Magnetic induction in bounded domains

Simulations of magnetohydrodynamic (MHD) flows in bounded domains using spectral methods can suffer from a number of serious limitations.
 Alternative methods based on local discretisation raise the problem of non-local boundary conditions implementation for the magnetic field.
    We propose a strategy for the numerical solution of
    MHD problems in bounded conducting domains, which combines the flexibility of a local discretisation
with a rigorous formulation of magnetic boundary conditions next to an insulator in arbitrary geometries.
 Following the nature of underlying equations, we apply a global integral approach (B.E.M.) at the boundary and differential approach (V.F.)
inside the conducting domain. We illustrate the approach in a sphere as well as in a finite cylinder.