Potential benefits of a block-space GPU approach for discrete tetrahedral domains

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 (λ) : 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(λ) 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
ρ
³
) with ρ ∊ O(1). From the analysis, we obtained that a block based succinct data re-organization can provide up to 2× improved performance over a linear data organization while the map can be up to 6× 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.