NekRS, a GPU-Accelerated Spectral Element Navier-Stokes Solver

Fischer, Paul; Kerkemeier, Stefan; Min, Misun; Lan, Yu-Hsiang; Phillips, Malachi; Rathnayake, Thilina; Merzari, Elia; Tomboulides, Ananias; Karakuş, Ali; Chalmers, Noel; Warburton, Tim

doi:10.48550/arxiv.2104.05829

Cited by 12 publications

(18 citation statements)

References 32 publications

(63 reference statements)

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“…In this section, we will briefly cover the algorithmic aspects of SEM and how we use it to discretize the Poisson equation in particular. Since the computation of the Pressure in incompressible flow corresponds to the Poisson equation, and as it is the main source of stiffness, it frequently dominates the compute time of solvers such as Nek5000 and its successors NekRS [17] and Neko. By solving the Poisson equation we, therefore, capture the core of the entire solver.…”

Section: The Spectral Element Methodsmentioning

confidence: 99%

A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays

Karp,

Podobas,

Kenter

et al. 2021

Preprint

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The impending termination of Moore's law motivates the search for new forms of computing to continue the performance scaling we have grown accustomed to. Among the many emerging Post-Moore computing candidates, perhaps none is as salient as the Field-Programmable Gate Array (FPGA), which offers the means of specializing and customizing the hardware to the computation at hand.In this work, we design a custom FPGA-based accelerator for a computational fluid dynamics (CFD) code. Unlike prior workwhich often focuses on accelerating small kernels -we target the entire unstructured Poisson solver based on the high-fidelity spectral element method (SEM) used in modern state-of-the-art CFD systems. We model our accelerator using an analytical performance model based on the I/O cost of the algorithm. We empirically evaluate our accelerator on a state-of-the-art Intel Stratix 10 FPGA in terms of performance and power consumption and contrast it against existing solutions on general-purpose processors (CPUs). Finally, we propose a novel data movement-reducing technique where we compute geometric factors on the fly, which yields significant (700+ GFlop/s) single-precision performance and an upwards of 2x reduction in runtime for the local evaluation of the Laplace operator.We end the paper by discussing the challenges and opportunities of using reconfigurable architecture in the future, particularly in the light of emerging (not yet available) technologies.

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Section: The Spectral Element Methodsmentioning

confidence: 99%

A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays

Karp,

Podobas,

Kenter

et al. 2021

Preprint

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“…Darknet [39] Cello [25] Exploitdb [36] Ffmpeg [16] Hpgmg [1] Nekrs [17] Total skipped due to the unstable state of the CIL front-end. Table 1 shows the number of idiom occurrences detected per input program.…”

Section: Idiommentioning

confidence: 99%

Source Matching and Rewriting

Couto¹,

Zago²,

Yviquel³

et al. 2022

Preprint

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A typical compiler flow relies on a uni-directional sequence of translation/optimization steps that lower the program abstract representation, making it hard to preserve higherlevel program information across each transformation step. On the other hand, modern ISA extensions and hardware accelerators can benefit from the compiler's ability to detect and raise program idioms to acceleration instructions or optimized library calls. Although recent works based on Multi-Level IR (MLIR) have been proposed for code raising, they rely on specialized languages, compiler recompilation, or in-depth dialect knowledge. This paper presents Source Matching and Rewriting (SMR), a user-oriented source-codebased approach for MLIR idiom matching and rewriting that does not require a compiler expert's intervention. SMR uses a two-phase automaton-based DAG-matching algorithm inspired by early work on tree-pattern matching. First, the idiom Control-Dependency Graph (CDG) is matched against the program's CDG to rule out code fragments that do not have a control-flow structure similar to the desired idiom. Second, candidate code fragments from the previous phase have their Data-Dependency Graphs (DDGs) constructed and matched against the idiom DDG. Experimental results show that SMR can effectively match idioms from Fortran (FIR) and C (CIL) programs while raising them as BLAS calls to improve performance.

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“…The libParanumal library is highly modular and early fork of the project has been used with modifications as a platform for the custom physics requirements of the Nek5000 user community [34] as described in the next section albeit without the most recent developments in portable streaming and operator kernels. The algorithms and design principles of libParanumal kernels have also influenced the design of kernels produced by the libCEED cuda-gen backend (see Section 2.1).…”

Section: Libparanumalmentioning

confidence: 99%

“…(iii) Projection-based initial guesses to avoid redundant iteration work in successive timesteps [43,44]. The performance impact of these developments are described in detail in [34].…”

Section: Nek5000/rsmentioning

confidence: 99%

GPU Algorithms for Efficient Exascale Discretizations

Abdelfattah¹,

Barra²,

Beams³

et al. 2021

Preprint

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In this paper we describe the research and development activities in the Center for Efficient Exascale Discretization within the US Exascale Computing Project, targeting state-of-the-art high-order finite-element algorithms for high-order applications on GPU-accelerated platforms. We discuss the GPU developments in several components of the CEED software stack, including the libCEED, MAGMA, MFEM, libParanumal, and Nek projects. We report performance and capability improvements in several CEED-enabled applications on both NVIDIA and AMD GPU systems.

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NekRS, a GPU-Accelerated Spectral Element Navier-Stokes Solver

Cited by 12 publications

References 32 publications

A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays

A High-Fidelity Flow Solver for Unstructured Meshes on Field-Programmable Gate Arrays

Source Matching and Rewriting

GPU Algorithms for Efficient Exascale Discretizations

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