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Preconditioners for Batched Iterative Linear Solvers on GPUs

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Part of the Communications in Computer and Information Science book series (CCIS,volume 1690)


Batched iterative solvers can be an attractive alternative to batched direct solvers if the linear systems allow for fast convergence. In non-batched settings, iterative solvers are often enhanced with sophisticated preconditioners to improve convergence. In this paper, we develop preconditioners for batched iterative solvers that improve the iterative solver convergence without incurring detrimental resource overhead and preserving much of the iterative solver flexibility. We detail the design and implementation considerations, present a user-friendly interface to the batched preconditioners, and demonstrate the convergence and runtime benefits over non-preconditioned batched iterative solvers on state-of-the-art GPUs for a variety of benchmark problems from finite difference stencil matrices, the Suitesparse matrix collection and a computational chemistry application.


  • Sparse linear systems
  • Batched solvers
  • Batched preconditioners
  • GPU
  • Ginkgo

This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration.

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  • DOI: 10.1007/978-3-031-23606-8_3
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  1. 1.

    Ginkgo features also batched versions of other Krylov solvers, BiCGStab is however the most lightweight Krylov solver for general problems available.

  2. 2.

    This work was performed on the HoreKa supercomputer funded by the Ministry of Science, Research and the Arts Baden-Württemberg and by the Federal Ministry of Education and Research.


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Correspondence to Pratik Nayak .

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Aggarwal, I., Nayak, P., Kashi, A., Anzt, H. (2022). Preconditioners for Batched Iterative Linear Solvers on GPUs. In: Doug, K., Al, G., Pophale, S., Liu, H., Parete-Koon, S. (eds) Accelerating Science and Engineering Discoveries Through Integrated Research Infrastructure for Experiment, Big Data, Modeling and Simulation. SMC 2022. Communications in Computer and Information Science, vol 1690. Springer, Cham.

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