Modern HPC architecture combines the use of CPUs with accelerators to obtained better performance and shorter time-to-solution. But in most cases, accelerators such as GPUs or NPUs benefit from low precision computations, to obtain faster arithmetic, and also reduce the overall memory footprint by reducing the total amount of data to be stored. In order to effectively offload as much of the computational workload to low-precision devices, it is important to use an algorithm that would ensure convergence of the final results to a level of accuracy that is acceptable by the user. Mixed-precision algorithms allow for recovery of high precision arithmetic while offloading most of the computation to low-precision arithmetic. Most available mixed-precision algorithm are based on iterative refinement approaches in which a correction is computed and added to the latest estimate of the solution in an iterative manner. In this study, we propose a defect correction approach that allows for recovery of high precision accuracy for linear and non-linear iterative solvers. The results are tested using an in-house solver, and then implemented within the OpenFOAM solver using the Ginkgo library. Current results are showing up to 40% acceleration while recovering accuracy close to double precision computation.

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A Novel Mixed Precision Defect Correction Solver for Heterogeneous Computing

  • Yann T. Delorme,
  • Mark Wasserman,
  • Alon Zameret,
  • Zhaohui Ding

摘要

Modern HPC architecture combines the use of CPUs with accelerators to obtained better performance and shorter time-to-solution. But in most cases, accelerators such as GPUs or NPUs benefit from low precision computations, to obtain faster arithmetic, and also reduce the overall memory footprint by reducing the total amount of data to be stored. In order to effectively offload as much of the computational workload to low-precision devices, it is important to use an algorithm that would ensure convergence of the final results to a level of accuracy that is acceptable by the user. Mixed-precision algorithms allow for recovery of high precision arithmetic while offloading most of the computation to low-precision arithmetic. Most available mixed-precision algorithm are based on iterative refinement approaches in which a correction is computed and added to the latest estimate of the solution in an iterative manner. In this study, we propose a defect correction approach that allows for recovery of high precision accuracy for linear and non-linear iterative solvers. The results are tested using an in-house solver, and then implemented within the OpenFOAM solver using the Ginkgo library. Current results are showing up to 40% acceleration while recovering accuracy close to double precision computation.