Skip to main content
SpringerLink
Log in

Solving reactor problems to determine the multiplication: A new method of accelerating outer iterations

  • Published:
Computational Mathematics and Mathematical Physics Aims and scope Submit manuscript

Abstract

A new cyclic iterative method with variable parameters is proposed for accelerating the outer iterations in a process used to calculate K eff in multigroup problems. The method is based on the use of special extremal polynomials that are distinct from Chebyshev polynomials and take into account the specific nature of the problem. To accelerate the convergence with respect to K eff, the use of three orthogonal functionals is proposed. Their values simultaneously determine the three maximal eigenvalues. The proposed method was incorporated in the software for neutron-physics calculations for WWER reactors.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. I. Lebedev and G. I. Marchuk, Numerical Methods in the Theory of Neutron Transport (Atomizdat, Moscow, 1981) [in Russian].

    Google Scholar 

  2. V. I. Lebedev, Functional Analysis and Computational Mathematics (Fizmatlit, Moscow, 2005) [in Russian].

    Google Scholar 

  3. V. I. Lebedev, “A New Method for Determining the Roots of Polynomials of Least Deviation on a Segment with Weight and Subject to Additional Conditions. Part I,” Russ. J. Numer. Anal. Math. Model. 8, 195–222 (1993).

    MATH  Google Scholar 

  4. V. I. Lebedev, “A New Method for Determining the Roots of Polynomials of Least Deviation on a Segment with Weight and Subject to Additional Conditions. Part II,” Russ. J. Numer. Anal. Math. Model. 8, 397–426 (1993).

    Article  MATH  Google Scholar 

  5. V. I. Lebedev, “Extremal Polynoials and Optimization Techniques for Computational Algorithms,” Mat. Sb. 195(10), 21–66 (2004).

    Google Scholar 

  6. V. I. Lebedev and S. A. Finogenov, “Some Algorithms for Computing of Chebyshev Normalized First Kind Polynomials by Roots,” Russ. J. Numer. Anal. Model. 20, 353–363 (2005).

    Article  MATH  MathSciNet  Google Scholar 

  7. V. I. Lebdev, “On Formulae for Roots of Cubic Equations,” Sov. J. Numer. Anal. Math. Model. 6, 315–324 (1991).

    Article  Google Scholar 

  8. A. Yu. Kurchenkov and V. D. Sidorenko, “Estimate of the Doppler Effect Change Taking into Account the Thermal Motion of Nuclei and the Resonance Behavior of the Scattering Cross Section in the Scattering Indicatrix” (Atomizdat, Moscow, 1997), Vol. 82, issue 4, pp. 321–327.

    Google Scholar 

  9. V. D. Sidorenko, S. N. Bolschagin, A. P. Lazarenko, et al., Spectral Code TVS-M for Calculation of Characteristics of Cells, Supercells and Fuel Assemblies of VVER-Type Reactors,” in Proc. of the 5th AER Symp., 1995, pp. 121–127.

  10. I. Aborina, P. Bolobov, and Yu. Krainov, “Calculation and Experimental Studies of Power Distribution in the Normal and Modernized CR of the WWER-440 Reactor,” in Simp. of AER, Inst. Nucl. Reactors, RRC Kurchatov Institute, Moscow, 2000, pp. 52–58.

  11. A. N. Novikov, V. V. Pshenin, M. P. Lizorkin, et al., “A Package of Programs for the Analysis of Cells in WWER and Improving the Fuel Cycle,” VANT, Ser. Fiz. Nucl. Reactors, 1, 57–66 (1992).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kurchatov Institute Russian Research Center, pl. Akademika Kurchatova 1, Moscow, 123182, Russia

    G. I. Kurchenkova

  2. Institute of Numerical Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119333, Russia

    V. I. Lebedev

Authors
  1. G. I. Kurchenkova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. I. Lebedev
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © G.I. Kurchenkova, V.I. Lebedev, 2007, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2007, Vol. 47, No. 6, pp. 1007–1014.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kurchenkova, G.I., Lebedev, V.I. Solving reactor problems to determine the multiplication: A new method of accelerating outer iterations. Comput. Math. and Math. Phys. 47, 962–969 (2007). https://doi.org/10.1134/S0965542507060073

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0965542507060073

Keywords

Search

Navigation