supercomputers have risen dramatically in their computational powers last few decades due to Moore's law & also increasing parallelism technology in hardware and software. many different types of analysis algorithms are run now for many diverse areas of science.
what can be said about the complexity of typical supercomputing jobs/ applications? are they "mostly" in P? are there examples of major supercomputing projects that tackle NP hard problems or harder? is there some published study/ survey of the complexity of supercomputing problems?
my (rough) understanding is that maybe "most" are in P. for example "grid" calculations for 3d volumes are typically something like O(n3) where n is the grid distance/ length. molecular dynamics simulations have O(n2) calculations where n is the number of particles. many other calculations are done on matrices which are typically O(n2). etc. (not sure about fluid dynamics simulations.) PageRank might be O(n) or at least Ptime.
(this question is partly motivated by discussion on Aaronsons blog/ comments "introducing some British people to P vs NP" where there is questions about using supercomputers for theorem proving in the comments etc.)