The strategy is to examine the closely coupled clusters in isolation, and then somehow couple this information together to deduce the global steady state behaviour. This is accomplished by so-called aggregation/disaggregation methods based on the Simon-Ando theory for nearly uncoupled systems. This amounts to first uncoupling a particular eigenvector problem followed by a coupled eigenvector problem reminiscent of an unsymmetric divide-and-conquer scheme involving an unsymmetric Rayleigh-Ritz like step.
The presentation will include a survey and intuitive overview of the Simon-Ando theory followed by and intuitive derivation of the basic aggregation/disaggregation process. It will conclude with a short error analysis. The development will be in the context of linear algebra together with some elementary finite Markov chain techniques.