On solving the magnetostatics equations for convex domains

We solve the magnetostatics equations for convex domains, bounded by a thin heterogeneous isotropic ferromagnetic layer. The problem reduces to determining the internal and external solutions of a system of Laplace equations with mixed boundary conditions on a surface. Potential theory allows us to reduce the problem to a system of Fredholm equations of the second kind. Analytical solution for an arbitrary surface is not available. In this paper, we propose a numerical approach implemented in the Python framework.