Rafael Diez Sanhueza, Jurriaan Peeters, Pedro Costa
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Our results confirm that, while 1D domain decompositions are favorable for smaller systems, they become inefficient or even impossible at large scales. This restriction is relaxed by adopting a pencil-distributed approach. The results show that, at scale, the revised Poisson solver is about twice as fast as the baseline approach with the full-transpose algorithm for 2D domain decompositions. Strong and weak scalability tests show that the performance gains are due to the lower communication footprint. Additionally, to secure high performance when solving for wall-normal implicit diffusion, we propose a reworked flavor of parallel cyclic reduction (PCR) that is split into pre-processing and runtime steps. During pre-processing, small sub-arrays with independent 1D coefficients are computed by parallel GPU threads, without any global GPU communication. Then, at runtime, the reworked PCR enables a fast solution of implicit 1D diffusion without computational overhead. Our results show that the entire numerical solver, coupled with the PCR algorithm, enables extreme-scale simulations with 2D pencil decompositions, which do not suffer performance losses even when compared to the best 1D slab configurations available for smaller systems.</div></div>","PeriodicalId":285,"journal":{"name":"Computer Physics Communications","volume":"316 ","pages":"Article 109811"},"PeriodicalIF":3.4000,"publicationDate":"2025-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A pencil-distributed finite-difference solver for extreme-scale calculations of turbulent wall flows at high Reynolds number\",\"authors\":\"Rafael Diez Sanhueza, Jurriaan Peeters, Pedro Costa\",\"doi\":\"10.1016/j.cpc.2025.109811\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz equations using a pencil-distributed parallel tridiagonal solver to improve computational performance at scale. The benefits of this approach were investigated for high-Reynolds-number turbulent channel flow simulations, with up to about 80 billion grid points and 1024 GPUs on the European flagship supercomputers Leonardo and LUMI. An additional GPU porting effort of the entire solver had to be undertaken for the latter. Our results confirm that, while 1D domain decompositions are favorable for smaller systems, they become inefficient or even impossible at large scales. This restriction is relaxed by adopting a pencil-distributed approach. The results show that, at scale, the revised Poisson solver is about twice as fast as the baseline approach with the full-transpose algorithm for 2D domain decompositions. Strong and weak scalability tests show that the performance gains are due to the lower communication footprint. Additionally, to secure high performance when solving for wall-normal implicit diffusion, we propose a reworked flavor of parallel cyclic reduction (PCR) that is split into pre-processing and runtime steps. During pre-processing, small sub-arrays with independent 1D coefficients are computed by parallel GPU threads, without any global GPU communication. Then, at runtime, the reworked PCR enables a fast solution of implicit 1D diffusion without computational overhead. 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A pencil-distributed finite-difference solver for extreme-scale calculations of turbulent wall flows at high Reynolds number
We present a computational method for extreme-scale simulations of incompressible turbulent wall flows at high Reynolds numbers. The numerical algorithm extends a popular method for solving second-order finite differences Poisson/Helmholtz equations using a pencil-distributed parallel tridiagonal solver to improve computational performance at scale. The benefits of this approach were investigated for high-Reynolds-number turbulent channel flow simulations, with up to about 80 billion grid points and 1024 GPUs on the European flagship supercomputers Leonardo and LUMI. An additional GPU porting effort of the entire solver had to be undertaken for the latter. Our results confirm that, while 1D domain decompositions are favorable for smaller systems, they become inefficient or even impossible at large scales. This restriction is relaxed by adopting a pencil-distributed approach. The results show that, at scale, the revised Poisson solver is about twice as fast as the baseline approach with the full-transpose algorithm for 2D domain decompositions. Strong and weak scalability tests show that the performance gains are due to the lower communication footprint. Additionally, to secure high performance when solving for wall-normal implicit diffusion, we propose a reworked flavor of parallel cyclic reduction (PCR) that is split into pre-processing and runtime steps. During pre-processing, small sub-arrays with independent 1D coefficients are computed by parallel GPU threads, without any global GPU communication. Then, at runtime, the reworked PCR enables a fast solution of implicit 1D diffusion without computational overhead. Our results show that the entire numerical solver, coupled with the PCR algorithm, enables extreme-scale simulations with 2D pencil decompositions, which do not suffer performance losses even when compared to the best 1D slab configurations available for smaller systems.
期刊介绍:
The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper.
Computer Programs in Physics (CPiP)
These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged.
Computational Physics Papers (CP)
These are research papers in, but are not limited to, the following themes across computational physics and related disciplines.
mathematical and numerical methods and algorithms;
computational models including those associated with the design, control and analysis of experiments; and
algebraic computation.
Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.