Abstract
An effective hybrid Monte Carlo--deterministic implementation typically requires
the approximation of a continuous geometry description with a discretized
piecewise-constant material field. The inherent geometry discretization error
can be reduced somewhat by using material mixing, where multiple materials
inside a discrete mesh voxel are homogenized. Material mixing
requires the construction of a ``mix table,'' which stores the volume fractions
in every mixture so that multiple voxels with similar compositions can reference
the same mixture.
Mix table construction is a potentially expensive serial operation for large
problems with many materials and voxels. We formulate an efficient algorithm to
construct a sparse mix table in $O(\text{number of voxels}\times
\log \text{number of mixtures})$ time.
The new algorithm is implemented in ADVANTG and used to discretize continuous
geometries onto a structured Cartesian grid.
When applied to an end-of-life MCNP model of the High Flux Isotope Reactor
with 270 distinct materials, the new method improves the material mixing time by
a factor of 100 compared to a naive mix table implementation.
