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SUMMARYThis contribution is an extension of the authors' work in modelling multi-scale systems which are of significant importance in many applications such as Electromagnetic Compatibility (EMC). By its very nature EMC analysis often requires consideration of systems characterized by many different physical scales, for example when thin wires, gaps and slots are present in otherwise physically large structures. For the Transmission Line Modelling (TLM) simulation method, nodes that explicitly embed fine structures smaller than the mesh size within them have previously been demonstrated for a number of special cases where the fields in close proximity to the object may be represented in terms of known local analytic solutions. This approach enables the presence of general sub cell objects to be correctly and efficiently modelled in coarse grids without incurring excessive computational effort. The work presented here differs in that it permits the use of purely numerical calculations of these local fields and therefore provides a powerful extension to more general structures for which local analytic field representations are unavailable. A full derivation of the formulation in terms of these local solutions is discussed as well as the procedure for linking them to the rest of the numerical network. Illustrative results are then obtained from an application to a canonical scattering problem.