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Understanding the electromagnetic interactions between broadband signals and the environment is important, especially in the area of aerospace design. In this area the accurate modelling of realistic engineering problems often leads to a computational domain which is geometrically complex, often with different types of materials interfaces and even the modelling of wiring for some EMC problems. The development of suitable computational tools that allows the modelling of such complex and large-scale problems is of paramount importance. A time domain heterogeneous hybrid computational electro-magnetics method is presented. The algorithm uses a time-domain finite element method and a finite-difference time-domain Yee scheme to compute the fields in two regions. The two regions overlap in a buffer zone to allow for stable solution interpolation between the two parts. This enables different parts of the simulation domain to be treated by different methods, thus enabling the most appropriate method to be used for each part. As an illustration of the approach, we will present the results for a number of challenging examples, including scattering from complete aircraft and coupled cavities modelling.