A NUMERICAL IMPLEMENTATION OF THE DIRAC EQUATION ON A HYPERCUBE MULTICOMPUTER

J. C. Wells, A. S. Umar, V. E. Oberacker, C. Bottcher, M. R. Strayer, J.-S. Wu, J. Drake and R. Flanery
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J. C. Wells: Center for Computationally Intensive Physics, Oak Ridge National Laboratory Oak Ridge, TN 37831, USA;
A. S. Umar: Center for Computationally Intensive Physics, Oak Ridge National Laboratory Oak Ridge, TN 37831, USA;
V. E. Oberacker: Center for Computationally Intensive Physics, Oak Ridge National Laboratory Oak Ridge, TN 37831, USA;
C. Bottcher: Center for Computationally Intensive Physics, Oak Ridge National Loboratory Oak Ridge, TN 37831, USA;
M. R. Strayer: Center for Computationally Intensive Physics, Oak Ridge National Loboratory Oak Ridge, TN 37831, USA;
J.-S. Wu: Center for Computationally Intensive Physics, Oak Ridge National Loboratory Oak Ridge, TN 37831, USA;
J. Drake: Engineering Physics and Mathematics Division, Oak Ridge National Laboratory Oak Ridge, TN 37831, USA
R. Flanery: Engineering Physics and Mathematics Division, Oak Ridge National Laboratory Oak Ridge, TN 37831, USA

International Journal of Modern Physics C (IJMPC), 1993, vol. 04, issue 03, 459-492

Abstract: We describe the numerical methods used to solve the time-dependent Dirac equation on a three-dimensional Cartesian lattice. Efficient algorithms are required for computationally intensive studies of nonperturbative electromagnetic lepton-pair production in relativistic heavy-ion collisions. Discretization is achieved through the lattice basis-spline collocation method, in which quantum-state vectors and coordinate-space operators are expressed in terms of basis-spline functions on a spatial lattice. For relativistic lepton fields on a lattice, the fermion-doubling problem is central in the formulation of the numerical method. All numerical procedures reduce to a series of matrix-vector operations which we perform on the Intel iPSC/860 hypercube, making full use of parallelism. We discuss solutions to the problems of limited node memory and node-to-node communication overhead inherent in using distributed-memory, multiple-instruction, multiple-data stream parallel computers.

Keywords: Dirac Equation; Basis-spline Collocation Method; Massively Parallel Computing (search for similar items in EconPapers)
Date: 1993
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DOI: 10.1142/S0129183193000501

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