An important factor in determining the accuracy of the wavefunction
obtained by variance minimisation is the size of the ensemble of
independent configurations used in the optimisation procedure,
Eq.(
). During this work large ensembles of up to 100,000
configurations have been used. Each of these ensembles contained 64
electrons and had 20-40 parameters associated with it. The CPU and
memory requirements for these problems are such that the advantages of
using a parallel computer are considerable.
Therefore a parallel version of the variance minimisation procedure
was developed using the ``master-slave'' programming model where one
processor, the ``master'', delegates work to the other processors, the
``slaves''. The master processor sends work to the slaves who complete
the required work and return the results back to the master. The
numerical optimisation routine runs on the master processor and the
ensemble of configurations is divided out among the slaves. The
master processor broadcasts the values of the variational parameters
to the slaves. Each of the slaves evaluates the reweighting factors,
, and the contributions to the variance (see
Eq.() and Figure ) for its subset of
configurations. These are returned to the master which, via the NAG\
minimisation routine, determines new values for the variational
parameters. The procedure is repeated until the imposed limit on the
change in the values of the parameters is reached, or until a minimum
in the variance is found.
Figure: Variance minimisation on a
parallel machine using the ``master-slave'' programming model. The
master processor runs the numerical optimisation routine and farms out
the evaluation of the variance of each configuration to the slave
processors.