Sparsifying Synchronization for High-Performance Shared-Memory Sparse Triangular Solver

Park, Jongsoo; Smelyanskiy, Mikhail; Sundaram, Narayanan; Dubey, Pradeep

doi:10.1007/978-3-319-07518-1_8

Cited by 54 publications

(55 citation statements)

References 23 publications

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“…Point-to-point synchronizations for level scheduling was introduced as an effective way to parallelize sparse triangular solve [11], [12]. Here we use the observation that incomplete factorization done with up-looking LU has the same dependency structure as sparse triangular solve.…”

Section: A Level Scheduling Upper Stagementioning

confidence: 99%

“…Because these operations dominate the solve time, having an incomplete decomposition that can allow us to make use of these operations efficiently is critically important. There has been a vast amount of research in this area over the past 10 years as large many-core systems are becoming the norm [1], [11]- [13]. Many of these methods require reordering and special data-structures [1], [13].…”

Section: Introductionmentioning

confidence: 99%

“…Segmented scan has been shown to be an ideal way to implement spmv and stri on vector based machines [14], with most many-core systems having large vector register lanes. The second work [11], [12] focuses on improving stri on standard CSR format storage using general level scheduling and sparsifying synchronization. This work demonstrates that many of the overheads dealing with level scheduling could be removed, and allowing stri to scale.…”

Section: Introductionmentioning

confidence: 99%

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Javelin: A Scalable Implementation for Sparse Incomplete LU Factorization

Booth

Bolet

2019

2019 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)

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In this work, we present a new scalable incomplete LU factorization framework called Javelin to be used as a preconditioner for solving sparse linear systems with iterative methods. Javelin allows for improved parallel factorization on shared-memory many-core systems by packaging the coefficient matrix into a format that allows for high performance sparse matrix-vector multiplication and sparse triangular solves with minimal overheads. The framework achieves these goals by using a collection of traditional permutations, point-to-point thread synchronizations, tasking, and segmented prefix scans in a conventional compressed sparse row format. Moreover, this framework stresses the importance of co-designing dependent tasks, such as sparse factorization and triangular solves, on highly-threaded architectures. Using these changes, traditional fill-in and drop tolerance methods can be used, while still being able to have observed speedups of up to ∼ 42× on 68 Intel Knights Landing cores and ∼ 12× on 14 Intel Haswell cores.

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Section: A Level Scheduling Upper Stagementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Javelin: A Scalable Implementation for Sparse Incomplete LU Factorization

Booth

Bolet

2019

2019 IEEE International Parallel and Distributed Processing Symposium Workshops (IPDPSW)

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“…Esta performance sugere que a abordagem de escalonamento por níveis gera resultados positivos mas ainda nãoé suficiente para garantir um paralelismo adequado para as matrizes de interesse. Testes preliminares mostraram um potencial superior nestas mesmas matrizes utilizando as técnicas descritas em [4].…”

Section: Solver Triangularunclassified

“…Para alcançar uma performance otimizada utilizando OpenMP, iremos considerar a abordagem apresentada em [4] nos próximos passos da pesquisa.…”

Section: Conclusõesunclassified

Construção e aplicação de precondicionador ILUk por blocos com paralelismo em memória compartilhada

Nievinski¹,

Zanardi²,

Carvalho³

2018

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. Apresentamos a implementação paralela, em memória compartilhada, do precondicionador BILUk para matrizes BCSR, através do OpenMP, utilizando a técnica de escalonamento por níveis na construção numérica e na aplicação.Palavras-chave. paralelismo em memória compartilhada, solver triangular, precondicionadores, núcleos de cálculos intensivos, escalonamento por níveis, matrizes esparsas em bloco IntroduçãoDiscutimos a construção e a aplicação de um precondicionador ILU (fatoração LU incompleta) por blocos, com preenchimento por níveis (BILUk) [5] e com paralelismo de memória compartilhada, utilizando o OpenMP. Baseamo-nos na técnica de escalonamento por níveis (level scheduling) [3], focando na sua implementação em CPU e MIC (Many Integrated Core Architecture) da Intel, cujo nome comercialé Xeon Phi, em particular nesse trabalho testamos o KNC (Knights Corner). Nosso contexto de interesseé a simulação da explotação de petróleo, onde um sistema de equações diferenciais parciais não-linearesé discretizado, dando origem a um sistema de equações algébricas não-lineares, queé resolvido por um método de Newton. Em cada passo desse método, temos que tratar sistemas lineares de grande porte, com matrizes esparsas tendo pequenos blocos densos relativos a cada nó da malha de discretização, através de métodos iterativos de Krylov. Nesse caso, podem ser resolvidos centenas de sistemas lineares que manterão as mesmas esparsidade e estrutura da matriz original, apesar de sofrerem alterações em suas entradas numéricas. Nosso objetivoé apresentar um método que leve em conta essas características e, por isso, possa se concentrar na paralelização da fatoração numérica e da aplicação do precondicionador. Além dessa breve introdução, essa contribuição apresenta, em sua segunda seção, a técnica utilizada para a paralelização do algoritmo; enquanto que na seção 3 mostramos detalhes da implementação do BILUk. A seção 4 trata do solver triangular, a rotina que aplica o precondicionador em cada iteração do solver linear. As seções 5 e 6 apresentam os 1

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Fast synchronization‐free algorithms for parallel sparse triangular solves with multiple right‐hand sides

Liu

Hogg

et al. 2017

Concurrency and Computation

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The sparse triangular solve kernels, SpTRSV and SpTRSM, are important building blocks for a number of numerical linear algebra routines. Parallelizing SpTRSV and SpTRSM on today's manycore platforms, such as GPUs, is not an easy task since computing a component of the solution may depend on previously computed components, enforcing a degree of sequential processing. As a consequence, most existing work introduces a preprocessing stage to partition the components into a group of level-sets or coloursets so that components within a set are independent and can be processed simultaneously during the subsequent solution stage. However, this class of methods requires a long preprocessing time as well as significant runtime synchronization overheads between the sets. To address this, we propose in this paper novel approaches for SpTRSV and SpTRSM in which the ordering between components is naturally enforced within the solution stage. In this way, the cost for preprocessing can be greatly reduced, and the synchronizations between sets are completely eliminated. To further exploit the data-parallelism, we also develop an adaptive scheme for efficiently processing multiple right-hand sides in SpTRSM. A comparison with a state-of-the-art library supplied by the GPU vendor, using 20 sparse matrices on the latest GPU device, shows that the proposed approach obtains an average speedup of over two for SpTRSV and up to an order of magnitude speedup for SpTRSM. In addition, our method is up to two orders of magnitude faster for the preprocessing stage than existing SpTRSV and SpTRSM methods.

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Sparsifying Synchronization for High-Performance Shared-Memory Sparse Triangular Solver

Cited by 54 publications

References 23 publications

Javelin: A Scalable Implementation for Sparse Incomplete LU Factorization

Javelin: A Scalable Implementation for Sparse Incomplete LU Factorization

Construção e aplicação de precondicionador ILUk por blocos com paralelismo em memória compartilhada

Fast synchronization‐free algorithms for parallel sparse triangular solves with multiple right‐hand sides

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