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Computer Science > Mathematical Software

arXiv:2308.13615 (cs)
[Submitted on 24 Aug 2023]

Title:Alternative quadrant representations with Morton index and AVX2 vectorization for AMR algorithms within the p4est software library

Authors:Mikhail Kirilin (1), Carsten Burstedde (1) ((1) INS, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany)
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Abstract:We present a technical enhancement within the p4est software for parallel adaptive mesh refinement. In p4est primitives are stored as octants in three and quadrants in two dimensions. While, classically, they are encoded by the native approach using its spatial and refinement level, any other mathematically equivalent encoding might be used instead.
Recognizing this, we add two alternative representations to the classical, explicit version, based on a long monotonic index and 128-bit AVX quad integers, respectively. The first one requires changes in logic for low-level quadrant manipulating algorithms, while the other exploits data level parallelism and requires algorithms to be adapted to SIMD instructions. The resultant algorithms and data structures lead to higher performance and lesser memory usage in comparison with the standard baseline.
We benchmark selected algorithms on a cluster with two Intel(R) Xeon(R) Gold 6130 Skylake family CPUs per node, which provides support for AVX2 extensions, 192 GB RAM per node, and up to 512 computational cores in total.
Comments: 10 pages, 7 figures and 12 algorithms, submitted to Proceedings of the 2024 SIAM Conference on Parallel Processing for Scientific Computing (PP). For reprodusing results use branches this https URL and this https URL and executable build_dir>/example/timings/p8est3_p3time
Subjects: Mathematical Software (cs.MS)
ACM classes: G.4; I.6.8; E.2
Cite as: arXiv:2308.13615 [cs.MS]
  (or arXiv:2308.13615v1 [cs.MS] for this version)
  https://doi.org/10.48550/arXiv.2308.13615

Submission history

From: Mikhail Kirilin [view email]
[v1] Thu, 24 Aug 2023 14:05:05 UTC (107 KB)
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