothetic layers. It has the advantage of being well
suited for catching the decay of the solution at infinity and giving a
rigidity matrix that can be very efficiently stored. All aspects are
described here, from the practical construction of the mesh, the storage
of the matrix, the error estimation of the method, the boundary conditions
and a simple preconditionning technique. At the end of the
paper, a typical computation of a uniformly magnetized
ball is done and compared to the analytic solution. This method
gives a natural alternatives to boundary elements methods for 3D
computations.