  The demagnetization field in micromagnetism is given as the gradient of a
potential which solves a partial differential equation (PDE) posed in R^d. In
its most general form, this PDE is supplied with continuity condition on the
boundary of the magnetic domain and the equation includes a discontinuity in
the gradient of the potential over the boundary. Typical numerical algorithms
to solve this problem relies on the representation of the potential via the
Green's function, where a volume and a boundary integral terms need to be
accurately approximated. From a computational point of view, the volume
integral dominates the computational cost and can be difficult to approximate
due to the singularities of the Green's function. In this article, we propose a
hybrid model, where the overall potential can be approximated by solving two
uncoupled PDEs posed in bounded domains, whereby the boundary conditions of one
of the PDEs is obtained by a low cost boundary integral. Moreover, we provide a
convergence analysis of the method under two separate theoretical settings;
periodic magnetisation, and high-frequency magnetisation. Numerical examples
are given to verify the convergence rates.
