Reproducibility strategies for parallel Preconditioned Conjugate Gradient

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:371

Article

Iakymchuk, Roman^1,2  Barreda, Maria³  Wiesenberger, Matthias⁴  Aliaga, Jose I.³  Quintana-Orti, Enrique S.⁵ 

[1] Fraunhofer ITWM, Kaiserslautern, Germany

[2] Sorbonne Univ, Paris, France

[3] Univ Jaime I, Castellon de La Plana, Castello, Spain

[4] Tech Univ Denmark, Lyngby, Denmark

[5] Univ Politecn Valencia, Valencia, Spain

关键词: Reproducibility;    Accuracy;    Floating-point expansion;    Long accumulator;    Preconditioned Conjugate Gradient;    High-Performance Computing;   

DOI  :  10.1016/j.cam.2019.112697

来源: Elsevier

【 摘 要 】

The Preconditioned Conjugate Gradient method is often used in numerical simulations. While being widely used, the solver is also known for its lack of accuracy while computing the residual. In this article, we aim at a twofold goal: enhance the accuracy of the solver but also ensure its reproducibility in a message-passing implementation. We design and employ various strategies starting from the ExBLAS approach (through preserving every bit of information until final rounding) to its more lightweight performance-oriented variant (through expanding the intermediate precision). These algorithmic strategies are reinforced with programmability suggestions to assure deterministic executions. Finally, we verify these strategies on modern HPC systems: both versions deliver reproducible number of iterations, residuals, direct errors, and vector-solutions for the overhead of only 29% (ExBLAS) and 4% (lightweight) on 768 processes. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free