The study of data-parallel domain re-organization and thread-mapping techniques
are relevant topics as they can increase the efficiency of GPU computations on
spatial discrete domains with non-box-shaped geometry. In this work we study
the potential benefits of applying a succinct data re-organization of a
tetrahedral data-parallel domain of size O(n^3) combined with an efficient
block-space GPU map of the form g(l) : N -> N^3. Results from the analysis
suggest that in theory the combination of these two optimizations produce
significant performance improvement as block-based data reorganization allows a
coalesced one-to-one correspondence at local thread-space while g(l) produces
an efficient block-space spatial correspondence between groups of data and
groups of threads, reducing the number of unnecessary threads from O(n^3) to
O(n^2 * r^3) with r in O(1). From the analysis, we obtained that a block based
succinct data re-organization can provide up to 2x improved performance over a
linear data organization while the map can be up to 6x more efficient than a
bounding box approach. The results from this work can serve as a useful guide
for a more efficient GPU computation on tetrahedral domains found in spin
lattice, finite element and special n-body problems, among others.