It is well known that the electromagnetic coupling constant alpha is an energy scale dependent quantity. Some of these dependencies originate from hadrons and can therefore be computed using Lattice QCD. The value at the mass of the Z boson is of particular interest. The large energy range makes a direct simulation unfeasible, so it has to be split up into several ranges. Setting the scale of the smaller and finer lattices, which cover the higher energies, is a challenging task. We present a general method to handle this issue in lattice gauge theories. A test of this strategy in two-dimensional QED is done and the hadronic vacuum polarization is computed on an energy range that spans two orders of magnitude.