Numerical Treatment of a Time Dependent Inverse Problem in Photon Transport

Sandra Pieraccini; Riccardo Riganti; Aldo Belleni-Morante

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 1, page 195-211
  • ISSN: 0392-4041

Abstract

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The time-dependent intensity of a UV -photon source, located inside an interstellar cloud, is determined by formulating and solving an inverse problem for the integro-differential transport equation of photons in a one-dimensional slab. Starting from a discretizazion of the direct problem, an iterative procedure is used to compute the values of the source intensity at increasing values of time, and it is applied in some numerical simulations, whose results are presented and discussed.

How to cite

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Pieraccini, Sandra, Riganti, Riccardo, and Belleni-Morante, Aldo. "Numerical Treatment of a Time Dependent Inverse Problem in Photon Transport." Bollettino dell'Unione Matematica Italiana 10-B.1 (2007): 195-211. <http://eudml.org/doc/290381>.

@article{Pieraccini2007,
abstract = {The time-dependent intensity of a UV -photon source, located inside an interstellar cloud, is determined by formulating and solving an inverse problem for the integro-differential transport equation of photons in a one-dimensional slab. Starting from a discretizazion of the direct problem, an iterative procedure is used to compute the values of the source intensity at increasing values of time, and it is applied in some numerical simulations, whose results are presented and discussed.},
author = {Pieraccini, Sandra, Riganti, Riccardo, Belleni-Morante, Aldo},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {195-211},
publisher = {Unione Matematica Italiana},
title = {Numerical Treatment of a Time Dependent Inverse Problem in Photon Transport},
url = {http://eudml.org/doc/290381},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Pieraccini, Sandra
AU - Riganti, Riccardo
AU - Belleni-Morante, Aldo
TI - Numerical Treatment of a Time Dependent Inverse Problem in Photon Transport
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/2//
PB - Unione Matematica Italiana
VL - 10-B
IS - 1
SP - 195
EP - 211
AB - The time-dependent intensity of a UV -photon source, located inside an interstellar cloud, is determined by formulating and solving an inverse problem for the integro-differential transport equation of photons in a one-dimensional slab. Starting from a discretizazion of the direct problem, an iterative procedure is used to compute the values of the source intensity at increasing values of time, and it is applied in some numerical simulations, whose results are presented and discussed.
LA - eng
UR - http://eudml.org/doc/290381
ER -

References

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  2. BELLENI-MORANTE, A., A time dependent inverse problem in photon transport, World Scientific, Singapore (in press). Zbl1109.82022MR2163962
  3. BELLENI-MORANTE, A. - MONACO, R. - RIGANTI, R. - SALVARANI, F., A numerical approach to inverse problems in photon transport inside an intersetllar cloud, Appl. Math. Comput., 154 (2004), 115-126. Zbl1063.65152MR2066184DOI10.1016/S0096-3003(03)00695-7
  4. BELLENI-MORANTE, A. - MONACO, R. - SALVARANI, F., Approximated solutions of photon transport in a time-dependent region, Transp. Theory Stat. Phys.30 (2001), 421-438. Zbl1086.45503
  5. BELLENI-MORANTE, A. - RIGANTI, R., Inverse problems in photon transport. Part II: features of a source inside an interstellar cloud, Proceedings of the XII Int. Conference on Waves and Stability in Continuous Media (R. Monaco, S. Pennisi, S. Rionero, T. Ruggeri, Eds.), World Scientific, Singapore (2004), 60-69. Zbl1066.35106MR2089832DOI10.1142/9789812702937_0008
  6. DYSON, J. E. - WILLIAMS, D. A., The physics of interstellar medium, Inst. of Phys. Publ., Bristol, 1997. Zbl1090.85500
  7. GRYN', V. I. - NITISHINSKAY, L. V., Inverse three-dimensional problems of the simultaneous determination of the absorption coefficient and the source function for the transport equation, Comput. Math. Math. Phys., 32 (1992), 81-95. Zbl0788.45009MR1164462
  8. POMRANING, G. C., Radiation Hydrodynamics, Prentice Hall Series in Computational Mathematics, Pergamon Press, Oxford, 1973. 
  9. SHARAFUTDINOV, V. A., The inverse problem of determining a source in a stationary transport equation, Dokl. Math., 53 (1996), 251-253. Zbl0892.58088MR1398761
  10. SHU, C.-W., Essentially Non-oscillatory and Weighted Essentially Non-oscillatory Schemes for Hyperbolic Conservation Laws, in Advanced numerical approximation of nonlinear hyperbolic equations, Lecture Notes in Mathematics1697, Springer, 2000. MR1728856DOI10.1007/BFb0096355
  11. STEFANOV, P., Inverse problems in transport theory, in: Inside Out: Inverse Problems and Applications (G. Uhlmann, Ed.), MSRI Publications, 47, Cambridge Univ. Press, Cambridge (2003), 111-131. Zbl1083.45008MR2029679

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