A stencil-scaling method with a correction term reproduces nodal-integration finite element solutions for vector-valued PDEs on hierarchical hybrid grids, with relative time-to-solution from 0.45 to 0.87 versus on-the-fly integration.
Understanding HPC Benchmark Performance on Intel Broadwell and Cascade Lake Processors
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abstract
Hardware platforms in high performance computing are constantly getting more complex to handle even when considering multicore CPUs alone. Numerous features and configuration options in the hardware and the software environment that are relevant for performance are not even known to most application users or developers. Microbenchmarks, i.e., simple codes that fathom a particular aspect of the hardware, can help to shed light on such issues, but only if they are well understood and if the results can be reconciled with known facts or performance models. The insight gained from microbenchmarks may then be applied to real applications for performance analysis or optimization. In this paper we investigate two modern Intel x86 server CPU architectures in depth: Broadwell EP and Cascade Lake SP. We highlight relevant hardware configuration settings that can have a decisive impact on code performance and show how to properly measure on-chip and off-chip data transfer bandwidths. The new victim L3 cache of Cascade Lake and its advanced replacement policy receive due attention. Finally we use DGEMM, sparse matrix-vector multiplication, and the HPCG benchmark to make a connection to relevant application scenarios.
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Stencil scaling for vector-valued PDEs on hybrid grids with applications to generalized Newtonian fluids
A stencil-scaling method with a correction term reproduces nodal-integration finite element solutions for vector-valued PDEs on hierarchical hybrid grids, with relative time-to-solution from 0.45 to 0.87 versus on-the-fly integration.