Compressed basis GMRES on high-performance graphics processing units
- Universitat Jaume I, Castelló (Spain)
- Karlsruhe Inst. of Technology (KIT) (Germany); Univ. of Tennessee, Knoxville, TN (United States)
- Karlsruhe Inst. of Technology (KIT) (Germany)
- Universitat Politècnica de València (Spain)
Krylov methods provide a fast and highly parallel numerical tool for the iterative solution of many large-scale sparse linear systems. To a large extent, the performance of practical realizations of these methods is constrained by the communication bandwidth in current computer architectures, motivating the investigation of sophisticated techniques to avoid, reduce, and/or hide the message-passing costs (in distributed platforms) and the memory accesses (in all architectures). This article leverages Ginkgo’s memory accessor in order to integrate a communication-reduction strategy into the (Krylov) GMRES solver that decouples the storage format (i.e., the data representation in memory) of the orthogonal basis from the arithmetic precision that is employed during the operations with that basis. Given that the execution time of the GMRES solver is largely determined by the memory accesses, the cost of the datatype transforms can be mostly hidden, resulting in the acceleration of the iterative step via a decrease in the volume of bits being retrieved from memory. Together with the special properties of the orthonormal basis (whose elements are all bounded by 1), this paves the road toward the aggressive customization of the storage format, which includes some floating-point as well as fixed-point formats with mild impact on the convergence of the iterative process. We develop a high-performance implementation of the “compressed basis GMRES” solver in the Ginkgo sparse linear algebra library using a large set of test problems from the SuiteSparse Matrix Collection. We demonstrate robustness and performance advantages on a modern NVIDIA V100 graphics processing unit (GPU) of up to 50% over the standard GMRES solver that stores all data in IEEE double-precision.
- Research Organization:
- US Department of Energy (USDOE), Washington, DC (United States). Office of Science, Exascale Computing Project
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI ID:
- 2424930
- Journal Information:
- International Journal of High Performance Computing Applications, Journal Name: International Journal of High Performance Computing Applications Journal Issue: 2 Vol. 37; ISSN 1094-3420
- Publisher:
- SAGECopyright Statement
- Country of Publication:
- United States
- Language:
- English
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