Splitting d'opérateur pour l'équation de transport neutronique en géométrie bidimensionnelle plane

Samir Akesbi

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 6, page 1109-1122
  • ISSN: 0764-583X

Abstract

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The aim of this work is to introduce and to analyze new algorithms for solving the transport neutronique equation in 2D geometry. These algorithms present the duplicate favors to be, on the one hand faster than some classic algorithms and easily to be implemented and naturally deviced for parallelisation on the other hand. They are based on a splitting of the collision operator holding amount of caracteristics of the transport operator. Some numerical results are given at the end of this work.

How to cite

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Akesbi, Samir. "Splitting d'opérateur pour l'équation de transport neutronique en géométrie bidimensionnelle plane." ESAIM: Mathematical Modelling and Numerical Analysis 34.6 (2010): 1109-1122. <http://eudml.org/doc/197409>.

@article{Akesbi2010,
abstract = { The aim of this work is to introduce and to analyze new algorithms for solving the transport neutronique equation in 2D geometry. These algorithms present the duplicate favors to be, on the one hand faster than some classic algorithms and easily to be implemented and naturally deviced for parallelisation on the other hand. They are based on a splitting of the collision operator holding amount of caracteristics of the transport operator. Some numerical results are given at the end of this work. },
author = {Akesbi, Samir},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Algorithms; convergence; neutronic transport; integro partial differential equations.; neutron transport equation; iterative method; convergence acceleration; algorithm; comparison of methods; operator splitting method; Gauss-Seidel method; successive overrelaxtion (SOR); Jacobi method; numerical examples},
language = {eng},
month = {3},
number = {6},
pages = {1109-1122},
publisher = {EDP Sciences},
title = {Splitting d'opérateur pour l'équation de transport neutronique en géométrie bidimensionnelle plane},
url = {http://eudml.org/doc/197409},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Akesbi, Samir
TI - Splitting d'opérateur pour l'équation de transport neutronique en géométrie bidimensionnelle plane
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 6
SP - 1109
EP - 1122
AB - The aim of this work is to introduce and to analyze new algorithms for solving the transport neutronique equation in 2D geometry. These algorithms present the duplicate favors to be, on the one hand faster than some classic algorithms and easily to be implemented and naturally deviced for parallelisation on the other hand. They are based on a splitting of the collision operator holding amount of caracteristics of the transport operator. Some numerical results are given at the end of this work.
LA - eng
KW - Algorithms; convergence; neutronic transport; integro partial differential equations.; neutron transport equation; iterative method; convergence acceleration; algorithm; comparison of methods; operator splitting method; Gauss-Seidel method; successive overrelaxtion (SOR); Jacobi method; numerical examples
UR - http://eudml.org/doc/197409
ER -

References

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  2. S. Akesbi, M.R. Laydi et M. Mokhtar-Kharroubi, Décomposition d'opérateurs et accélération de la convergence en neutronique. C.R. Acad. Sci. Paris Sér. I319 (1994) 765-770.  Zbl0806.65143
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  4. S. Akesbi et M. Nicolet, Nouveaux algorithmes performants en théorie du transport. ESAIM: M2AN32 (1998) 341-358.  
  5. S. Akesbi et M. Nicolet, Nouveaux algorithmes pour l'équation de transport en géométrie bidimensionnelle plane. C.R. Acad. Sci. Paris Sér. I324 (1997) 699-706.  Zbl0872.65113
  6. R.E. Alcoofe, Diffusion synthetic acceleration method for the diamond-differenced discrete-ordinates equations. Nucl. Sci. and Eng.64 (1977) 344-345.  
  7. P.G. Ciarlet, Introduction à l'analyse numérique matricielle et à l'optimisation. Masson (1982).  Zbl0488.65001
  8. R. Kress, Linear integral equations. Springer-Verlag (1989).  Zbl0671.45001
  9. E.W. Larsen, Unconditionally stable diffusion-synthetic acceleration methods for the slab geometry discrete-ordinates equations, Part I, Part II. Nucl. Sci. and Eng.82 (1982) 47-63.  
  10. I. Marek, Frobenius theory of positive operators, Comparison theorems and applications. SIAM J. Appl. Math.19 (1970).  Zbl0219.47022
  11. M. Mokhtar-Kharroubi, On the approximation of a class of transport equations. Transport Theory Statist. Phys.22 (1993) 561-570.  Zbl0788.65139
  12. P. Nelson, A Survey Convergence Results in Numerical Transport Theory, in: Com. Proceedings in honor of G.M. Wing's 65th birthday, Transport Theory, Invariant Imbedding, and Integral, P. Nelson et al. Eds. (1989).  
  13. R. Sanchez et N.J. McCormick, A review of Neutron Transport Approximations. Nucl. Sci. and Eng.80 (1982) 481-535.  
  14. R.S. Varga, Matrix Iterative Analysis. Prentice-Hall, Engelwood Cliffs, N.J. (1962).  

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