DOI: https://doi.org/10.26089/NumMet.v19r444

Parallelization technologies and grid data structures for solving three-dimensional boundary value problems in complex domains on quasistructured grids

Authors

  • V.D. Korneev
  • V.M. Sveshnikov

Keywords:

boundary value problems
quasistructured grids
parallelization technologies
data structures
structured arrays

Abstract

When parallelizing the solution of three-dimensional boundary value problems, especially in domains with complex geometry, the сomputational technologies and data structureы are important. The amount of stored information and the computational time depend on them. In this paper we propose the technologies for parallelizing the method of decomposition of the computational domain into subdomains conjugated without overlapping on a quasistructured grid. Parallel grid data structures oriented mainly to work with structured data arrays are developed. An illustrative example clarifying the fundamentals of the proposed approach is discussed.

New computational technologies

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Published

2018-12-24

Issue

Vol. 19 (2018): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biographies

V.D. Korneev

The Institute of Computational Mathematics and Mathematical Geophysics of SB RAS (ICM&MG SB RAS)
• Senior Researcher

V.M. Sveshnikov

The Institute of Computational Mathematics and Mathematical Geophysics of SB RAS (ICM&MG SB RAS)
• Chief Researcher

References

  1. I. V. Alyamovskii, Electron Beams and Electron Guns (Sov. Radio, Moscow, 1966) [in Russian].
  2. V. P. Il’in, Numerical Methods for Solving Electrophysical Problems (Nauka, Moscow, 1985) [in Russian].
  3. S. I. Molokovskii and A. D. Sushkov, Intense Electron and Ion Beams (Energoatomizdat, Moscow, 1991) [in Russian].
  4. V. A. Syrovoi, Introduction to the Theory of Intense Beams of Charged Particles (Energoatomizdat, Moscow, 2004) [in Russian].
  5. NETGEN mesh generator.
    https://sourceforge.net/projects/netgen-mesher . Cited November 20, 2018.
  6. Yu. V. Vasilevskii and M. A. Ol’shanskii, A Short Course on Multigrid and Domain Decomposition Methods (Mosk. Gos. Univ., Moscow, 2007) [in Russian].
  7. A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations (Clarendon Press, Oxford, 1999).
  8. V. Dolean, P. Jolivet, and F. Nataf, An Introduction to Domain Decomposition Methods: Algorithms, Theory, and Parallel Implementation (SIAM Press, Philadelphia, 2015).
  9. V. D. Korneev and V. M. Sveshnikov, “Parallel Algorithms and Domain Decomposition Techniques for Solving Three-Dimensional Boundary Value Problems on Quasi-Structured Grids,” Sib. Zh. Vych. Mat. 19 (2), 183-194 (2016) [Numer. Anal. Appl. 9 (2), 141-149 (2016)].
  10. I. A. Klimonov, V. D. Korneev, and V. M. Sveshnikov, “Parallelization Technologies for Solving Three-Dimensional Boundary Value Problems on Quasi-Structured Grids Using the CPU+GPU Hybrid Computing Environment,” Vychisl. Metody Programm. 17, 65-71 (2016).
  11. V. P. Il’in and B. I. Golubtsov, Automation of Solving Boundary Value Problems for Poisson’s Equation (Novosibirsk, Nauka 1969) [in Russian].
  12. A. N. Kozyrev and V. M. Sveshnikov, “On the Construction of Two-Dimensional Local-Modified Quasistructured Grids and Solving on Them Two-Dimensional Boundary Value Problems in the Domains with Curvilinear Boundary,” Vestn. Yuzhn. Ural. Gos. Univ. Ser. Vychisl. Mat. Inf. 6 (2), 5-21 (2017).
  13. V. M. Sveshnikov and B. D. Rybdylov, “About Parallelization of Solving of Boundary Value Problems on Quasistructured Grids,” Vestn. Yuzhn. Ural. Gos. Univ. Ser. Vychisl. Mat. Inf. 2 (3), 63-72 (2013).
  14. 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)].
  15. V. P. Il’in, Methods and Technologies of Finite Elements (Inst. Comput. Math. Math. Geophys., Novosibirsk, 2007) [in Russian].
  16. V. P. Il’in, Finite Difference and Finite Volume Methods for Elliptic Equations (Inst. Comput. Math. Math. Geophys., Novosibirsk, 2001) [in Russian].