In this talk we will discuss a general modelling process of modern coupled engineering problems, as well as numerical methods for their solution. In the first part of the talk, we will show that the modelling process must be at first addressed on the conceptual level by means of abstract mathematics. A category theory-based point of view on the modelling is proposed in this talk along with some practical examples from engineering. After that, the transition from the conceptual level to concrete boundary value problems is discussed on example of a coupled analytical-numerical method. The second part of the talk is devoted to discussion on hypercomplex interpolation by help of reproducing kernel Hilbert spaces, which is the basis for an extension of the coupled method to hypercomplex setting. Finally, some numerical examples for hypercomplex interpolation and general strategy for the spatial coupled method will be presented.