In:
ACM Transactions on Mathematical Software, Association for Computing Machinery (ACM), Vol. 47, No. 1 ( 2021-03-31), p. 1-31
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.
Type of Medium:
Online Resource
ISSN:
0098-3500
,
1557-7295
Language:
English
Publisher:
Association for Computing Machinery (ACM)
Publication Date:
2021
detail.hit.zdb_id:
2006421-4
detail.hit.zdb_id:
191812-6
Bookmarklink