Abstract
Quantum corrections to the mean-field equation of state for nuclear matter are estimated in a lattice simulation of quantum hadrodynamics on a CRAY Y-MP. In contrast with lattice quantum chromodynamics, where coordinate space methods are the standard, the calculations are carried out in momentum space and on nonhypercubic (irregular) lattices. The quantum corrections to the known, mean-field equation of state were found to be considerable. The time frame of the project and the large computational needs of the program required the use of powerful supercomputers, like the CRAY Y-MP, which are capable of performing at a very high computing speed by using both vector and parallel hardware, the latter being exploited by means of autotasking. The paper describes the applied analytical and the numerical methods as well as the changes needed for the program to be executed in parallel. After some code modifications a very efficient version could be obtained on a CRAY Y-MP8/832, leading to an overall performance of 2.13 gigaflops.
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Anderson, J.J., Bai, Z., Bischof, C., Demmel, J., Dongarra, J., DuCroz, J., Greenbaum, A., Hammarling, S., McKenney, A., and Sorensen, D. 1990. LAPACK: A portable linear algebra library for high-performance computers. CS-90–105, Univ. of Tennessee, Knoxville, Tenn. (LAPACK Working Note 20).
Cray Research. 1989. Library Reference Manuals, Vol. 3: UNICOS Math and Scientific Library Reference Manual. Cray Research, Inc., SR-2081 5.0.
Cray Research. 1990. CF77 Compiling System, Vol. 4: Parallel Processing Guide. Cray Research, Inc., SR-3074 4.0.
Creutz, M. 1977. Gauge fixing, the transfer matrix and confinement on a lattice. Phys. Rev., D15: 1128–1136.
Creutz, M. 1979. Monte Carlo study of Abelian lattice gauge theories. Phys. Rev., D20: 1915–1922.
Creutz, M. 1983. Quarks, Gluons, and Lattices. Cambridge Univ. Press, Cambridge.
Detert, U. 1989. Memory performance of CRAY X-MP and CRAY Y-MP. In Proc.—Cray User Group Fall Meeting (Trondheim, Sept. 18–22), pp. 50–54.
Dongarra, J.J., DuCroz, J., Hammarling, S., and Duff, I. 1990. A set of Level 3 BLAS. ACM TOMS, 16, 1 (Mar.): 1–17.
Dongarra, J.J., DuCroz, J., Hammarling, S., and Hanson, R.J. 1988. An extended set of Fortran basic linear algebra subprograms. ACM TOMS, 14, 1 (Mar.): 1–17.
Frank, J., and Brockmann, R. 1992. Lattice quantum hadrodynamics. Phys. Rev. Lett., 68: 1830–1833.
Furnstahl, R.J., Perry, R.J., and Serot, B.D. 1989. Two-loop corrections for nuclear matter in the Walecka model. Phys. Rev., C40: 321–353.
Gavai, R.V., and Ostendorf, A. 1983. Finite size effects for the non-interacting Fermi system at finite temperature and finite density. Phys. Lett., 132B: 137–140.
Hasenfratz, P., and Karsch, F. 1983. Chemical potential on the lattice. Phys. Lett., 125B: 308–310.
Hossfeld, F., Knecht, R., and Nagel, W.E. 1989. Multitasking: Experiences with applications on a CRAY X-MP. Parallel Computing, 12, 3 (Dec.): 259–283.
Knecht, S., Laermann, E., and Nagel, W.E. 1990. Parallelizing QCD with dynamical fermions on a CRAY multiprocessor system. Parallel Computing, 15, 1–3 (Sept.): 3–20.
Kogut, J., and Susskind, L. 1975. Hamiltonian formulation of Wilson's lattice gauge theories. Phys. Rev., D11: 395–408.
Lawson, C.L., Hanson, R.J., Kincaid, D.R., and Krogh, F.T. 1979. Basic linear algebra subprograms for Fortran usage. ACM TOMS, 5, 3 (Sept.): 308–323.
Linn, M.A., Nagel, W.E., Vaessen, M., and Detert, U. 1991. UNICOS 5.1 vs. UNICOS 6.0: Performance evaluation of autotasking. In Proc.—Cray User Group Fall Meeting (Santa Fe, Sept. 23–27), pp. 321–330.
Merchant, M., Carney, S., Heroux, M., Sheikh, O., and Yang, C.W. 1990. Parallel processing in the math and science library. In Proc.—Cray User Group Fall Meeting (Austin, Oct. 1–5), pp. 392–402.
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., and Teller, E. 1953. Equation of state calculation by fast computing machines. J. Chem. Phys., 21: 1087–1095.
NAG. 1988. NAG Library Manual Mark 13, Vol. 5. NAG, Oxford.
Nagel, W.E., and Szelényi, F. 1989. Multitasking on supercomputers: Concepts and experiences. IBM Tech. Rept. ICE-VS05, IBM ECSEC, Rome.
Negele, J.W., and Orland, H. 1988. Quantum many-particle systems. In Frontiers in Physics, vol. 68. Addison-Wesley, Reading, Mass.
Polychronopoulos, C.D. 1988. Toward auto-scheduling compilers. The J. Supercomputing, 2, 3 (Nov): 297–330.
Polychronopoulos, C.D., and Kuck, D.J. 1987. Guided self-scheduling: A practical scheduling scheme for parallel supercomputers. IEEE Trans. Comput., C-36, 12 (Dec.): 1425–1439.
Reger, H. 1989. Ein Vergleich der Multitasking—Implementierungen auf CRAY X-MP und IBM 3090. Jül-Spez-542, Kernforschungsanlage Jülieh.
Serot, B.D., and Walecka, J.D. 1986. The relativistic nuclear many-body problem. In Adv. in Nuclear Physics, vol. 16, (J.W. Negele and E. Vogt, eds.), Plenum Press, New York.
Walecka, J.D. 1974. A theory of highly condensed matter. Ann. Phys., 83: 491–529.
Wilson, K.G. 1974. Confinement of quarks. Phys. Rev., D10: 2445–2459.
Wilson, K.G. 1977. Quarks and strings on a lattice. In New Phenomena in Subnuclear Physics, Part A. (A. Zichichi, ed.), Plenum Press, New York.
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Frank, J., Knecht, S. Lattice quantum hadrodynamics on a CRAY Y-MP. J Supercomput 6, 195–209 (1992). https://doi.org/10.1007/BF00155799
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DOI: https://doi.org/10.1007/BF00155799