Preconditioned Krylov solvers on GPUs |
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| Affiliation: | 1. Department for Electrical Engineering and Computer Science, University of Tennessee, Innovative Computing Lab Knoxville, Tennessee 37996, United States;2. University of Manchester, UK;3. Oak Ridge National Laboratory, USA;4. Friedrich-Alexander University of Nuermberg-Erlangen, Germany;5. Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg, Germany;1. Institute for Computational and Mathematical Engineering, Stanford University, Stanford, USA;2. Department of Mechanical Engineering, Stanford University, Stanford, USA;3. Center for Computing Research, Sandia National Laboratories, Albuquerque, USA;2. Oak Ridge National Laboratory, USA;3. School of Computer Science, University of Manchester, United Kingdom;4. Depto. Ingeniería y Ciencia de Computadores, Universidad Jaume I (UJI), Castellón, Spain |
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| Abstract: | In this paper, we study the effect of enhancing GPU-accelerated Krylov solvers with preconditioners. We consider the BiCGSTAB, CGS, QMR, and IDR(s) Krylov solvers. For a large set of test matrices, we assess the impact of Jacobi and incomplete factorization preconditioning on the solvers’ numerical stability and time-to-solution performance. We also analyze how the use of a preconditioner impacts the choice of the fastest solver. |
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