Chebyshev acceleration of criticality calculations in boundary element applications to neutron diffusion

References

1 Ozgener, B.; Ozgener, H. A.: The solution of the criticality eigenvalue problems in the application of the boundary element method to the neutron diffusion equation. Annals of Nuclear Energy20 (7) (1993) 503 10.1016/0306-4549(93)90090-CSearch in Google Scholar

2 Brebbia, C. A.; Dominguez, J.: Boundary Elements an Introductory Course. Computational Mechanics Publications. Avon. 1989Search in Google Scholar

3 Itagaki, M.: Boundary element methods applied to two-dimensional neutron diffusion Equation. Journal of Nuclear Science and Technology22 (1985) 565Search in Google Scholar

4 Purwadi, M. D.; Tsuji, M. N.; Narita, M.; Itagaki, M.: An application of the domain decomposition method into the boundary element method for solving the multi-region neutron diffusion equation. Engineering Analysis with Boundary Elements20 (1998) 197Search in Google Scholar

5 Ozgener, B.; Ozgener, H. A.: A multi-region boundary element method for multigroup neutron diffusion calculations. Annals of Nuclear Energy28 (6) (2001) 585 10.1016/S0306-4549(00)00074-8Search in Google Scholar

6 Maiani, M.; Montagnini, B.: A Galerkin approach to the boundary element-response matrix method for the multigroup neutron diffusion equations. Annals of Nuclear Energy31 (2004) 1447Search in Google Scholar

7 Cavdar, S.; Ozgener, H. A.: A finite element/boundary element hybrid method for 2-D neutron diffusion calculations. Annals of Nuclear Energy31 (2004) 1555 10.1016/j.anucene.2004.04.006Search in Google Scholar

8 Ozgener, B.; Cavdar, S.; Ozgener, H. A.: The extension of the 2-D finite element/boundary element hybrid method to general multigroup neutron diffusion theory. Kerntechnik72 (2007) 280Search in Google Scholar

9 Nowak, A. J.; Neves, A. C.: The Multiple Reciprocity Boundary Element Methods, Computational Mechanics Publications. Southampton, Boston. 1994Search in Google Scholar

10 Ozgener, B.; Ozgener, H. A.: The application of the multiple reciprocity method to the boundary element formulation of the neutron diffusion equation. Annals of Nuclear Energy21 (11) (1994) 711 10.1016/0306-4549(94)90037-XSearch in Google Scholar

11 Ozgener, B.: A boundary integral equation for boundary element applications in multigroup neutron diffusion theory. Annals of Nuclear Energy25 (6) (1998) 347 10.1016/S0306-4549(97)00073-XSearch in Google Scholar

12 Alp, C.: The calculation of neutron physics design of a new type pool reactor in the form of a checker-board core (in Turkish), Ph.D. Thesis, Institute of Nuclear Energy, Istanbul Technical University, 1976Search in Google Scholar

13 Saad, Y.: Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems. Mathematics of Computation42 (166) (1984) 567 10.1090/S0025-5718-1984-0736453-8Search in Google Scholar

14 Ozgener, B.; Kabadayi, Y.: The acceleration of the finite element solutions of the diffusion theory criticality eigenvalue problem by Chebyshev polynomial extrapolation (in Turkish). In Proceedings of the Seventh National Meetings on Nuclear Sciences and Technology, Istanbul, September 1–6, 1996Search in Google Scholar

15 Woznicki, Z. I.: The numerical analysis of eigenvalue problem solutions in the multigrup neutron diffusion theory. Progress in Nuclear Energy33 (3) (1998) 301 10.1016/S0149-1970(96)00026-1Search in Google Scholar

16 Wang, Y.; Bangerth, W.; Ragusa, J.: Three-dimensional h-adaptivity for the multigroup neutron diffusion equations. Progress in Nuclear Energy51 (3) (2009) 543 10.1016/j.pnucene.2008.11.005Search in Google Scholar

17 Nakamura, S.: Coarse mesh acceleration of iterative solution of neutron diffusion equation. Nuclear Science and Engineering43 (1971) 116Search in Google Scholar

18 Vidal, V.; Verdu, G.; Ginestar, D.; Munoz-Cobo, J. L.: Variational acceleration for subspace iteration method. Application to Nuclear Power Reactors. International Journal for Numerical Methods in Engineering41 (1998) 391Search in Google Scholar

19 Engin, O.: Chebyshev polynomial acceleration in the application of the boundary element method to the neutron diffusion equation (in Turkish), Ph.D. Thesis. Institute of Energy, Istanbul Technical University, 2006Search in Google Scholar

20 Varga, R. S.: Matrix iterative analysis. Prentice-Hall, Englewood Cliffs, N.J.1962Search in Google Scholar

21 Faddeeva, V. N.: Computational Methods of Linear Algebra (Translated by C. D.Benster). Dover Pub. Inc., New York. 1959Search in Google Scholar

22 Fox, L.; Parker, I. B.: Chebyshev Polynomials in Numerical Analysis. Oxford University Press, London. 1968Search in Google Scholar

23 Mason, J. C.; Handscomb, D. C.: Chebyshev polynomials. Chapman & Hall/CRC, Boca Raton, Fla. 200310.1201/9781420036114Search in Google Scholar

24 Hageman, L. A.; Young, D. M.: Applied Iterative Methods. Academics Press, Inc.New York1981Search in Google Scholar

25 Varga, R. S.: Numerical methods for solving multigroup diffusion equations. Proceedings of Symposia in Applied Mathematics, Nuclear Reactor Theory, American Mathematical Society, Providence, Rhode Islands11 (1961) 164Search in Google Scholar