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The paper addresses a particular feature of EMC, namely the presence of multi-scale objects, which make it a very challenging modelling problem. By a multi-scale problem we mean the presence in the same solution space of features which are electrically small (relatively to the wavelength) and electrically large. The “brute force” approach requiring as it does increasingly faster and larger computers has its limits. What is needed is an innovative modelling approach which employs hybrid techniques to maintain acceptable accuracy and modest computational demands. In this paper we focus on two approaches. First, the embedding of local solutions around fine features in the form of macro-models. Second, the hybridization of structured and unstructured meshes to facilitate feature description and adapt spatial resolution to local conditions and requirements.