Simulating the Birth of the Universe on a PetaFlop
In the beginning, when the universe was less than one microsecond old and more than one trillion degrees hot, it transformed from a plasma of quarks and gluons into bound states of quarks we reefer to as protons and neutrons, the fundamental building blocks of nuclear matter that make up most of the visible universe. We believe this happened because the theory of quantum chromodynamics (QCD), which governs the interactions of the strong nuclear force, predicts it should happen when such conditions occur. Recent experiments at the Relativistic Heavy Ion Collider at Brookhaven National Laboratory have provided direct evidence of the existence of this phase transition in collisions between gold nuclei at the highest attainable energies. But calculating the properties of this phase transition has been notoriously difficult and computationally challenging. What we've been able to discern via this theory has come by situating space and time onto a 4D grid of lattice points, on a volume no bigger than the size of a large nucleus. This discrete formulation of QCD known as lattice QCD (LQCD) can be tamed in a way that's numerically amenable to massively parallel machines. Indeed, our LQCD code scaled with perfect speedup all the way to the 131,072 CPU cores on the world's fastest supercomputer, the BlueGene/L (BG/L) system at Lawrence Livermore National Laboratory (LLNL). Efforts are currently under way to calculate this phase transition's properties using tens of teraflops spread across many of the world's fastest computers. However, the lattice discretization used in our calculations of space-time breaks one of the most crucial properties of the underlying theory: the basic symmetry of chiral rotations. Chiral symmetry can't be fully restored on the lattice, but it can be restored and controlled to a high degree by using the method of domain wall fermions (DWF). DWF introduces an extra fifth dimension, in which chiral symmetry is restored with only a small amount of breaking, which decreases as the fifth dimension's size increases. In particular, researchers have estimated that a fifth dimension of roughly 64 lattice points is sufficient to restore symmetry with a systematic error of only a few percent, even around the transition temperature. Studies have also shown that DWF exhibits excellent fidelity in incorporating the transition's basic driving forces. But the computational cost of this calculation is roughly 2 x 64 = 128 times higher than the cost of current methods that don't preserve this symmetry on the lattice, and thus it falls outside the realm of current terascale supercomputing. With petascale supercomputing, however, this restriction is lifted. If we had petascale supercomputing for our calculation, we could use computational techniques similar to those used on BG/L to calculate the thermodynamic properties--or more precisely, the equation of state--of the quark-gluon plasma just as it begins to form protons and neutrons as it did in the very early universe. The basic level of parallelism again comes from the division of the 4D grid into subgrids assigned to nodes on a massively parallel machine, thereby providing perfect speedup. DWF's fifth dimension provides yet another level of parallelism: given that the nodes of a massively parallel petascale supercomputer will likely consist of several CPU cores per chip, it's natural to fully map the fifth dimension along the node chip's CPU cores. On a 16-CPU core chip, for example, we could assign four fifth-dimension 'slices' per CPU core for a total of 64. In this way, the new level of parallelism in the application matches the new level of parallelism in the hardware. The communication patterns along the fifth dimension are nearest-lattice-neighbor only and can be handled via shared memory or any other on-chip data transfer mechanism, thus alleviating off-chip data transfers while exploiting the hardware's native capability.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 945802
- Report Number(s):
- LLNL-JRNL-404088; TRN: US0901100
- Journal Information:
- Computing in Science and Engineering, vol. 9, no. 6, November 1, 2007, pp. 55-56, Vol. 9, Issue 6
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
99 GENERAL AND MISCELLANEOUS
BOUND STATE
CHIRAL SYMMETRY
COMPUTERS
DIMENSIONS
FERMIONS
GLUONS
HEAVY IONS
NEUTRONS
NUCLEAR FORCES
NUCLEAR MATTER
NUCLEI
PROTONS
QUANTUM CHROMODYNAMICS
QUARK MATTER
QUARKS
SPACE-TIME
SUPERCOMPUTERS
SYMMETRY
THERMODYNAMICS
TRANSITION TEMPERATURE
UNIVERSE
SIMULATION