AmgX: A Library for GPU Accelerated Algebraic Multigrid and Preconditioned Iterative Methods

Naumov, Maxim; Arsaev, M.; Castonguay, Patrice; Cohen, Jonathan; Demouth, Julien; Eaton, Joe; Layton, Simon K.; Markovskiy, N.; Reguly, István Z.; Sakharnykh, Nikolai; Sellappan, V.; Strzodka, Robert

doi:10.1137/140980260

Cited by 111 publications

(66 citation statements)

References 36 publications

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“…In other words, the pipe hydraulic conductivity becomes effectively equal to 0, which produces a strongly ill conditioned Kirchoff matrix and some serious numerical difficulties. We solved the Kirchoff equations using the Graphic Processing Units (GPU)‐accelerated algebraic multigrid generalized minimal residual algorithm (AMG‐GMRES) in the AmgX library package (Naumov et al, 2015). The GPU‐accelerated algorithm is crucial to allow a large increase of the network size and, consequently, a significant decrease of the statistical fluctuations associated with individual simulations.…”

Section: Numerical Proceduresmentioning

confidence: 99%

Viscous Fingering and Preferential Flow Paths in Heterogeneous Porous Media

Tang

Bernabé

et al. 2020

JGR Solid Earth

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Preferential flow channeling and viscous fingering are widely observed phenomena in heterogeneous porous media from the pore scale to the core and reservoir scales. The transition from capillary to viscous fingering with increasing injection rate is also a well‐known phenomenon. Based on the previously observed visual similarity of viscous fingers and preferential single‐phase flow paths in 2‐D simulations, we postulate that these single‐ and two‐phase flow patterns should also be interrelated in 3‐D porous media. Capillary fingering is a manifestation of invasion percolation, a process restricted to the subnetwork of pores obtained from the critical path analysis. We investigated single‐phase flow channeling by applying a method similar to critical path analysis to the flow rate field and compared the subnetwork thus determined to the set of invaded pipes in drainage simulations. Our aim is to quantify the relation between preferential flow paths and viscous fingering, its dependence on pore‐scale heterogeneity and pore connectivity, and ultimately to upscale the network observations to the field scale appropriate for the engineering applications involving drainage in heterogeneous media.

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Section: Numerical Proceduresmentioning

confidence: 99%

Viscous Fingering and Preferential Flow Paths in Heterogeneous Porous Media

Tang

Bernabé

et al. 2020

JGR Solid Earth

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“…A description of the algorithms included in the publicly available Nvidia AmgX library [33], running on single and multiple-GPUs, is in [34]. AmgX implements both classical and unsmoothed aggregation-based AMG methods, with different choices for coarsening and prolongation operators.…”

Section: Related Workmentioning

confidence: 99%

AMG based on compatible weighted matching for GPUs

Bernaschi¹,

D'Ambra²,

Pasquini

2020

Parallel Computing

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We describe main issues and design principles of an efficient implementation, tailored to recent generations of Nvidia Graphics Processing Units (GPUs), of an Algebraic MultiGrid (AMG) preconditioner previously proposed by one of the authors and already available in the open-source package BootCMatch: Bootstrap algebraic multigrid based on Compatible weighted Matching for standard CPU. The AMG method relies on a new approach for coarsening sparse symmetric positive definite (s.p.d.) matrices, named coarsening based on compatible weighted matching. It exploits maximum weight matching in the adjacency graph of the sparse matrix, driven by the principle of compatible relaxation, providing a suitable aggregation of unknowns which goes beyond the limits of the usual heuristics applied in the current methods. We adopt an approximate solution of the maximum weight matching problem, based on a recently proposed parallel algorithm, referred as the Suitor algorithm, and show that it allow us to obtain good quality coarse matrices for our AMG on GPUs. We exploit inherent parallelism of modern GPUs in all the kernels involving sparse matrix computations both for the setup of the preconditioner and for its application in a Krylov solver, outperforming preconditioners available in Nvidia AmgX library. We report results about a large set of linear systems arising from discretization of scalar and vector partial differential equations (PDEs).

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“…Static workload mapping. We base our hash table-based SpGEMM on work by Naumov et al [41]. Following Naumov et al, we use a 2-step implementation of Gustavson's algorithm [26]: (1) In the first step, we count how many nonzeroes there will be in the output in order to populate the row pointers (deduplication done using the hash table, hash table size returns the number of nonzeroes), and (2) In the second step, we perform the multiplication.…”

Section: Spmmmentioning

confidence: 99%

HPGA: A High-Performance Graph Analytics Framework on the GPU

Yang

Wen

et al. 2018

2018 International Conference on Information Systems and Computer Aided Education (ICISCAE)

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pages. https://doi.org/10. 1145/nnnnnnn.nnnnnnn High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs because of three challenges: (1) the difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address some of these challenges, GraphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based in sparse linear algebra, which will allow graph algorithms to be expressed in a performant, succinct, composable and portable manner. In this paper, we examine the performance challenges of a linear-algebra-based approach to building graph frameworks and describe new design principles for overcoming these bottlenecks. Among the new design principles is exploiting input sparsity, which allows users to write graph algorithms without specifying push and pull direction. Exploiting output sparsity allows users to tell the backend which values of the output in a single vectorized computation they do not want computed. Load-balancing is an important feature for balancing work amongst parallel workers. We describe the important load-balancing features for handling graphs with different characteristics. The design principles described in this paper have been implemented in "GraphBLAST", the first open-source linear algebra-based graph framework on GPU targeting high-performance computing. The results show that on a single GPU, GraphBLAST has on average at least an order of magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL, comparable performance to the fastest GPU hardwired primitives and shared-memory graph frameworks Ligra and Gunrock, and better performance than any other GPU graph framework, while offering a simpler and more concise programming model.

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AmgX: A Library for GPU Accelerated Algebraic Multigrid and Preconditioned Iterative Methods

Cited by 111 publications

References 36 publications

Viscous Fingering and Preferential Flow Paths in Heterogeneous Porous Media

Viscous Fingering and Preferential Flow Paths in Heterogeneous Porous Media

AMG based on compatible weighted matching for GPUs

HPGA: A High-Performance Graph Analytics Framework on the GPU

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