Numerical treatment of a time dependent inverse problem in photon transport

S. Pieraccini; R. Riganti; A. Belleni-Morante

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 3, page 773-779
  • 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 forward problem, an iterative procedure is used to compute the values of the source intensity at increasing values of the time.

How to cite

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Pieraccini, S., Riganti, R., and Belleni-Morante, A.. "Numerical treatment of a time dependent inverse problem in photon transport." Bollettino dell'Unione Matematica Italiana 8-B.3 (2005): 773-779. <http://eudml.org/doc/195161>.

@article{Pieraccini2005,
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 forward problem, an iterative procedure is used to compute the values of the source intensity at increasing values of the time.},
author = {Pieraccini, S., Riganti, R., Belleni-Morante, A.},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {773-779},
publisher = {Unione Matematica Italiana},
title = {Numerical treatment of a time dependent inverse problem in photon transport},
url = {http://eudml.org/doc/195161},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Pieraccini, S.
AU - Riganti, R.
AU - Belleni-Morante, A.
TI - Numerical treatment of a time dependent inverse problem in photon transport
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/10//
PB - Unione Matematica Italiana
VL - 8-B
IS - 3
SP - 773
EP - 779
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 forward problem, an iterative procedure is used to compute the values of the source intensity at increasing values of the time.
LA - eng
UR - http://eudml.org/doc/195161
ER -

References

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  1. ANIKONOV, E. - BUBNOV, B. A., Inverse problems of transport theory, Sov. Math. Dokl., 37 (1988), 497-500. Zbl0699.35251MR947226
  2. BELLENI-MORANTE, A., A time dependent inverse problem in photon transport, in: New Trends in Mathematical Physics, World Scientific, Singapore (2004), 1-11. Zbl1109.82022MR2163962
  3. BELLENI-MORANTE, A. - MONACO, R. - RIGANTI, R. - SALVARANI, F., A numerical approach to inverse problems in photon transport inside an interstellar cloud, Appl. Math. Comput., 154 (2004), 115-126. Zbl1063.65152MR2066184
  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. DYSON, J. E. - WILLIAMS, D. A., The physics of interstellar medium, Inst. of Phys. Publ. (Bristol, 1997). Zbl1090.85500
  6. 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
  7. POMRANING, G. C., Radiation Hydrodynamics, Prentice Hall Series in Computational Mathematics, Pergamon Press, Oxford, 1973. 
  8. SHARAFUTDINOV, V. A., The inverse problem of determining a source in a stationary transport equation, Dokl. Math., 53 (1996), 251-253. Zbl0892.58088
  9. 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. Zbl0927.65111MR1728856
  10. STEFANOV, P., Inverse problems in transport theory, in: InsideOut: Inverse Problems and Applications (G. Uhlmann, Ed.), MSRI Publications, vol. 47, Cambridge Univ. Press, Cambridge (2003), 111-131. Zbl1083.45008MR2029679

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