A Geometric Multigrid Solver on GPU Clusters

Köstler, Harald; Ritter, Daniel; Feichtinger, Christian

doi:10.1007/978-3-642-16405-7_26

Cited by 5 publications

(4 citation statements)

References 13 publications

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“…An aggregation based AMG, reaching beyond 10 11 degrees of freedom on 300,000 cores, is reported in [8]. A study of the scalability of FE solvers on clusters with GPU accelerators is given in [20]; see also [2,11,23,25,28] for other recent contributions in this direction.…”

Section: Introductionmentioning

confidence: 99%

Towards Textbook Efficiency for Parallel Multigrid

Gmeiner

Rüde

Stengel³

et al. 2015

Numer. math.: theory methods appl.

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In this work, we extend Achi Brandt's notion of textbook multigrid efficiency (TME) to massively parallel algorithms. Using a finite element based geometric multigrid implementation, we recall the classical view on TME with experiments for scalar linear equations with constant and varying coefficients as well as linear systems with saddle-point structure. To extend the idea of TME to the parallel setting, we give a new characterization of a work unit (WU) in an architecture-aware fashion by taking into account performance modeling techniques. We illustrate our newly introduced parallel TME measure by large-scale computations, solving problems with up to 200 billion unknowns on a TOP-10 supercomputer.

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Section: Introductionmentioning

confidence: 99%

Towards Textbook Efficiency for Parallel Multigrid

Gmeiner

Rüde

Stengel³

et al. 2015

Numer. math.: theory methods appl.

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“…For instance, [21] analyzes the performance of an optimized GPU-based implementation of the geometric multigrid method on different state-of-the-art NVIDIA GPUs. Similar work also includes [22][23][24][25][26]. [27] takes portability into account and provides a unified user interface so that optimized multigrid solvers can run on diverse platforms including multicore CPUs and GPUs.…”

Section: Related Workmentioning

confidence: 99%

Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs

Chen¹,

Wan²,

Liang³

et al. 2020

Preprint

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Rapid growth in scientific data and a widening gap between computational speed and I/O bandwidth makes it increasingly infeasible to store and share all data produced by scientific simulations. Multigrid-based hierarchical data refactoring is a class of promising approaches to this problem. These approaches decompose data hierarchically; the decomposed components can then be selectively and intelligently stored or shared, based on their relative importance in the original data. Efficient data refactoring design is one key to making these methods truly useful. In this paper, we describe highly optimized data refactoring kernels on GPU accelerators that are specialized for refactoring scientific data. We demonstrate that our optimized design can achieve 45.42 TB/s aggregated data refactoring throughput when using 4,096 GPUs of the Summit supercomputer. Finally, we showcase our optimized design by applying it to a large-scale scientific visualization workflow and the MGARD lossy compression software.

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“…Efforts are made on compilation to improve the performance of geometric multi-grid, leveraging function fusion [7,8]. Optimization of geometric multigrid on modern GPUs has also been studied, leveraging auto-tuning technique to find the best thread block configuration and loop tiling [9], and using the unified memory and nvlink to reduce the overhead of communication [24,23,32,31]. For Taihu-Light, we reduce the memory copy overhead with the ghost area by fusing the copy for boundary into the kernel, as introduced in Section 4.3.…”

Section: Related Workmentioning

confidence: 99%

Solving a trillion unknowns per second with HPGMG on Sunway TaihuLight

Yang

et al. 2019

Cluster Comput

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Benchmarks for supercomputers are important tools, not only for evaluating and ranking modern supercomputers, but also for providing hints for future architecture design. As a new benchmark, HPGMG (High Performance Geometric Multigrid) solves a linear equation set with a full geometric multi-grid algorithm. It involves computation on different scales, data movement with various volumes, global communication and neighbor communication with both large and small messages, etc., and is more correlated to real world applications than traditional benchmarks such as LINPACK. Therefore, it is desirable to examine how well HPGMG can perform on leadership supercomputers such as Sunway Taihulight. Sunway Taihulight, the No. 1 supercomputer in the Top 500 list from June 2016 to June 2018, which uses a specially designed many-core architecture SW26010, is of great interest to the community of high performance computing. With careful analysis and code design, we came up with an efficient implementation of HPGMG on SW26010 processors. We not only employed traditional optimization techniques such as 2.5D

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A Geometric Multigrid Solver on GPU Clusters

Cited by 5 publications

References 13 publications

Towards Textbook Efficiency for Parallel Multigrid

Towards Textbook Efficiency for Parallel Multigrid

Accelerating Multigrid-based Hierarchical Scientific Data Refactoring on GPUs

Solving a trillion unknowns per second with HPGMG on Sunway TaihuLight

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