Coupled models technology and its applications in the geometrical multi-scale modelling of complex systems

The need to simulate the complex behavior of large systems comprising relevant physical phenomena at different geometrical levels poses the challenge
of setting up proper mathematical representations capable of providing an accurate insight of the whole picture. The goal of this presentation is to
gather a series of recent advances in terms of the development of mathematical concepts and computational models aimed at tackling such complex problems. In order to do this we start by making use of the concept of coupled dimensionally-heterogeneous models (or kinematically incompatible models), whose derivation follows a consistent variational approach. Two natural questions arise in this context that go beyond the mere formulation
of the problem: (i) how to assess the quality of the representation of the original problems by means of dimensionally-heterogeneous models (the quality in the definition of the different scales); and (ii) how to decompose the coupled
problem into more simple sub-systems in a strong iterative manner. These two points will be also addressed in this presentation together with some
examples of applications.