A Numerical Implementation Of The Dirac Equation On A Hypercube Multicomputer

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.