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Mixed-Precision AMG method for Many Core Accelerators

Published: 09 September 2014 Publication History

Abstract

There is a large gap between single- and double-precision performances on GPUs. Single-precision arithmetic is more than twice as fast as double-precision arithmetic on GPUs. However, single-precision arithmetic cannot achieve sufficient accuracy. By using a combination of single- and double-precision arithmetics, accuracy is maintained and calculations are performed quickly. We introduce a mixed precision method to the algebraic multigrid (AMG) method and evaluate the performance on various GPUs. The results indicate that, for anisotropic problems, the performance of the mixed-precision AMG is approximately 1.9 times greater than the double-precision AMG at a size of 1003.

References

[1]
A. Buttari, J. Dongarra, J. Langou, J. Langou, P. Luszczek, and J. Kurzak: Mixed Precision Iterative Refinement Techniques for the Solution of Dense Linear Systems, International Journal of High Performance Computing Applications November 2007 vol. 21 no. 4 457-466.8.
[2]
M. Emans, Albert van der Meer: Mixed-precision AMG as linear equation solver for definite systems, International Conference on Computational Science, 2010, Volume 1, Issue 1, Pages 175--183.
[3]
JE. Stone, D. Gohara, G. Shi: OpenCL: A parallel programming standard for heterogeneous computing systems. Comput. in Sci. and Eng. 2010;12:66--73.
[4]
AMD: Accelerated Parallel Processing OpenCL Programming Guide, http://developer.amd.com/download/AMD_Accelerated_Parallel_Processing_OpenCL_Programming_Guide.pdf.
[5]
P. Vanek, J. Mandel, and M. Brezina: "Algebraic Multigrid By Smoothed Aggregation For Second And Fourth Order Elliptic Problems," Computing, Vol. 56, pp. 179--196 (1995)
[6]
A. Fujii Y.Oyanagi: Evaluation of Algebraic Multi-grid Method: An Efficient Linear Solver for Scientific Simulations 28(4), 149-154, 2009-12-15, pp.9--14 (2009).
[7]
K. Takahashi, A. Fujii, T. Tanaka: GPGPU-based Algebraic Multigrid Method, Proceedings of the 23rd IASTED International Conference on Parallel and Distributed Computing and Systems, 2011, track757-061.

Cited By

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  • (2023)Three-precision algebraic multigrid on GPUsFuture Generation Computer Systems10.1016/j.future.2023.07.024149(280-293)Online publication date: Dec-2023
  • (2022)Mixed precision algorithms in numerical linear algebraActa Numerica10.1017/S096249292200002231(347-414)Online publication date: 9-Jun-2022
  • (2021)A survey of numerical linear algebra methods utilizing mixed-precision arithmeticInternational Journal of High Performance Computing Applications10.1177/1094342021100331335:4(344-369)Online publication date: 1-Jul-2021

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cover image ACM Other conferences
EuroMPI/ASIA '14: Proceedings of the 21st European MPI Users' Group Meeting
September 2014
183 pages
ISBN:9781450328753
DOI:10.1145/2642769
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

In-Cooperation

  • Kyoto University: Kyoto University
  • University of Tokyo
  • University of Tsukuba: University of Tsukuba

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 09 September 2014

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Author Tags

  1. AMG
  2. GPU
  3. Heterogeneous
  4. Mixed precision
  5. OpenCL

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  • Research-article
  • Research
  • Refereed limited

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EuroMPI/ASIA '14

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EuroMPI/ASIA '14 Paper Acceptance Rate 18 of 39 submissions, 46%;
Overall Acceptance Rate 18 of 39 submissions, 46%

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Cited By

View all
  • (2023)Three-precision algebraic multigrid on GPUsFuture Generation Computer Systems10.1016/j.future.2023.07.024149(280-293)Online publication date: Dec-2023
  • (2022)Mixed precision algorithms in numerical linear algebraActa Numerica10.1017/S096249292200002231(347-414)Online publication date: 9-Jun-2022
  • (2021)A survey of numerical linear algebra methods utilizing mixed-precision arithmeticInternational Journal of High Performance Computing Applications10.1177/1094342021100331335:4(344-369)Online publication date: 1-Jul-2021

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