arXiv subjects

Xavier Álvarez-Farré

Publications and source records attributed to Xavier Álvarez-Farré.

4 recordsLinked to original sources

arXiv2026

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

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.

physics.flu-dyn↗

arXiv2025

An efficient eigenvalue bounding method: CFL condition revisited

Direct and large-eddy simulations of turbulence are often solved using explicit temporal schemes. However, this imposes very small time-steps because the eigenvalues of the (linearized) dynamical system, re-scaled by the time-step, must lie inside the stability region. In practice, fast and accurate estimations of the spectral radii of both the discrete convective and diffusive terms are therefore needed. This is virtually always done using the so-called CFL condition. On the other hand, the large heterogeneity and complexity of modern supercomputing systems are nowadays hindering the efficient cross-platform portability of CFD codes. In this regard, our leitmotiv reads: relying on a minimal set of (algebraic) kernels is crucial for code portability and maintenance! In this context, this work focuses on the computation of eigenbounds for the above-mentioned convective and diffusive matrices which are needed to determine the time-step à la CFL. To do so, a new inexpensive method, that does not require to re-construct these time-dependent matrices, is proposed and tested. It just relies on a sparse-matrix vector product where only vectors change on time. Hence, both implementation in existing codes and cross-platform portability are straightforward. The effectiveness and robustness of the method are demonstrated for different test cases on both structured Cartesian and unstructured meshes. Finally, the method is combined with a self-adaptive temporal scheme, leading to significantly larger time-steps compared with other more conventional CFL-based approaches.

physics.flu-dyn↗

arXiv2024

A multigrid reduction framework for domains with symmetries

Divergence constraints are present in the governing equations of numerous physical phenomena, and they usually lead to a Poisson equation whose solution represents a bottleneck in many simulation codes. Algebraic Multigrid (AMG) is arguably the most powerful preconditioner for Poisson's equation, and its effectiveness results from the complementary roles played by the smoother, responsible for damping high-frequency error components, and the coarse-grid correction, which in turn reduces low-frequency modes. This work presents several strategies to make AMG more compute-intensive by leveraging reflection, translational and rotational symmetries. AMGR, our final proposal, does not require boundary conditions to be symmetric, therefore applying to a broad range of academic and industrial configurations. It is based on a multigrid reduction framework that introduces an aggressive coarsening to the multigrid hierarchy, reducing the memory footprint, setup and application costs of the top-level smoother. While preserving AMG's excellent convergence, AMGR allows replacing the standard sparse matrix-vector product with the more compute-intensive sparse matrix-matrix product, yielding significant accelerations. Numerical experiments on industrial CFD applications demonstrated up to 70% speed-ups when solving Poisson's equation with AMGR instead of AMG. Additionally, strong and weak scalability analyses revealed no significant degradation.

math.NA↗

arXiv2021

On the implementation of flux limiters in algebraic frameworks

The use of flux limiters is widespread within the scientific computing community to capture shock discontinuities and are of paramount importance for the temporal integration of high-speed aerodynamics, multiphase flows, and hyperbolic equations in general. Meanwhile, the breakthrough of new computing architectures and the hybridization of supercomputer systems pose a huge portability challenge, particularly for legacy codes, since the computing subroutines that form the algorithms, the so-called kernels, must be adapted to various complex parallel programming paradigms. From this perspective, the development of innovative implementations relying on a minimalist set of kernels simplifies the deployment of scientific computing software on state-of-the-art supercomputers, while it requires the reformulation of algorithms, such as the aforementioned flux limiters. Equipped with basic algebraic topology and graph theory underlying the classical mesh concept, a new flux limiter formulation is presented based on the adoption of algebraic data structures and kernels. As a result, traditional flux limiters are cast into a stream of only two types of computing kernels: sparse matrix-vector multiplication and generalized pointwise binary operators. The newly proposed formulation eases the deployment of such a numerical technique in massively parallel, potentially hybrid, computing systems and is demonstrated for a canonical advection problem.

physics.comp-ph↗