### Finite Element Method with Spectral Green's Function in Slab Geometry for Neutron Diffusion in Multiplying Media and One Energy Group

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R.E. Attar. “Legendre Polynomials and Functions”. CreateSpace, (2009).

R.C. Barros & E.W. Larsen. A Numerical Method for Multigroup Slab-Geometry Discrete Ordinates Problems with No Spatial Truncation Error. Transport Theory and Statistical Physics, 20 (1991), 441–462.

R.C. Barros & E.W. Larsen. A spectral nodal method for one-group X,Y-geometry discrete ordinates problems. Nuclear Science and Engineering, 111(1) (1992), 34–45.

R.C. Barros, H.A. Filho, E.T.V. Orellana, F.C. Silva, N. Couto, D.S. Dominguez & C.R.G. Hernandez. The Application of Spectral Nodal Methods to Discrete Ordinates and Diffusion Problems in Cartesian Geometry for Neutron Multiplying Systems. Progress in Nuclear Energy, 42 (2003), 385-426.

G.I. Bell & S. Glasstone. “Nuclear reactor theory”. Van Nostrand Reinhold Co., (1970).

S.C. Brenner & L.R. Scott. “The Mathematical Theory of Finite Element Methods”. Springer-Verlag New York, Inc., (1996).

R.L. Burden & D.J. Faires. “Numerical Analysis”. Ninth Edition, BROOKS/COLE – CENGAGE Learning, (2011).

K.M. Case & P.F. Zweifel. “Linear transport theory”. Addison-Wesley Pub. Co., (1967).

C. Ceolin, M. Schramm, B.E.J. Bodmann, M.T. Vilhena & S.B. Leite. On an analytical evaluation of the flux and dominant eigenvalue problem for the steady state multi-group multi-layer neutron diffusion equation. Kerntechnik, 79 (2014), 430–435.

D.S. Dominguez & R.C. Barros. The spectral Green’s function linear-nodal method for one-speed X,Y-geometry discrete ordinates deep penetration problems. Annals of Nuclear Energy, 34 (2007), 958.

D.S. Dominguez, C.R.G. Hernandez & R.C. Barros. Spectral nodal method for numerically solving two-energy group X,Y geometry neutron diffusion eigenvalue problems. International Journal of Nuclear Energy, Science and Technology (Print), 5 (2010), 66.

J.J. Duderstadt & L.J. Hamilton. “Nuclear Reactor Analysis”. John Wiley & Sons Inc, (1975).

Empresa de Pesquisa Energética. “Plano Nacional de Energia 2030”, Ministério de Minas e Energia, Rio de Janeiro, Brasil, (2007).

T. Hayashi & D. Inoue. Calculation of leaky Lamb waves with a semi-analytical finite element method. Ultrasonics, 54(6) (2014), 1460–1469.

J.D. Jung & W. Becker. Semi-analytical modeling of composite beams using the scaled boundary finite element method. Composite Structures, 137 (2016), 121–129.

J.R. Lamarsh & A.J. Baratta. “Introduction to Nuclear Engineering”. Prentice Hall, (2001).

E.E. Lewis & W.F. Miller Jr. “Computational Methods of Neutron Transport”. American Nuclear Society, Illinois, USA, (1993).

P. Liu, D. Wang & M. Oeser. Application of semi-analytical finite element method coupled with infinite element for analysis of asphalt pavement structural response. Journal of Traffic and Trans- portation Engineering (English Edition), 2(1) (2015), 48–58.

E. Sauter, F.S. Azevedo, M. Thompson & M.T. Vilhena. Eigenvalues of the Anisotropic Transport Equation in a Slab. Transport Theory and Statistical Physics, (2012), 448–472.

E. Sauter, F.S. Azevedo, M. Thompson & M.T.M.B. Vilhena. Solution of the one-dimensional trans- port equation by the vector Green function method: Error bounds and simulation. Applied Mathemat- ics and Computation, 219, (2013), 11291–11301.

A.C. da Silva, A.S. Martinez & A. da C. Gonçalves. Reconstruction of the Flux in a Slab Reactor. World Journal of Nuclear Science and Technology, (2012), 181–186.

W.M. Stacey. “Nuclear Reactor Physics”, Wiley-VCH, (2007).

O.C. Zienkiewicz. “The Finite Element Methods in Engineering Science”. McGraw-Hill, (1971).

DOI: https://doi.org/10.5540/tema.2016.017.02.0173

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