An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modelling

Detalhes bibliográficos
Autor(a) principal: Acevedo,Nancy I. Alvarez
Data de Publicação: 2010
Outros Autores: Roberty,Nilson Costa, Silva Neto,Antônio J
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Computational & Applied Mathematics
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300002
Resumo: In the present work the inverse problem of identification of radiative properties, the total extinction and scattering coefficients, is analyzed and explicitly formulated based in an elementary semi-group theory. The Chandrasekhar discrete ordinates finite dimensional approximation of the angular variables is used for the direct problem representation with the stationary Linear Transport (Boltzmann) Equation in absorbing and scattering media in matrix form. For the inverse problem we suppose known the albedo operator from measured intensities at the boundaries of the medium. Here we analize the inverse problem for an N-dimensional medium and from the solution of the transmission problem we present an explicit form for the matrix that contains the total extinction and scattering coefficients. Mathematical subject classification: 80A23, 15A29.
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spelling An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modellinginverse problemsDiscrete Ordinates Methodlinear transport equationradiative propertiesIn the present work the inverse problem of identification of radiative properties, the total extinction and scattering coefficients, is analyzed and explicitly formulated based in an elementary semi-group theory. The Chandrasekhar discrete ordinates finite dimensional approximation of the angular variables is used for the direct problem representation with the stationary Linear Transport (Boltzmann) Equation in absorbing and scattering media in matrix form. For the inverse problem we suppose known the albedo operator from measured intensities at the boundaries of the medium. Here we analize the inverse problem for an N-dimensional medium and from the solution of the transmission problem we present an explicit form for the matrix that contains the total extinction and scattering coefficients. Mathematical subject classification: 80A23, 15A29.Sociedade Brasileira de Matemática Aplicada e Computacional2010-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300002Computational & Applied Mathematics v.29 n.3 2010reponame:Computational & Applied Mathematicsinstname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)instacron:SBMAC10.1590/S1807-03022010000300002info:eu-repo/semantics/openAccessAcevedo,Nancy I. AlvarezRoberty,Nilson CostaSilva Neto,Antônio Jeng2010-11-22T00:00:00Zoai:scielo:S1807-03022010000300002Revistahttps://www.scielo.br/j/cam/ONGhttps://old.scielo.br/oai/scielo-oai.php||sbmac@sbmac.org.br1807-03022238-3603opendoar:2010-11-22T00:00Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)false
dc.title.none.fl_str_mv An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modelling
title An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modelling
spellingShingle An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modelling
Acevedo,Nancy I. Alvarez
inverse problems
Discrete Ordinates Method
linear transport equation
radiative properties
title_short An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modelling
title_full An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modelling
title_fullStr An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modelling
title_full_unstemmed An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modelling
title_sort An explicit formulation for the inverse transport problem using only external detectors: Part I: computational modelling
author Acevedo,Nancy I. Alvarez
author_facet Acevedo,Nancy I. Alvarez
Roberty,Nilson Costa
Silva Neto,Antônio J
author_role author
author2 Roberty,Nilson Costa
Silva Neto,Antônio J
author2_role author
author
dc.contributor.author.fl_str_mv Acevedo,Nancy I. Alvarez
Roberty,Nilson Costa
Silva Neto,Antônio J
dc.subject.por.fl_str_mv inverse problems
Discrete Ordinates Method
linear transport equation
radiative properties
topic inverse problems
Discrete Ordinates Method
linear transport equation
radiative properties
description In the present work the inverse problem of identification of radiative properties, the total extinction and scattering coefficients, is analyzed and explicitly formulated based in an elementary semi-group theory. The Chandrasekhar discrete ordinates finite dimensional approximation of the angular variables is used for the direct problem representation with the stationary Linear Transport (Boltzmann) Equation in absorbing and scattering media in matrix form. For the inverse problem we suppose known the albedo operator from measured intensities at the boundaries of the medium. Here we analize the inverse problem for an N-dimensional medium and from the solution of the transmission problem we present an explicit form for the matrix that contains the total extinction and scattering coefficients. Mathematical subject classification: 80A23, 15A29.
publishDate 2010
dc.date.none.fl_str_mv 2010-01-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300002
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1807-03022010000300002
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1590/S1807-03022010000300002
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv Computational & Applied Mathematics v.29 n.3 2010
reponame:Computational & Applied Mathematics
instname:Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
instacron_str SBMAC
institution SBMAC
reponame_str Computational & Applied Mathematics
collection Computational & Applied Mathematics
repository.name.fl_str_mv Computational & Applied Mathematics - Sociedade Brasileira de Matemática Aplicada e Computacional (SBMAC)
repository.mail.fl_str_mv ||sbmac@sbmac.org.br
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