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Efficient High-Order Discontinuous Galerkin Finite Elements with Matrix-Free Implementations

In: Advances and New Trends in Environmental Informatics

Author

Listed:
  • Martin Kronbichler

    (Technical University of Munich)

  • Momme Allalen

    (Leibniz-Rechenzentrum der Bayerischen Akademie der Wissenschaften)

Abstract

This work presents high-order discontinuous Galerkin finite element kernels optimized for node-level performance on a series of Intel architectures ranging from Sandy Bridge to Skylake. The kernels implement matrix-free evaluation of integrals with sum factorization techniques. In order to increase performance and thus to help to achieve higher energy efficiency, this work proposes an element-based shared-memory parallelization option and compares it to a well-established shared-memory parallelization with global face data. The new algorithm is supported by the relevant metrics in terms of arithmetics and memory transfer. On a single node with $$2\times 24$$ 2 × 24 cores of Intel Skylake Scalable, we report more than 1,200 GFLOPs/s in double precision for the full operator evaluation and up to 175 GB/s of memory throughput. Finally, we also show that merging the more arithmetically heavy operator evaluation with vector operations in application code allows to more than double efficiency on the latest hardware both with respect to energy as well as regarding time to solution.

Suggested Citation

  • Martin Kronbichler & Momme Allalen, 2018. "Efficient High-Order Discontinuous Galerkin Finite Elements with Matrix-Free Implementations," Progress in IS, in: Hans-Joachim Bungartz & Dieter Kranzlmüller & Volker Weinberg & Jens Weismüller & Volker Wohlgemuth (ed.), Advances and New Trends in Environmental Informatics, pages 89-110, Springer.
    • Handle: RePEc:spr:prochp:978-3-319-99654-7_7
    DOI: 10.1007/978-3-319-99654-7_7
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