In many applications strong variations in temporal or spatial scales in the differential equations pose serious challenge to numerical simulations. We shall describe a framework for computations on the macroscale but where the forces and fluxes are computed on the microscale. This means that macroscale computations can be done without the knowledge of effective equations but also without the high computational complexity of a full microscale simulation. Examples will be given from homogenization theory for hyperbolic problems with oscillatory solutions.