Geodesic
Solving reactor problems to determine the multiplication: A new method of accelerating outer iterations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 6, pp. 1007-1014 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new cyclic iterative method with variable parameters is proposed for accelerating the outer iterations in a process used to calculate $K_{\text{эфф}}$ 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 $K_{\text{эфф}}$, 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. 
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G. I. Kurchenkova; V. I. Lebedev. Solving reactor problems to determine the multiplication: A new method of accelerating outer iterations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 6, pp. 1007-1014. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_6_a6/

[1] Lebedev V. I., Marchuk G. I., Chislennye metody v teorii perenosa neitronov, Izd. 2-e, Atomizdat, M., 1981 | MR

[2] Lebedev V. I., Funktsionalnyi analiz i vychislitelnaya matematika, Izd. 4-e, Fizmatlit, M., 2005

[3] Lebedev V. I., “A new method for determining the roofs of polynomials otleast devicetion on a segment with weight and subject to additional conditions. Part I”, Russ. J. Numer. Analys. and Math. Modelling, 8:3 (1993), 195–222 | DOI | MR | Zbl

[4] Lebedev V. A., “A new method for determining the roofs of polynomials otleast devicetion on a segment with weight and subject to additional conditions. Part II”, Russ. J. Numer. Analys. and Math. Modelling, 8:5 (1993), 397–426 | DOI | MR | Zbl

[5] Lebedev V. I., “Ekstremalnye mnogochleny i metody optimizatsii vychislitelnykh algoritmov”, Matem. sb., 195:10 (2004), 21–66 | Zbl

[6] Lebedev V. I., Finogenov S. A., “Some algorithms for computing of Chebyshev normalized first Kind polynomials by roots”, Russ. J. Numer. Analys. Modelling, 20:4 (2005), 353–363 | DOI | MR | Zbl

[7] Lebedev V. I., “On formulae for roots of cubic equations”, Sovjet J. Numer. Analys. Math. Modelling, 6:4 (1991), 315–324 | DOI | MR | Zbl

[8] Kurchenkov A. Yu., Sidorenko V. D., “Otsenka izmeneniya doppler-effekta pri uchete teplovogo dvizheniya yader i rezonansnogo povedeniya secheniya rasseyaniya v indikatrise rasseyaniya”, Atomnaya energiya, 82:4 (1997), 321–327

[9] Sidorenko V. D., Bolschagin S. N., Lazarenko A. P. et al., “Spectral code TVS-M for calculation of characteristics of cells, supercells and fuel assemblies of VVER-type reactors”, Material of 5 AER Symp., Bulgaria, 1995, 121–127

[10] Aborina I., Bolobov P., Krainov Yu., “Calculation and experimental studies of power distribution in the normal and modernized CR of the VVER-440 reactor”, Simposium of AER, Inst. Nucl. Reactors, RRC “Kurchatov Institute”, M., sept. 2000, 52–58

[11] Novikov A. H., Pshenin V. V., Lizorkin M. P. i dr., “Paket programm dlya analiza yacheek VVER i nekotorye aspekty uluchsheniya toplivnykh tsiklov”, VANT. Ser. Fiz. yadernykh reaktorov, 1 (1992), 57–66