Automatic code generation for high-performance Discontinuous Galerkin methods on modern architectures

• Verfasst von: Kempf, Dominic [VerfasserIn]
• Verfasst von: Heß, René [VerfasserIn]
• Verfasst von: Müthing, Steffen [VerfasserIn]
• Verfasst von: Bastian, Peter [VerfasserIn]
• Titel: Automatic code generation for high-performance Discontinuous Galerkin methods on modern architectures
• Verf.angabe: Dominic Kempf, René Heß, Steffen Müthing, and Peter Bastian
• E-Jahr: 2020
• Jahr: December 2020
• Umfang: 31 S.
• Fussnoten: Gesehen am 13.02.2022
• Titel Quelle: Enthalten in: Association for Computing MachineryACM transactions on mathematical software
• Ort Quelle: New York, NY : ACM, 1975
• Jahr Quelle: 2020
• Band/Heft Quelle: 47(2020), 1, Artikel-ID 6, Seite 1-31
• ISSN Quelle: 1557-7295
• DOI: doi:10.1145/3424144
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Code generation
• Sach-SW: Galerkin methods
• K10plus-PPN: 1789487293

Abstract

SIMD vectorization has lately become a key challenge in high-performance computing. However, hand-written explicitly vectorized code often poses a threat to the software’s sustainability. In this publication, we solve this sustainability and performance portability issue by enriching the simulation framework dune-pdelab with a code generation approach. The approach is based on the well-known domain-specific language UFL but combines it with loopy, a more powerful intermediate representation for the computational kernel. Given this flexible tool, we present and implement a new class of vectorization strategies for the assembly of Discontinuous Galerkin methods on hexahedral meshes exploiting the finite element’s tensor product structure. The performance-optimal variant from this class is chosen by the code generator through an auto-tuning approach. The implementation is done within the open source PDE software framework Dune and the discretization module dune-pdelab. The strength of the proposed approach is illustrated with performance measurements for DG schemes for a scalar diffusion reaction equation and the Stokes equation. In our measurements, we utilize both the AVX2 and the AVX512 instruction set, achieving 30% to 40% of the machine’s theoretical peak performance for one matrix-free application of the operator.