Even after optimization, I might need a lot of computation time. Can anyone host me on a supercomputer running Mathematica? If so, could you compare your speed to an Intel i7 with 16 gigs of RAM? I believe I am CPU limited but not memory limited.
You may consider trying to run Mathematica in the cloud, maybe AWS. You can then scale up the number of machines and CPU/hours as necessary to solve the problem. Of course, you then have to write distributed code for the kernels to communicate with each other, but that's something you'd have to do with any cluster set-up.