A least square finite element formulation of the collimated irradiation in frequency domain for optical tomography applications

Journal of Quantitative Spectroscopy and Radiative Transfer

Volumn 111, Issue 2, 2010, Pages 280-286

  Balima, O ^a   Pierre, T ^a   Charette, A ^a   Marceau, D ^a  

^a UNIVERSITÉ DU QUÉBEC À CHICOUTIMI   (Canada)

Author keywords

Discrete ordinates method; Finite element method; Frequency modulation; Radiative transfer equation

Indexed keywords

ANISOTROPIC SCATTERING MEDIA; COLLIMATED IRRADIATION; DIRICHLET TYPE; DISCRETE ORDINATES METHOD; FINITE ELEMENT FORMULATIONS; FREQUENCY DOMAINS; LEAST SQUARE; NUMERICAL TESTS; RADIATIVE TRANSFER EQUATIONS; REFERENCE SOLUTION;

FREQUENCY DOMAIN ANALYSIS; FREQUENCY MODULATION; HEAT RADIATION; IRRADIATION; OPTICAL TOMOGRAPHY; RADIATIVE TRANSFER;

FINITE ELEMENT METHOD;

BOUNDARY CONDITION; FINITE ELEMENT METHOD; LEAST SQUARES METHOD; RADIATIVE TRANSFER; TOMOGRAPHY;

EID: 70449718838     PISSN: 00224073     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jqsrt.2009.07.002     Document Type: Review

References (17)

1. Arridge S.R. Optical tomography in medical imaging. Inverse Problems 15 (1999) R41-R93
2. Charette A, Boulanger J, Kim HK. Optical tomography as an inverse radiation problem. In: Fifth international symposium on radiation transfer, Bodrum, Turkey, 2007.
3. Ren K., Ball G., and Hielscher A.H. Frequency domain optical tomography based on the equation of radiative transfer. Society for Industrial and Applied Mathematics 28 4 (2006) 1463-1489
4. Kim H.K., and Charette A. Frequency domain optical tomography using a conjugate gradient method without line search. Journal of Quantitative Spectroscopy and Radiative Transfer 104 (2007) 248-256
5. Klose A., Netz U., Beuthan J., and Hielscher A. Optical tomography using the time-independent equation of radiative transfer-part 1: forward model. Journal of Quantitative Spectroscopy and Radiative Transfer 72 (2002) 691-713
6. Brooks A.N., and Hughes T.J.R. Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and Engineering (1990) 199-259
7. Pontaza J., and Reddy J. Least-square finite element formulation for one-dimensional radiative transfer. Journal of Quantitative Spectroscopy & Radiative Transfer 95 (2004) 387-406
8. Cockburn B., and Shu C. TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: general framework. Mathematics of Computation 52 (1989) 411-435
9. Balima O, Charette A, Marceau D. Comparison of light transport models in view of optical tomography applications. In: Advanced computational methods in engineering, Liege, Belgium, May, 2008. URL 〈http://www.ltas.ulg.ac.be/acomen2008/proceedings_all.htm〉.
10. Modest M.F. Radiative heat transfer, mechanical engineering (1993), McGraw-Hill, New York
11. Kim T., and Lee H. Radiative transfer in two-dimensional anisotropic scattering media with collimated incidence. Journal of Quantitative Spectroscopy & Radiative Transfer 42 3 (1989) 225-238
12. Fiveland W. Discrete ordinates solutions of the radiation transport equation for rectangular enclosures. Journal of Heat Transfer 106 (1984) 699-706
13. Chai J., Lee H., and Patankar S. Improved treatment of scattering using the discrete ordinates method. Journal of Heat Transfer 116 (1994) 260-263
14. Boulanger J., and Charette A. Reconstruction optical tomography using transient radiative transfer equation and pulse laser: a numerical study. Journal of Quantitative Spectroscopy & Radiative Transfer 93 (2005) 325-336
15. Hecht F., Pironneau O., Hyaric A.L., and Ohtsuka K. Freefem++. 2nd ed. (2008), Universite Pierre et Marie Curie, Paris. http://www.freefem.org/ff++/ftp/freefem++doc.pdf (URL 〈http://www.freefem.org/ff++/ftp/freefem++doc.pdf〉).
16. Kim T., and Lee H. Effect of anisotropic scattering on radiative heat transfer in two-dimensional rectangular enclosures. Journal of Heat and Mass Transfer 31 8 (1988) 1711-1721
17. Thurgood C. A critical evaluation of the discrete ordinates method using the HEART and Tn quadrature. PhD thesis, Departement of Chemical Engineering Queen's University, Kingston; 1992.