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Comparison of Two Methods for Paralleling Computations When Solving the Integro-Differential Radiation Transport Equation

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Abstract

The problem of paralleling computations is considered when solving the integro-differential equation of radiation transport in strongly scattering media. Parallelization is performed for a two-step iterative algorithm for solving a system of mesh equations. The first step is a simple iteration. At the second step, a correction accelerating the convergence of iterations is added to the mesh values obtained at the first step. The equation for the correction is solved by the Krylov subspace method. The efficiency of the two methods of parallelization of the two-step iterative algorithm is compared. In the Block Jacobi (BJ) method, a simple iteration calculation is performed locally in each spatial subregion. The Block Seidel (BS) method performs an end-to-end analysis over the entire region. Both methods are implemented in the RADUGA T program for solving the transport equation on unstructured meshes. The effectiveness of the methods was studied on the model of a light-water reactor.

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REFERENCES

  1. M. P. Adams, M. L. Adams, W. D. Hawkins, T. Smith, L. Rauchwerger, N. M. Amato, T. S. Bailey, and R. D. Falgout, “Provably optimal parallel transport sweeps on regular grids,” in Proc. Int. Conf. on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2013) (Sun Valley, ID, USA, May 5–9, 2013) (ANS, LaGrange Park, IL, 2013), Vol. 4, pp. 2535–2553. URL: https://experts.illinois.edu/en/publications/provably-optimal-parallel-transport-sweeps-on-regular-grids;

  2. J. Comput. Phys. 407, 109234 (2020).

  3. Sh. D. Pautz and T. S. Bailey, “Parallel deterministic transport sweeps of structured and unstructured meshes with overloaded mesh decompositions,” Nucl. Sci. Eng. 185 (1), 70–77 (2017). https://doi.org/10.13182/NSE16-34

    Article  Google Scholar 

  4. T. Deakin, S. McIntosh-Smith, and W. Gaudin, “Many-core acceleration of a discrete ordinates transport mini-app at extreme scale,” in High Performance Computing, Proc. 31st Int. Conf. ISC High Performance 2016, Frankfurt, Germany, June 19–23, 2016, Ed. by J. M. Kunkel, P. Balaji, and J. Dongarra, Lecture Notes in Computer Science (Springer, Cham, 2016), Vol. 9697, pp. 429–448. https://doi.org/10.1007/978-3-319-41321-1_22

  5. R. S. Baker, “An SN Algorithm for modern architectures,” Nucl. Sci. Eng. 185 (1), 107–116 (2017). https://doi.org/10.13182/NSE15-124

    Article  Google Scholar 

  6. J. J. Jarrell, T. M. Evans, G. G. Davidson, and A. T. Godfrey, “Full core reactor analysis: Running Denovo on Jaguar,” Nucl. Sci. Eng. 175 (3), 283–291 (2013). https://doi.org/10.13182/NSE12-60

    Article  Google Scholar 

  7. D. F. Baydin and E. N. Aristova, “3D hexagonal parallel code QuDiff for calculating a fast reactor’s critical parameters,” Math. Models Comput. Simul. 8 (4), 446–452 (2016). https://doi.org/10.1134/S2070048216040025

    Article  MathSciNet  MATH  Google Scholar 

  8. A. M. Voloschenko, “Adaptive positive approximations and a consistent KP1 iteration acceleration scheme for the transport equation in radiation protection problems,” Doctoral (Phys. Math.) Dissertation (IPM im. M. V. Keldysha Ross. Akad. Nauk, Moscow, 2015) [in Russian].

  9. B. Turcksin, “Parallel Sn sweeps on adapted meshes,” in Proc. Joint Int. Conf. on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method (M&C+SNA+MC 2015) (Nashville, TN, USA, April 19–23, 2015) (ANS, LaGrange Park, IL, 2015), Vol. 3, pp. 1206–1217.

  10. Sh. D. Pautz, “An algorithm for parallel S n sweeps on unstructured meshes,” Nucl. Sci. Eng. 140 (2), 111–136 (2002). https://doi.org/10.13182/NSE02-1

    Article  Google Scholar 

  11. S. J. Plimpton, B. Hendrickson, Sh. P. Burns, W. McLendon III, and L. Rauchwerger, “Parallel S n sweeps on unstructured grids: algorithms for prioritization, grid partitioning, and cycle detection,” Nucl. Sci. Eng. 150 (3), 267–283 (2005). https://doi.org/10.13182/NSE150-267

    Article  Google Scholar 

  12. G. Colomer, R. Borrell, F. X. Trias, and I. Rodríguez, “Parallel algorithms for S n transport sweeps on unstructured meshes,” J. Comput. Phys. 232 (1), 118–135 (2013). https://doi.org/10.1016/j.jcp.2012.07.009

    Article  Google Scholar 

  13. J. Yan, G.-M. Tan, and N.-H. Sun, “Optimizing parallel S n sweeps on unstructured grids for multi-core clusters,” J. Comput. Sci. Technol. 28 (4), 657–670 (2013). https://doi.org/10.1007/s11390-013-1366-9

    Article  Google Scholar 

  14. R. Lenain, E. Masiello, F. Damian, and R. Sanchez, “Domain decomposition method for 2D and 3D transport calculations using Hybrid MPI/OPENMP parallelism,” in Proc. Joint Int. Conf. on Mathematics and Computation (M&C), Supercomputing in Nuclear Applications (SNA) and the Monte Carlo (MC) Method (M&C+SNA+MC 2015) (Nashville, TN, USA, April 19–23, 2015) (ANS, LaGrange Park, IL, 2015), Vol. 1, pp. 424–441. URL: https://hal-cea.archives-ouvertes.fr/cea-02506817/document.

  15. R. Yessayan, Y. Azmy, and S. Schunert, “Development of a parallel performance model for the THOR neutral particle transport code,” in Proc. Int. Conf. on Mathematics and Computational Methods Applied to Nuclear Science & Engineering (M&C 2017) (Jeju, South Korea, April 16–20, 2017) (ANS, LaGrange Park, IL, 2017), Vol. 1. URL: https://www.osti.gov/servlets/purl/1369430.

  16. O. V. Nikolaeva, “Methods for parallelizing computations in the “RADUGA T” code to solve the neutron transport equation on unstructured grids,” Vopr. At. Nauki Tekh. Ser. Mat. Model. Fiz. Protsessov, No. 1, 53–67 (2021).

    Google Scholar 

  17. N. I. Kokonkov and O. V. Nikolaeva, “An iterative KP1 method for solving the transport equation in 3D domains on unstructured grids,” Comput. Math. Math. Phys. 55 (10), 1698–1712 (2015). https://doi.org/10.1134/S0965542515100140

    Article  MathSciNet  MATH  Google Scholar 

  18. T. Takeda and H. Ikeda, “3-D neutron transport benchmarks,” J. Nucl. Sci. Technol. 28 (7), 656–669 (1991). https://doi.org/10.3327/jnst.28.65610.3327/jnst.28.656https://doi.org/10.1080/18811248.1991.9731408

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  1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

    O. V. Nikolaeva

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Nikolaeva, O.V. Comparison of Two Methods for Paralleling Computations When Solving the Integro-Differential Radiation Transport Equation. Math Models Comput Simul 13, 1087–1096 (2021). https://doi.org/10.1134/S2070048221060168

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