  The method of discrete ordinates ($S_N$) is a popular choice for the solution
of the neutron transport equation. It is however well known that it suffers
from slow convergence of the scattering source in optically thick and diffusive
media, such as pressurized water nuclear reactors (PWR). In reactor physics
applications, the $S_N$ method is thus often accompanied by an acceleration
algorithm, such as the Diffusion Synthetic Acceleration (DSA). With the recent
increase in computational power, whole core transport calculations have become
a reasonable objective. It however requires using large computers and
parallelizing the transport solver. Due to the elliptic nature of the DSA
operator, its parallelization is not straightforward. In this paper, we present
an acceleration operator derived from the DSA, but defined in a piecewise way
such that its parallel implementation is straightforward. We show that, for
optically thick enough media, this Piecewise Diffusion Synthetic Acceleration
(PDSA) preserves the good properties of the DSA. This conclusion is supported
by numerical experiments.
