AmgX: a library for GPU accelerated algebraic multigrid and preconditioned iterative methods. The solution of large sparse linear systems arises in many applications, such as computational fluid dynamics and oil reservoir simulation. In realistic cases the matrices are often so large that they require large scale distributed parallel computing to obtain the solution of interest in a reasonable time. In this paper we discuss the design and implementation of the AmgX library, which provides drop-in GPU acceleration of distributed algebraic multigrid (AMG) and preconditioned iterative methods. The AmgX library implements both classical and aggregation-based AMG methods with different selector and interpolation strategies, along with a variety of smoothers and preconditioners, including block-Jacobi, Gauss-Seidel, and incomplete-LU factorization. The library contains many of the standard and flexible preconditioned Krylov subspace iterative methods, which can be combined with any of the available multigrid methods or simpler preconditioners. The parallelism in the aggregation scheme exploits parallel graph matching techniques, while the smoothers and preconditioners often rely on parallel graph coloring algorithms. The AMG algorithm implemented in the AmgX library achieves $2-5 imes$ speedup on a single GPU against a competitive implementation on the CPU. As will be shown in the numerical experiments section, both setup and solve phases scale well across multiple nodes, sustaining this performance advantage.

References in zbMATH (referenced in 14 articles , 1 standard article )

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  1. Nathan Bell, Luke N. Olson, Jacob Schroder: PyAMG: Algebraic Multigrid Solvers in Python (2022) not zbMATH
  2. Li, Ruipeng; Sjögreen, Björn; Meier Yang, Ulrike: A new class of AMG interpolation methods based on matrix-matrix multiplications (2021)
  3. Schiano Di Cola, Vincenzo; Cuomo, Salvatore; Severino, Gerardo: Remarks on the numerical approximation of Dirac delta functions (2021)
  4. Becerra-Sagredo, Julián-Tercero; Málaga, Carlos; Mandujano, Francisco: A GPU-based multi-level algorithm for boundary value problems (2020)
  5. Massimo Bernaschi, Pasqua D’Ambra, Dario Pasquini: BootCMatchG: An adaptive Algebraic MultiGrid linear solver for GPUs (2020) not zbMATH
  6. Reguly, István Z.; Mudalige, Gihan R.: Productivity, performance, and portability for computational fluid dynamics applications (2020)
  7. Sashikumaar Ganesan, Manan Shah: SParSH-AMG: A library for hybrid CPU-GPU algebraic multigrid and preconditioned iterative methods (2020) arXiv
  8. Bernaschi, Massimo; Carrozzo, Mauro; Franceschini, Andrea; Janna, Carlo: A dynamic pattern factored sparse approximate inverse preconditioner on graphics processing units (2019)
  9. Averkin, Sergey N.; Gatsonis, Nikolaos A.: A parallel electrostatic particle-in-cell method on unstructured tetrahedral grids for large-scale bounded collisionless plasma simulations (2018)
  10. Pi-Yueh Chuang; Olivier Mesnard; Anush Krishnan; Lorena A. Barba: PetIBM: toolbox and applications of the immersed-boundary method on distributed-memory architectures (2018) not zbMATH
  11. Ganis, Benjamin; Singh, Gurpreet; Wheeler, Mary F.: A parallel framework for a multipoint flux mixed finite element equation of state compositional flow simulator (2017)
  12. Gao, Jiaquan; Wu, Kesong; Wang, Yushun; Qi, Panpan; He, Guixia: GPU-accelerated preconditioned GMRES method for two-dimensional Maxwell’s equations (2017)
  13. Pi-Yueh Chuang; Lorena A. Barba: AmgXWrapper: An interface between PETSc and the NVIDIA AmgX library (2017) not zbMATH
  14. Naumov, M.; Arsaev, M.; Castonguay, P.; Cohen, J.; Demouth, J.; Eaton, J.; Layton, S.; Markovskiy, N.; Reguly, I.; Sakharnykh, N.; Sellappan, V.; Strzodka, R.: AmgX: a library for GPU accelerated algebraic multigrid and preconditioned iterative methods (2015)