Pith Number

pith:BKLQD5BG

pith:2025:BKLQD5BGJPHM33RLRICXXKX4YV

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Exploiting repeated matrix block structures for more efficient CFD on modern supercomputers

\`Adel Alsalti-Baldellou, Assensi Oliva, F.Xavier Trias, Guillem Colomer, Josep Plana-Riu, Xavier \'Alvarez-Farr\'e

By grouping repeated matrix blocks, CFD codes can replace sparse matrix-vector multiplies with matrix-matrix multiplies to raise arithmetic intensity and cut run times.

arxiv:2508.06710 v5 · 2025-08-08 · physics.flu-dyn · physics.comp-ph

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Claims

C1strongest claim

Results demonstrate substantial speed-ups - from modest improvements in basic configurations to over 50% in the mesh-refinement setup - highlighting the benefits of integrating SpMM across all CFD operators, including divergence, gradient, and Laplacian.

C2weakest assumption

The method assumes that the discrete operators in the target CFD codes contain enough identical matrix blocks for the SpMM reformulation to deliver measurable arithmetic-intensity gains, and that switching from coarse to fine mesh mid-simulation does not alter the statistically steady statistics or introduce unacceptable transient errors.

C3one line summary

Exploiting repeated block structures converts SpMV to SpMM in CFD operators while an inline coarse-to-fine mesh strategy reduces time to statistically steady state, producing speed-ups up to over 50 percent on tested cases.

References

35 extracted · 35 resolved · 0 Pith anchors

[1] Roofline: An in- sightful visual performance model for multicore architectures 2009 · doi:10.1145/1498765.1498785

[2] Greathouse and Mayank Daga 2015 · doi:10.1109/sc.2014.68

[3] V . Makarashvili, E. Merzari, A. Obabko, A. Siegel, P. Fischer, A performance analysis of ensemble averaging for high fidelity turbulence simulations at the strong scaling limit, Computer Physics Comm 2017 · doi:10.1016/j.cpc.2017.05.023

[4] G. Nastac, J. W. Labahn, L. Magri, M. Ihme, Lyapunov exponent as a metric for assessing the dynamic content and predictability of large-eddy simulations, Physical Review Fluids 2 (2017). doi:10.1103/P 2017 · doi:10.1103/physrevfluids.2.094606

[5] R. Tosi, M. Núñez, J. Pons-Prats, J. Principe, R. Rossi, On the use of ensemble averaging techniques to accelerate the Uncer- tainty Quantification of CFD predictions in wind engineering, Journal of W 2022 · doi:10.1016/j.jweia.2022.105105

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Receipt and verification

First computed	2026-05-25T02:02:08.212161Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0a9701f4264bcecdee2b8a057baafcc54924d9f844e4f9f7417bb426cd1e2916

Aliases

arxiv: 2508.06710 · arxiv_version: 2508.06710v5 · doi: 10.48550/arxiv.2508.06710 · pith_short_12: BKLQD5BGJPHM · pith_short_16: BKLQD5BGJPHM33RL · pith_short_8: BKLQD5BG

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BKLQD5BGJPHM33RLRICXXKX4YV \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 0a9701f4264bcecdee2b8a057baafcc54924d9f844e4f9f7417bb426cd1e2916

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c00574fd9425155312c30c6b9afa2a3937a3e3257bad59095ac8fa6369d2be00",
    "cross_cats_sorted": [
      "physics.comp-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.flu-dyn",
    "submitted_at": "2025-08-08T21:26:12Z",
    "title_canon_sha256": "85a120e1f07fb06e05426fa11abccd3a6650107199167cccae316fc385fde9ae"
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  "source": {
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