A fine-grained block ILU scheme on regular structures for GPGPUs

Luo, Lixiang; Edwards, Jack R.; Luo, Hong; Mueller, Frank

doi:10.1016/j.compfluid.2015.07.005

Cited by 8 publications

(5 citation statements)

References 36 publications

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“…Thus, ρ(|D −1 L|) = ρ(D −1 L) = 0. By theorem 1, the chaotic relaxation (11) for this splitting converges.…”

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confidence: 81%

“…In this approach, an analysis phase computes (without necessarily reordering the unknowns) sets of rows that can be eliminated in parallel due to the sparsity of the matrix [9,10]. On structured grids with cells ordered by i, j, k, this approach gives rise to wavefront algorithms, where planes of cells having the same value of i + j + k are processed in parallel [11]. This method has the advantage of not adversely affecting the convergence rate while enabling reasonably good memory access patterns.…”

Section: Introductionmentioning

confidence: 99%

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An asynchronous incomplete block LU preconditioner for computational fluid dynamics on unstructured grids

Kashi¹,

Nadarajah²

2019

Preprint

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We present a study of the effectiveness of asynchronous incomplete LU factorization preconditioners for the time-implicit solution of compressible flow problems while exploiting thread-parallelism within a compute node. A block variant of the asynchronous fine-grain parallel preconditioner adapted to a finite volume discretization of the compressible Navier-Stokes equations on unstructured grids is presented, and convergence theory is extended to the new variant. Experimental (numerical) results on the performance of these preconditioners on inviscid and viscous laminar two-dimensional steady-state test cases are reported. It is found, for these compressible flow problems, that the block variant performs much better in terms of convergence, parallel scalability and reliability than the original scalar asynchronous ILU preconditioner. For viscous flow, it is found that the ordering of unknowns may determine the success or failure of asynchronous block-ILU preconditioning, and an ordering of grid cells suitable for solving viscous problems is presented.

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“…Thus, ρ(|D −1 L|) = ρ(D −1 L) = 0. By theorem 1, the chaotic relaxation (11) for this splitting converges.…”

mentioning

confidence: 81%

Section: Introductionmentioning

confidence: 99%

An asynchronous incomplete block LU preconditioner for computational fluid dynamics on unstructured grids

Kashi¹,

Nadarajah²

2019

Preprint

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“…Note that there are some classical papers for ILU factorizations of block matrices; for examples Saad and Zhang (1999a, 1999b) and Axelsson et al (1989), and the parallelization of block ILU factorization is realized from either level-scheduling or multi-coloring algorithm on point-wise matrices in Chen et al (2018) and Yang and Liu (2015). Some other parallel block ILU schemes are studied in Luo et al (2015a), Luo et al (2015b), Kim and Yun (2000) and Yun (2000).…”

Section: Introductionmentioning

confidence: 99%

Point-block incomplete LU preconditioning with asynchronous iterations on GPU for multiphysics problems

Cai

2020

The International Journal of High Performance Computing Applica

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Point-block matrices arise naturally in multiphysics problems when all variables associated with a mesh point are ordered together, and are different from the general block matrices since the sizes of the blocks are so small one can often invert some of the diagonal blocks explicitly. Motivated by the recent works of Chow and Patel and Chow et al., we propose an efficient incomplete LU (ILU) preconditioner for point-block matrices targeting applications on GPU. The construction of the preconditioner involves two critical steps: (1) the initial guessing of values for the lower and upper triangular matrices; and (2) several sweeps of asynchronous updating of the triangular matrices. Three representative problems are studied to show the advantage of the proposed point-block approach over the standard point-wise approach in terms of the number of GMRES iterations and also the total compute time. Moreover, we compare the proposed algorithm with the level-scheduling based parallel algorithm employed in NVIDIA’s cuSPARSE library as well as the serial method implemented in Intel MKL library, and the experiments show that a 2×–5× speedup can be achieved over the block-based ILU( p) factorizations from the cuSPARSE library.

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“…New algorithms are, nevertheless, trying to expose more parallelism and improve the performance of linear solvers on the GPU by accelerating the incomplete factorization and its use in the linear solver [Anzt et al, , 2016a. Reported speedups for implicit solvers are of one order of magnitude [Luo et al, 2015;Fu et al, 2014;Aissa et al, 2017].…”

Section: Introductionmentioning

confidence: 99%

GPU-accelerated CFD Simulations for Turbomachinery Design Optimization

Aissa¹

2018

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Curriculum vitae 157 List of publications and presentations 159 My research work within my Ph.D. started with the project AMEDEO enabling me to meet and exchange with great people, visit many research institutes and access valuable training all over the journey. For that, I am very grateful to my supervisor Dr. Tom Verstraete who believed on my small but growing GPU expertise back on 2013. Tom has done a fantastic supervising work with me by first giving me the freedom to act in my research but then closely checking my results. Moreover, I would like to thank Juliet Jopson for successfully coordinating the AMEDEO project and making the administration part much easier for all research fellows within the project. I would like also to thank Prof. Harvey Thomson for offering me a secondment within his team at the University of Leeds. During the short stay, I cooperated with Nicolas Delbosc from whom I learned so much about GPU performance assessment. I am very grateful to you Nic. I am thankful to all of AMEDEO people and a special thank to Dr. Roeland de Breuker for putting me in contact with Prof. Kees Vuik who later become my Ph.D. promoter. Prof. Vuik knows how to get a student fully motivated and prepared for the challenges within a Ph.D. project. You name a software library or a research facility and he would surely know someone to contact to make the stuff happen that you asked for (e.g. DAS-5, SURFsara, Paralution). For all the time and the effort you invested in my project I am really thankful. I would like also to thank the graduate school at TU Delft for the enriching courses and the possibility they bring to meet other Ph.D. students and exchange about ideas, challenges, views, fears, and ambitions. I would like to thank Deborah Dongor for helping me through the process of being an external Ph.D. student. My work would not have reached the maturity it has now without the constant support of the people of the TU department in VKI. My supervisor Tom and Prof. Tony Arts were always supportive when it comes to attending conferences and presenting my work. I owe a lot of what I learned during these last years to my colleague Lasse Müller. Besides the valuable discussions he provided me with the CPU version of the CFD simulation, the base of all my work. I am grateful to my colleague Christopher Chahine who taught me a lot of practical knowledge in design optimization. I would like to thank Roberto with whom I cooperated the last months and learned a lot. Eager to continue the collaboration. For the rest of the TU group I xi xii hope we will renew our biweekly department meeting to continue exchanging about our latest results. I would like to thank all the computer center staff here at VKI and also Christelle and Evelyne for supporting my numerous requests for papers and documentation. I am thankful to the VKI administration and especially to Dirk who made all administrative procedures so easy for me at the beginning of my Ph.D. and after him, Simone took over and facilitated all the paper work for me. I would ...

show abstract

A fine-grained block ILU scheme on regular structures for GPGPUs

Cited by 8 publications

References 36 publications

An asynchronous incomplete block LU preconditioner for computational fluid dynamics on unstructured grids

An asynchronous incomplete block LU preconditioner for computational fluid dynamics on unstructured grids

Point-block incomplete LU preconditioning with asynchronous iterations on GPU for multiphysics problems

GPU-accelerated CFD Simulations for Turbomachinery Design Optimization

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