Skip to main content
SpringerLink
Log in

Parallel Sorted Sparse Approximate Inverse Preconditioning Algorithm on GPU

  • Conference paper
  • First Online:
Benchmarking, Measuring, and Optimizing (Bench 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12614))

Included in the following conference series:

  • 898 Accesses

Abstract

In this study, we present an efficient thread-adaptive sparse approximate inverse preconditioning algorithm on GPU, called GSPAI-Adaptive. For GSPAI-Adaptive, there are three novelties: (1) a thread-adaptive allocation strategy is presented for each column of the preconditioner, (2) a parallel framework of constructing the sparse approximate inverse preconditioner is proposed on GPU, (3) each component of the preconditioner is computed in parallel inside a thread group of GPU. Experimental results show that GSPAI-Adaptive is effective, and is advantageous over the popular preconditioning algorithms in two public libraries, and a latest parallel sparse approximate inverse preconditioning algorithm.

The research has been supported by the Natural Science Foundation of China under grant number 61872422, and the Natural Science Foundation of Zhejiang Province, China under grant number LY19F020028, and the Natural Science Foundation of Jiangsu Province, China under grant number BK20171480.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Saad, Y., Schultz, M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856–869 (1986)

    Article  MathSciNet  Google Scholar 

  2. Van der Vorst, H.A.: Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems. SIAM J. Stat. Comput. 13(2), 631 (1992)

    Article  MathSciNet  Google Scholar 

  3. Kolotilina, L.Y., Yeremin, A.Y.: Factorized sparse approximate inverse preconditionings I: theory. Soc. Ind. Appl. Math. 14, 45–58 (1993)

    MathSciNet  MATH  Google Scholar 

  4. Benzi, M., Meyer, C.D., Tuma, M.: A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J. Sci. Comput. 17, 1135–1149 (1996)

    Article  MathSciNet  Google Scholar 

  5. Grote, M.J., Huckle, T.: Parallel preconditioning with sparse approximate inverses. Soc. Ind. Appl. Math. 18, 838–853 (1997)

    MathSciNet  MATH  Google Scholar 

  6. Chow, E.: A priori sparsity patterns for parallel sparse approximate inverse preconditioners. SIAM J. Sci. Comput. 21(5), 1804–1822 (2000)

    Article  MathSciNet  Google Scholar 

  7. Li, K., Yang, W., Li, K.: A hybrid parallel solving algorithm on GPU for quasi-tridiagonal system of linear equations. IEEE Trans. Parallel Distrib. Syst. 27(10), 2795–2808 (2016)

    Article  Google Scholar 

  8. Gao, J., Zhou, Y., He, G., Xia, Y.: A multi-GPU parallel optimization model for the preconditioned conjugate gradient algorithm. Parallel Comput. 63, 1–16 (2017)

    Article  MathSciNet  Google Scholar 

  9. He, G., Gao, J., Wang, J.: Efficient dense matrix-vector multiplication on GPU. Concurr. Comput.: Pract. Exp. 30(19), e4705 (2018)

    Article  Google Scholar 

  10. Gao, J., Wu, K., Wang, Y., Qi, P., He, G.: GPU-accelerated preconditioned GMRES method for two-dimensional Maxwell’s equations. Int. J. Comput. Math. 94(10), 2122–2144 (2017)

    Article  MathSciNet  Google Scholar 

  11. Lukash, M., Rupp, K., Selberherr, S.: Sparse approximate inverse preconditioners for iterative solvers on GPUs. In: Proceedings of the 2012 Symposium on High Performance Computing, pp. 1–8. Society for Computer Simulation International (2012)

    Google Scholar 

  12. Dehnavi, M.M., Fernandez, D.M., Gaudiot, J.L., Giannacopoulos, D.D.: Parallel sparse approximate inverse preconditioning on graphic processing units. IEEE Trans. Parallel Distrib. Syst. 24(9), 1852–1862 (2012)

    Article  Google Scholar 

  13. He, G., Yin, R., Gao, J.: An efficient sparse approximate inverse preconditioning algorithm on GPU. Concurr. Comput.: Pract. Exp. 32(7), e5598 (2020)

    Article  Google Scholar 

  14. Cusparse library, v10.1. https://docs.nvidia.com/cuda/cusparse/index.html

  15. Rupp, K., et al.: ViennaCL–linear algebra library for multi-and many-core architectures. SIAM J. Sci. Comput. 38(5), S412–S439 (2016)

    Article  MathSciNet  Google Scholar 

  16. Davis, T.A., Hu, Y.: The university of Florida sparse matrix collection. ACM Trans. Math. Softw. (TOMS) 38(1), 1–25 (2011)

    MathSciNet  MATH  Google Scholar 

  17. CUDA C programming guide, v10.1. https://docs.nvidia.com/cuda/cuda-c- programming-guide

Download references

Author information

Authors and Affiliations

  1. School of Computer and Electronic Information, Nanjing Normal University, Nanjing, 210023, China

    Qi Chen, Jiaquan Gao & Xinyue Chu

  2. Zhijiang College, Zhejiang University of Technology, Hangzhou, 310024, China

    Guixia He

Authors
  1. Qi Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiaquan Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinyue Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guixia He
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jiaquan Gao .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Technical University of Darmstadt, Darmstadt, Germany

    Felix Wolf

  2. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Wanling Gao

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Chen, Q., Gao, J., Chu, X., He, G. (2021). Parallel Sorted Sparse Approximate Inverse Preconditioning Algorithm on GPU. In: Wolf, F., Gao, W. (eds) Benchmarking, Measuring, and Optimizing. Bench 2020. Lecture Notes in Computer Science(), vol 12614. Springer, Cham. https://doi.org/10.1007/978-3-030-71058-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-71058-3_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-71057-6

  • Online ISBN: 978-3-030-71058-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation