Numerical analysis of iterative algorithms for an inverse boundary transport problem

Mathematical Models and Methods in Applied Sciences

Volumn 10, Issue 1, 2000, Pages 11-20

  Agoshkov, V I ^a   Parmuzin, E I ^a   Shutyaev, V P ^a   Bardos, C ^b  

^a INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0346225579     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0218202500000033     Document Type: Article

References (34)

1. V. A. Ambartsumyan, Scattering and absorption of light in planetary atmospheres, Uchen. Zap LGU 82 (1941) (in Russian).
2. S. Chandrasekhar, Radiative Transfer (Claderon Press, 1950).
3. V. I. Lebedev and V. I. Agoshkov, Generalized Schwartz's algorithm with variable parameters, preprint No. 18, Dept. of Numerical Math., USSR Academy of Sciences, Moscow, 1981 (in Russian).
4. V. I. Lebedev and V. I Agoshkov, The Poincaré-Steklov Operators and Applications to Analysis, Dept. of Numerical Math., USSR Academy of Sciences, Moscow, 1983 (in Russian).
5. V. I. Agoshkov, Generalized Solutions of Transport Equations and their Smoothness Properties (Nauka, 1988) (in Russian).
6. V. I. Agoshkov, Reflection operators and domain decomposition methods in transport theory problems, Sov. J. Numer. Anal. Math. Modelling 2 (1987) 325-347.
7. V. I. Agoshkov, On the existence of traces of functions in spaces used in transport theory problems, Dokl. Akad. Nauk SSSR 288 (1986) 265-269.
8. V. S. Vladimirov, Mathematical problems of monenergetic particle transport theory, Trudy Math. Stek. Inst., Akad. Nauk SSSR 61 (1961) (in Russian).
9. G. I. Marchuk, Design of Nuclear Reactors (Atomizdat, 1961) (in Russian).
10. V. V. Sobolev, Light Scattering in Planetary Atomspheres (Pergamon Press, 1973).
11. G. I. Marchuk and V. I. Agoshkov, Reflection operators and contemporary applications to radiative transfer, Appl. Math. Comput. 80 (1995) 1-19.
12. V. I. Agoshkov, Domain decomposition methods in problems of hydrodynamics. I. Problem of plain circulation in ocean, Department of Numerical Mathematics, Moscow, preprint No. 96, 1985 (in Russian).
13. V. I. Agoshkov, Domain decomposition methods and perturbation methods for solving some time dependent problems of fluid dynamics, in Proc. of the First International Interdisciplinary Conference. Olympia - 91, Athens, 1991, pp. 13-17.
14. G. I. Marchuk, Equation for importance of information from meteorological satellites and statement of inverse problems, Kosmicheskie Issledovaniya (Space Research) 2 (1964) 462-477.
15. Ed. A. N. Tikhonov, III-Posed Problems in Natural Science (VSP, 1992).
16. A. L. Ivankov, Inverse problems for the nonstationary kinetic transport equations, in Ref. 15.
17. A. I. Prilepko, D. G. Orlovskii and I. A. Vasin, Inverse problems in mathematical physics, in Ref. 15.
18. Yu. E. Anikonov, New methods and results in multidimensional inverse problems for kinetic equations, in Ref. 15.
19. R. Lattes and J.-L. Lions, Methode de Quasi-Reversibilité et Applications (Dunod, 1967).
20. C. Bardos, Mathematical approach for the inverse problem in radiative media (1986) unpublished.
21. K. M. Case, Inverse problem in transport theory, Phys. Fluids 16 (1973) 1607-1611.
22. L. P. Niznik and V. G. Tarasov, Reverse scattering problem for a transport equation with respect to directions, preprint, Institute of Mathematics, Academy Sciences of the Ukrainian SSR, 1980.
23. K. K. Hunt and N. J. McCormick, Numerical test of an inverse method for estimating single-scattering parameters from pulse multiple-scattering experiments, J. Opt. Soc. Am. A2 (1985) 11-25.
24. N. J. McCormick, Recent development in inverse scattering transport method, Transport Theory Statist. Phys. 13 (1984) 15-28.
25. C. Bardos, R. Santos and R. Sentis, Diffusion approximation and the computation of critical size, Tans. Amer. Math. Soc. 284 (1986) 617-649.
26. C. Bardos, R. Caflish and B. Nicolaenko, Different aspects of the Milne problem, Transport Theory Statist. Phys. 16 (1987) 561-585.
27. V. P. Shutyaev, Integral reflection operators and solvability of inverse transport problem, in Integral Equations in Applied Modelling, Kiev: Inst. of Electrodynamics, Academy of Sciences of Ukraine, 2 (1986) 243-244 (in Russian).
28. V. I. Agoshkov and C. Bardos, Inverse radiative transfer problems: the problem on boundary function, Centre de mathematiques et Leurs Applications, ENS CACHAN, France, preprint No. 9801, 1998.
29. G. I. Marchuk and V. I. Lebedev, Numerical Methods in the Theory of Neutron Transport (Academic Publisher, 1986).
30. V. P. Shutyaev, Some properties of the control operator in the problem of data assimilation and iterative algorithms, Russ. J. Numer. Anal. Math. Modelling 10 (1995) 357-371.
31. T. A. Germogenova, On inverse problems of atmospheric optics, Sov. Dokl. 285 (1985) 1091-1095.
32. H. van der Vorst, Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 13 (1992) 631-644.
33. T. A. Sushkevich, S. A. Strelkov and A. A. Ioltukhovski, Method of Characteristics in Problems of Atmospheric Optics (Nauka, 1990) (in Russian).
34. G. M. Vainikko and A. Yu. Veretennikov, Iterative Procedures in III-Posed Problems (Nauka, 1986) (in Russian).