Exploiting repeated matrix block structures for more efficient CFD on modern supercomputers
Fuente:
arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
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| _version_ | 1866913155965255680 |
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| author | Plana-Riu, Josep Trias, F. Xavier Alsalti-Baldellou, Àdel Álvarez-Farré, Xavier Colomer, Guillem Oliva, Assensi |
| author_facet | Plana-Riu, Josep Trias, F. Xavier Alsalti-Baldellou, Àdel Álvarez-Farré, Xavier Colomer, Guillem Oliva, Assensi |
| contents | 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 reusing matrix coefficients. Additionally, an inline mesh-refinement strategy is proposed: simulations initially run on a coarse mesh to establish a statistically steady flow, then refine to the target mesh. This reduces the wall-clock time to reach transition, leading to faster convergence with equivalent computational cost. The methodology is evaluated using theoretical performance bounds and validated through three test cases: a turbulent channel flow, Rayleigh-Bénard convection, and an industrial airfoil simulation. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06710 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exploiting repeated matrix block structures for more efficient CFD on modern supercomputers Plana-Riu, Josep Trias, F. Xavier Alsalti-Baldellou, Àdel Álvarez-Farré, Xavier Colomer, Guillem Oliva, Assensi Fluid Dynamics Computational Physics 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 reusing matrix coefficients. Additionally, an inline mesh-refinement strategy is proposed: simulations initially run on a coarse mesh to establish a statistically steady flow, then refine to the target mesh. This reduces the wall-clock time to reach transition, leading to faster convergence with equivalent computational cost. The methodology is evaluated using theoretical performance bounds and validated through three test cases: a turbulent channel flow, Rayleigh-Bénard convection, and an industrial airfoil simulation. 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. |
| title | Exploiting repeated matrix block structures for more efficient CFD on modern supercomputers |
| topic | Fluid Dynamics Computational Physics |
| url | https://arxiv.org/abs/2508.06710 |