Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Matthias Wiesenberger*, Lukas Einkemmer, Markus Held, Albert Gutierrez-Milla, Xavier Saez, Roman Iakymchuk

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two- and three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique. We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how were store accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of ourroutines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak).
Original languageEnglish
JournalComputer Physics Communications
Volume238
Pages (from-to)145-156
Number of pages12
ISSN0010-4655
DOIs
Publication statusPublished - 2019

Keywords

  • Feltor
  • Reproducibility
  • Performance
  • High-performance computing
  • Xeon Phi
  • GPU

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