While fighting with the interaction between local and global aspects for the solution of the Helmholtz equation, I realized that a hierarchical multilevel method may not necessarily be applicable for the global aspects. So even a crucial step in the construction of a multilevel method is the construction of a two level method, not every two level method will necessarily generalize to a multilevel method. And the interesting creative transition will normally occur in the design of the separation of concerns for the two level method, independent of whether it generalizes to a hierarchical multilevel method or not.

Why is separation of concerns so closely associated with hierarchy in my mind? It's true that even a two level hierarchy is still a hierarchy, but it seems as if the "separation of concerns" aspect deserves more attention than the "hierarchy" aspect. And why do I intuitively prefer a hierarchy for global order aspects, even so there may be other more useful orders in some contexts? For example, I prefer hierarchical file systems, even so an index based database (or something like google) might often be more useful for retrieving data. I see that hierarchical schemes offer better asymptotical "information compression potential" than two (or three) level schemes, but I'm unsure how relevant this is in practice.

My question is a reference request. What are good exposition of the problems related to the interactions between separation of concerns, hierarchy and order? I'm especially interested in discussions of the relations and differences between these concepts.

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