P. Valin et al., TOPOLOGY DEPENDENCE IN LATTICE SIMULATIONS OF NONLINEAR PDES ON A MIMD COMPUTER, International journal of modern physics C, 5(6), 1994, pp. 957-971
We tested the parallelization of explicit schemes for the solution of
non-linear classical field theories of complex scalar fields which are
capable of simulating; hadronic collisions. Our attention focused on
collisions in a fractional model with a particularly rich inelastic sp
ectrum of final states. Relativistic collisions of all types were perf
ormed by computer on large lattices (64 to 256 sites per dimension). T
he stability and accuracy of the objects were tested by the use of two
other methods of solutions: Pseudo-spectral and semi-implicit. Parall
elization of the Fortran code on a 64-transputer MIMD Volvox machine r
evealed, for certain topologies, communication deadlock and less-than-
optimum routing strategies when the number of transputers used was les
s than the maximum. The observed speedup, for N transputers in an appr
opriate topology, is shown to scale approximately as N, but the overal
l gain in execution speed, for physically interesting problems, is a m
odest 2-3 when compared to state-of-the-art workstations.