{"paper":{"title":"Exploiting repeated matrix block structures for more efficient CFD on modern supercomputers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"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.","cross_cats":["physics.comp-ph"],"primary_cat":"physics.flu-dyn","authors_text":"\\`Adel Alsalti-Baldellou, Assensi Oliva, F.Xavier Trias, Guillem Colomer, Josep Plana-Riu, Xavier \\'Alvarez-Farr\\'e","submitted_at":"2025-08-08T21:26:12Z","abstract_excerpt":"Computational Fluid Dynamics (CFD) simulations are often constrained by the memory-bound nature of sparse matrix-vector operations, which eventually limits performance on modern high-performance computing (HPC) systems. This work introduces a novel approach to increase arithmetic intensity in CFD by leveraging repeated matrix block structures. The method transforms the conventional sparse matrix-vector product (SpMV) into a sparse matrix-matrix product (SpMM), enabling simultaneous processing of multiple right-hand sides. This shifts the computation towards a more compute-bound regime by reusi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"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.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"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.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"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.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"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.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"775a14edbcaf44f42e686282b473e96287c29872fb3af604605b3a8116961748"},"source":{"id":"2508.06710","kind":"arxiv","version":5},"verdict":{"id":"3bd4bd96-e9ce-4350-ac78-6218f2edaf77","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-18T23:34:00.023731Z","strongest_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.","one_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.","pipeline_version":"pith-pipeline@v0.9.0","weakest_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.","pith_extraction_headline":"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."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.06710/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":35,"sample":[{"doi":"10.1145/1498765.1498785","year":2009,"title":"Roofline: An in- sightful visual performance model for multicore architectures","work_id":"d53b4029-f7d9-4dfb-83f0-f5d116d39ce1","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1109/sc.2014.68","year":2015,"title":"Greathouse and Mayank Daga","work_id":"8575b31f-dad2-44b8-b9c6-9b6f8b444ad6","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.cpc.2017.05.023","year":2017,"title":"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","work_id":"3cfdfc61-fa98-4dbf-8c41-e012ba7542fa","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1103/physrevfluids.2.094606","year":2017,"title":"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","work_id":"d0ddc4c3-d6c1-4f7a-8eae-ffa92577d469","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1016/j.jweia.2022.105105","year":2022,"title":"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","work_id":"e9a9d227-266d-4b27-bc87-0123bb4f72e4","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":35,"snapshot_sha256":"3ae54e7ca6510cbac0a1921fce818be6aa28c3dd2513859dfb881cdc2c839970","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"1b86867efec460674db0446c035b5b964cd43baa756e914ae82b598e44874ffd"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}