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

Abstract

The study of data-parallel domain re-organization and thread-mapping techniques are relevant topics as they can increase the efficiency of GPU computations when working on spatial discrete domains with non-box-shaped geometry. In this work we study the potential benefits of applying a succint 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 ) where ρ is the linear block-size and typically ρ 3 ≪ n. From the analysis, we obtained that a block based succint 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.

Squeeze: Efficient Compact Fractals for Tensor Core GPUs

“…Navarro et al [11,12,13] proposed a GPU block-space mapping for 2 and 3-simplex domains based on a linear numbering of discrete elements. Authors report an empirical speedup of up to 1.5× and 2.3× over a bounding-box approach, for 2 and 3-simplices, respectively.…”

“…Thanks to the 40GB of GPU memory of the A100, it was possible to push the maximum problem size up to 2 16 , except for the curve of S 1x1 that could not reach the maximum size because of CUDA's grid size limits. The TITAN RTX under-performed in comparison with the other GPUs for n ≤ 2 12 . Past that value, speedup increases above 1 for all values of ρ, reaching a top speedup of ∼ 3.2×.…”

Accelerating Compact Fractals with Tensor Core GPUs

“…Ries et al [15] developed in 2009 a method to compute the inverse of triangular matrices by developing a recursive parallel space mapping from a compact rectangular domain using GPU. Navarro et al proposed in 2014 a GPU block-space mapping for 2-simplex and 3-simplex shaped data [9,8,10]. Navarro et al [7,11] expanded the idea of GPU thread mapping for fractal domains, by proposing the λ(ω) map for NBB fractals.…”

“…Here, n ∈ N is the linear size of the fractal along one axis, k ∈ N the number of self-similar replicas to generate for the next scale level and s ∈ N the growth ratio of n in the next scale level, along an axis. For example, the Sierpiński Carpet (Figure 1) is F 8,3 n and the Sierpiński Triangle (Figure 2) is F 3,2 n . Many different NBB fractals can be described using the same parameters.…”