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  1. Proceedings of the 8th International Workshop on Programming Models and Applications for Multicores and Manycores (PMAM'17)
  2. Batched Gauss-Jordan Elimination for Block-Jacobi Preconditioner Generation on GPUs
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Batched Gauss-Jordan Elimination for Block-Jacobi Preconditioner Generation on GPUs
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Batched Gauss-Jordan Elimination for Block-Jacobi Preconditioner Generation on GPUs

Content Provider ACM Digital Library
Author Flegar, Goran Anzt, Hartwig Dongarra, Jack Quintana-OrtĂ­, Enrique S.
Abstract In this paper, we design and evaluate a routine for the efficient generation of block-Jacobi preconditioners on graphics processing units (GPUs). Concretely, to exploit the architecture of the graphics accelerator, we develop a batched Gauss-Jordan elimination CUDA kernel for matrix inversion that embeds an implicit pivoting technique and handles the entire inversion process in the GPU registers. In addition, we integrate extraction and insertion CUDA kernels to rapidly set up the block-Jacobi preconditioner. Our experiments compare the performance of our implementation against a sequence of batched routines from the MAGMA library realizing the inversion via the LU factorization with partial pivoting. Furthermore, we evaluate the costs of different strategies for the block-Jacobi extraction and insertion steps, using a variety of sparse matrices from the SuiteSparse matrix collection. Finally, we assess the efficiency of the complete block-Jacobi preconditioner generation in the context of an iterative solver applied to a set of computational science problems, and quantify its benefits over a scalar Jacobi preconditioner.
Starting Page 1
Ending Page 10
Page Count 10
File Format PDF
ISBN 9781450348836
DOI 10.1145/3026937.3026940
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2017-02-04
Publisher Place New York
Access Restriction Subscribed
Subject Keyword Matrix inversion Block-jacobi preconditioner Gauss-jordan elimination Iterative methods Graphics processing units (gpus) Sparse linear systems
Content Type Text
Resource Type Article
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