An advantage with the framework of the heterogeneous multiscale method is that the full knowledge of an effective or macroscale equation is not required for the numerical approximation of a homogenized or averaged solution. A higher fidelity microscale model is used to supply the missing data. The efficiency is gained by only applying the microscale model in sub domains. The structure of the macroscale equation must however be known. Often it is well known from the setting of the original problem, but if it is not, new techniques are required to find the form of a relevant effective or macroscale equation.