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Main Authors: Plana-Riu, Josep, Trias, F. Xavier, Alsalti-Baldellou, Àdel, Álvarez-Farré, Xavier, Colomer, Guillem, Oliva, Assensi
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2508.06710
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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