Presented is computational astrophysics and cosmological research featuring various extremes. Brief mention is given to a numerical complication in the context of ultra-relativistic, hydrodynamic simulations of winds from dead stars involving matter densities on the order of 10^-19 times smaller than that of the diffuse Galactic medium. Results are further presented for a two-pronged application of the Argonne Blue Gene/P (BG/P) supercomputer to the study of dark energy covering spatial scales from a single star to the entire Universe. The stellar scale, and relevance to matter densities on the order of 10^6 times that of the Sun, is represented by radiative transfer calculations for thermonuclear supernova explosions. The largest spatial scale known to science is represented by simulations of the cosmic structure of the Universe. SEDONA code radiative transfer calculations are shown to scale well on the BG/P for a minimally parallel case. BG/P scaling of the FLASH code cosmology module is shown to be complex, and pursuit of BG/P simulation runs incorporating 1024^3 particles are demonstrated to be a significant challenge. Key improvements enabled by the 2012 arrival of the next-generation Argonne Blue Gene/Q supercomputer are discussed.

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