Parallel Dual Tree Traversal on Multi-core and Many-core Architectures for Astrophysical N-body Simulations

Lange, Benoit; Fortin, Pierre

doi:10.1007/978-3-319-09873-9_60

Cited by 11 publications

(20 citation statements)

References 13 publications

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“…The line segments represent the original level-wise Hilbert orders. However, maximizing thread-level parallelism has been proven more successful using the Dual Tree Traversal (DTT) approach [38,25], which is known for its adaptability to multiand many-core emerging architectures. For example, to find the scattered field at target positions encoded by 0000 Hilbert order in Figure 2(b), DTT simultaneously traverses source and target trees, and recursively uncovers the cell-cell interaction list (see Figure 2(a)).…”

Section: 2mentioning

confidence: 99%

Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering

Abduljabbar¹,

Farhan²,

Al-Harthi³

et al. 2019

SIAM J. Sci. Comput.

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Algorithmic and architecture-oriented optimizations are essential for achieving performance worthy of anticipated energy-austere exascale systems. In this paper, we present an extreme scale FMM-accelerated boundary integral equation solver for wave scattering, which uses FMM as a matrix-vector multiplication inside the GMRES iterative method. Our FMM Helmholtz kernels are capable of treating nontrivial singular and near-field integration points. We implement highly optimized kernels for both shared and distributed memory, targeting emerging Intel extreme performance HPC architectures. We extract the potential thread-and data-level parallelism of the key Helmholtz kernels of FMM. Our application code is well optimized to exploit the AVX-512 SIMD units of Intel Skylake and Knights Landing architectures. We provide different performance models for tuning the task-based tree traversal implementation of FMM, and develop optimal architecturespecific and algorithm aware partitioning, load balancing, and communication reducing mechanisms to scale up to 6,144 compute nodes of a Cray XC40 with 196,608 hardware cores. With shared memory optimizations, we achieve roughly 77% of peak single precision floating point performance of a 56-core Skylake processor, and on average 60% of peak single precision floating point performance of a 72-core KNL. These numbers represent nearly 5.4x and 10x speedup on Skylake and KNL, respectively, compared to the the baseline scalar code. With distributed memory optimizations, on the other hand, we report near-optimal efficiency in the weak scalability study with respect to both the O(log P ) communication complexity as well as the theoretical scaling complexity of FMM. In addition, we exhibit up to 85% efficiency in strong scaling. We compute in excess of 2 billion DoF on the full-scale of the Cray XC40 supercomputer. The numerical results match the analytical solution with convergence at 1.0e-4 relative 2-norm residual accuracy. To the best of our knowledge, this work presents the fastest and the most scalable FMM-accelerated linear solver for oscillatory kernels.

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Section: 2mentioning

confidence: 99%

Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering

Abduljabbar¹,

Farhan²,

Al-Harthi³

et al. 2019

SIAM J. Sci. Comput.

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“…We rely on the pfalcON code 1 where the DTT is performed in parallel on multi-core CPUs thanks to task synchronizations based on atomic operations [Lange and Fortin, 2014]. Another task-based DTT parallelization has been achieved thanks to a rewriting of the DTT [Taura et al, 2012] and implemented in the exaFMM code 2 .…”

Section: Related Work and Positioningmentioning

confidence: 99%

“…17: end if In Lange and Fortin [2014], falcON has been parallelized in pfalcON on multi-core CPUs and on Intel Xeon Phi thanks to task-based parallelism (e.g. with OpenMP).…”

Section: Falcon and Pfalcon Codesmentioning

confidence: 99%

Dual tree traversal on integrated GPUs for astrophysical N-body simulations

Fortin

Touche

2019

The International Journal of High Performance Computing Applica

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In astrophysical N-body simulations, O( N) fast multipole methods (FMMs) with dual tree traversal (DTT) on multi-core CPUs are faster than O( N log N) CPU tree-codes but can still be outperformed by GPU ones. In this article, we aim at combining the best algorithm, namely FMM with DTT, with the most powerful hardware currently available, namely GPUs. In the astrophysical context requiring low accuracies and non-uniform particle distributions, we show that such combination can be achieved thanks to a hybrid CPU-GPU algorithm on integrated GPUs: while the DTT is performed on the CPU cores, the far- and near-field computations are all performed on the GPU cores. We show how to efficiently expose the interactions resulting from the DTT to the GPU cores, how to deploy both the far- and near-field computations on GPU, and how to overlap the parallel DTT on CPU with GPU computations. Based on the falcON code and using OpenCL on AMD Accelerated Processing Units and on Intel integrated GPUs, this first heterogeneous deployment of DTT for FMM outperforms standard multi-core CPUs and matches GPU and high-end CPU performance, being hence more cost- and power-efficient.

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“…O uso de paralelismo aliadoà vetorização SIMD/AVX2 foi explorado em diversos trabalhos envolvendo problemas de N -corpos e caminhamento emárvores [Yokota 2012, Long Wang et al 2015, Arora et al 2009, especialmente onde havia cálculo direto de forç as gravitacionais. Assimé o caso em [Lange and Fortin 2014] que usa o método dual tree e que não faz uso de instruções SIMD intrínsecas diretamente, deixando a cargo do compilador fazer o trabalho de vetorização. Issoé possível principalmente porque nesses métodos as interações são do tipo célula-célula (C-C) o que facilita a vetorização automática.…”

Section: Trabalhos Relacionadosunclassified

Caminhamento Paralelo Barnes-Hut com Vetorização AVX2

Zola

Delgado

Blanco

2019

Anais Do XX Simpósio Em Sistemas Computacionais De Alto Desempenho (SSCAD 2019)

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O algoritmo Barnes-Hut é um método aproximado amplamente usado na simulação gravitacional de N -Corpos. A natureza irregular desse código apresenta desafios para sua computação em sistemas paralelos. Obstáculos adicionais ocorrem nesse padrão de computação quando se deseja a utilização eficaz da capacidade computacional de arquiteturas multicore com instruçoes SIMD. O enfoque deste trabalho é implementar e analisar a eficiência do caminhamento paralelo Barnes-Hut com octrees implı́citas e uso de instruções vetoriais AVX2. Os experimentos demonstram a efetividade do método, que apresenta altas taxas de GFLOP/s e economia de energia nas simulações.

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Parallel Dual Tree Traversal on Multi-core and Many-core Architectures for Astrophysical N-body Simulations

Cited by 11 publications

References 13 publications

Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering

Extreme Scale FMM-Accelerated Boundary Integral Equation Solver for Wave Scattering

Dual tree traversal on integrated GPUs for astrophysical N-body simulations

Caminhamento Paralelo Barnes-Hut com Vetorização AVX2

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