Free Access
Volume 36, Number 1, January/February 2002
Page(s) 69 - 86
Published online 15 April 2002
  1. M.L. Adams and E.W. Larsen, Fast iterative methods for deterministic particle transport computations. Preprint (2001). [Google Scholar]
  2. R.E. Alcouffe, Diffusion synthetic acceleration methods for the diamond-differenced discrete-ordinates equations. Nucl. Sci. Eng. 64 (1977) 344. [Google Scholar]
  3. G. Allaire and G. Bal, Homogenization of the criticality spectral equation in neutron transport. ESAIM: M2AN 33 (1999) 721-746. [CrossRef] [EDP Sciences] [Google Scholar]
  4. S.R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions. Med. Phys. 27 (2000) 252-264. [CrossRef] [PubMed] [Google Scholar]
  5. G. Bal, Couplage d'équations et homogénéisation en transport neutronique. Thèse de Doctorat de l'Université Paris 6 (1997). In French. [Google Scholar]
  6. G. Bal, First-order corrector for the homogenization of the criticality eigenvalue problem in the even parity formulation of the neutron transport. SIAM J. Math. Anal. 30 (1999) 1208-1240. [CrossRef] [MathSciNet] [Google Scholar]
  7. G. Bal,Spatially varying discrete ordinates methods in XY-geometry. M 3AS (Math. Models Methods Appl. Sci.) 10 (2000) 1277-1303. [Google Scholar]
  8. G. Bal, Transport through diffusive and non-diffusive regions, embedded objects, and clear layers. To appear in SIAM J. Appl. Math. [Google Scholar]
  9. G. Bal, V. Freilikher, G. Papanicolaou, and L. Ryzhik, Wave transport along surfaces with random impedance. Phys. Rev. B 6 (2000) 6228-6240. [CrossRef] [Google Scholar]
  10. G. Bal and L. Ryzhik, Diffusion approximation of radiative transfer problems with interfaces. SIAM J. Appl. Math. 60 (2000) 1887-1912. [CrossRef] [MathSciNet] [Google Scholar]
  11. A. Bensoussan, J.-L. Lions, and G. Papanicolaou, Boundary layers and homogenization of transport processes. Res. Inst. Math. Sci. Kyoto Univ. 15 (1979)53-157. [Google Scholar]
  12. J.-F. Bourgat, P. Le Tallec, B. Perthame, and Y. Qiu, Coupling Boltzmann and Euler equations without overlapping, in Domain Decomposition Methods in Science and Engineering, The Sixth International Conference on Domain Decomposition, Como, Italy, June 15-19, 1992, Contemp. Math. 157, American Mathematical Society, Providence, RI (1994) 377-398. [Google Scholar]
  13. M. Cessenat, Théorèmes de trace Lp pour des espaces de fonctions de la neutronique. C. R. Acad. Sci. Paris Sér. I Math. 299 (1984) 831-834. [Google Scholar]
  14. S. Chandrasekhar, Radiative Transfer. Dover Publications, New York (1960). [Google Scholar]
  15. P.G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland Publishing Company, Amsterdam, New York, Oxford (1978). [Google Scholar]
  16. R. Dautray and J.-L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology 6. Springer-Verlag, Berlin (1993). [Google Scholar]
  17. J.J. Duderstadt and W.R. Martin, Transport Theory. Wiley-Interscience, New York (1979). [Google Scholar]
  18. M. Firbank, S.A. Arridge, M. Schweiger, and D.T. Delpy, An investigation of light transport through scattering bodies with non-scattering regions. Phys. Med. Biol. 41 (1996) 767-783. [CrossRef] [PubMed] [Google Scholar]
  19. F. Gastaldi, A. Quarteroni, and G. Sacchi Landriani, On the coupling of two-dimensional hyperbolic and elliptic equations: analytical and numerical approach, in Domain Decomposition Methods for Partial Differential Equations, Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, Houston, TX, 1989, SIAM, Philadelphia, PA (1990) 22-63. [Google Scholar]
  20. F. Golse, P.-L. Lions, B. Perthame, and R. Sentis, Regularity of the moments of the solution of a transport equation. J. Funct. Anal. 76 (1988) 110-125. [CrossRef] [MathSciNet] [Google Scholar]
  21. A.H. Hielscher, R.E. Alcouffe, and R.L. Barbour, Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues. Phys. Med. Biol. 43 (1998) 1285-1302. [CrossRef] [PubMed] [Google Scholar]
  22. A. Ishimaru, Wave Propagation and Scattering in Random Media. Academics, New York (1978). [Google Scholar]
  23. B. Lapeyre, E. Pardoux and R. Sentis, Méthodes de Monte-Carlo pour les équations de transport et de diffusion, in Mathématiques & Applications 29, Springer-Verlag, Berlin (1998). [Google Scholar]
  24. C.D. Levermore, W.J. Morokoff and B.T. Nadiga, Moment realizability and the validity of the Navier-Stokes equations for rarefied gas dynamics. Phys. Fluids 10 (1998) 3214-3226. [CrossRef] [MathSciNet] [Google Scholar]
  25. E.E. Lewis and W.F. Miller Jr., Computational Methods of Neutron Transport. John Wiley & Sons, New York (1984). [Google Scholar]
  26. L.D. Marini and A. Quarteroni, A Relaxation procedure for domain decomposition methods using finite elements. Numer. Math. 55 (1989) 575-598. [CrossRef] [MathSciNet] [Google Scholar]
  27. J. Planchard, Méthodes mathématiques en neutronique, in Collection de la Direction des Études et Recherches d'EDF, Eyrolles (1995). In French. [Google Scholar]
  28. L. Ryzhik, G. Papanicolaou, and J.B. Keller, Transport equations for elastic and other waves in random media. Wave Motion 24 (1996) 327-370. [CrossRef] [MathSciNet] [Google Scholar]
  29. H. Sato and M.C. Fehler, Seismic Wave Propagation and Scattering in the Heterogeneous Earth, in AIP Series in Modern Acoustics and Signal Processing, AIP Press, Springer, New York (1998). [Google Scholar]
  30. M. Tidriri, Asymptotic analysis of a coupled system of kinetic equations. C. R. Acad. Sci. Paris Sér. I 328 (1999) 637-642. [Google Scholar]
  31. S. Tiwari, Application of moment realizability criteria for the coupling of the Boltzmann and Euler equations. Transport Theory Statist. Phys. 29 (2000) 759-783. [CrossRef] [MathSciNet] [Google Scholar]

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