  In this paper we show the extension of the Nonlinear-Diffusion Acceleration
(NDA) to geometries containing small voids using a weighted least-squares (WLS)
high order equation. Even though the WLS equation is well defined in voids, the
low-order drift diffusion equation was not defined in materials with a zero
cross section.
  This paper derives the necessary modifications to the NDA algorithm. We show
that a small change to the NDA closure term and a non-local definition of the
diffusion coefficient solve the problems for voids regions. These changes do
not affect the algorithm for optical thick material regions, while making the
algorithm well defined in optically thin ones. We use a Fourier analysis to
perform an iterative analysis to confirm that the modifications result in a
stable and efficient algorithm.
  Numerical results of our method will be presented in the second part of the
paper. We test this formulation with a small, one-dimensional test problem.
Additionally we present results for a modified version of the C5G7 benchmark
containing voids as a more complex, reactor like problem. We compared our
results to PDT, Texas A\&M's transport code, utilizing a first order
discontinuous formulation as reference and the self-adjoint angular flux
equation with void treatment (SAAFt), a different second order form. The
results indicate, that the NDA WLS performed comparably or slightly worse then
the asymmetric SAAFt, while maintaining a symmetric discretization matrix.
