Parallelization technologies for solving three-dimensional boundary value problems on quasi-structured grids using the CPU+GPU hybrid computing environment

Authors

  • I.A. Klimonov Novosibirsk State University https://orcid.org/0000-0002-9720-2746
  • V.D. Korneev The Institute of Computational Mathematics and Mathematical Geophysics of SB RAS (ICM&MG SB RAS)
  • V.M. Sveshnikov The Institute of Computational Mathematics and Mathematical Geophysics of SB RAS (ICM&MG SB RAS)

DOI:

https://doi.org/10.26089/NumMet.v17r107

Keywords:

boundary value problems, domain decomposition methods, Poincare-Steklov equation, quasi-structured grids, Peaceman-Rachford method, graphics accelerators

Abstract

When parallelizing the solution processes of solving three-dimensional boundary value problems on quasi-structured grids by the method of decomposition of the computational domain into subdomains without imposition, the most time consuming computational procedure is a solution of subproblems in subdomains. The application of parallelepiped quasi-structured grids makes it possible to use the rapidly convergent method of alternating directions. The parallelization of iterative processes on subdomains is performed on CPU using MPI. In order to solve the subproblems, we propose to use the graphics accelerators (GPU). Experimental results of using the graphics accelerators to solve the subproblems by Peaceman-Rachford method are discussed. The computational acceleration achieved on the CPU+GPU hybrid computing environment is experimentally estimated compared to using the CPU only.

Author Biographies

I.A. Klimonov

V.D. Korneev

V.M. Sveshnikov

References

  1. Yu. V. Vasilevskii and M. A. Ol’shanskii, A Short Course on Multigrid and Domain Decomposition Methods (Mosk. Gos. Univ., Moscow, 2007) [in Russian].
  2. A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations (Clarendon Press, Oxford, 1999).
  3. V. M. Sveshnikov, “Construction of Direct and Iterative Decomposition Methods,” Sib. Zh. Ind. Mat. 12 (3), 99-109 (2009) [J. Appl. Ind. Math. 4 (3), 431-440 (2010)].
  4. V. M. Sveshnikov and D. O. Belyaev, “Construction of Quasi-Structured Locally Modified Grids to Solve the Problems of High Current Electronics,” Vestn. Yuzhn. Ural. Gos. Univ. Ser. Mat. Model. Programm., No. 40, 130-140 (2012).
  5. V. M. Sveshnikov and B. D. Rybdylov, “About Parallelization of Solving of Boundary Value Problems on Quasistruсtured Grids,” Vestn. Yuzhn. Ural. Gos. Univ. Ser. Vychisl. Mat. Inf. 2 (3), 63-72 (2013).
  6. V. D. Korneev, Parallel Programming with MPI (Inst. Comput. Math. Math. Geophys., Novosibirsk, 2002) [in Russian].
  7. V. P. Il’in, Finite Difference and Finite Volume Methods for Elliptic Equations (Inst. Comput. Math. Math. Geophys., Novosibirsk, 2000) [in Russian].
  8. NVIDIA. CUDA C Best Practices Guide.
    http://docs.nvidia.com/cuda/cuda-c-best-practices-guide . Cited February 22, 2016.

Published

25-02-2016

How to Cite

Климонов И., Корнеев В., Свешников В. Parallelization Technologies for Solving Three-Dimensional Boundary Value Problems on Quasi-Structured Grids Using the CPU+GPU Hybrid Computing Environment // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2016. 17. 65-71. doi 10.26089/NumMet.v17r107

Issue

Section

Section 1. Numerical methods and applications