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Relaxation schemes for the M 1 model with space-dependent flux: application to radiotherapy dose calculation

hal.structure.identifierCentre d'Etudes Lasers Intenses et Applications [CELIA]
dc.contributor.authorPICHARD, Teddy
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorAREGBA-DRIOLLET, Denise
hal.structure.identifierInstitut de Mathématiques de Toulouse UMR5219 [IMT]
dc.contributor.authorBRULL, Stéphane
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorDUBROCA, Bruno
dc.contributor.authorFRANK, Martin
dc.date.accessioned2024-04-04T03:03:55Z
dc.date.available2024-04-04T03:03:55Z
dc.date.issued2016
dc.identifier.issn1815-2406
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/193110
dc.description.abstractEnBecause of stability constraints, most numerical schemes applied to hyper-bolic systems of equations turn out to be costly when the flux term is multiplied by some very large scalar. This problem emerges with the M 1 system of equations in the field of radiotherapy when considering heterogeneous media with very disparate densities. Additionally, the flux term of the M 1 system is non-linear, and in order for the model to be well-posed the numerical solution needs to fulfill conditions called realizability. In this paper, we propose a numerical method that overcomes the stability constraint and preserves the realizability property. For this purpose, we relax the M 1 system to obtain a linear flux term. Then we extend the stencil of the difference quotient to obtain stability. The scheme is applied to a radiotherapy dose calculation example.
dc.language.isoen
dc.publisherGlobal Science Press
dc.subject.enRadiotherapy
dc.subject.enMoments models
dc.subject.enrelaxation models
dc.subject.enmethod of characteristics
dc.title.enRelaxation schemes for the M 1 model with space-dependent flux: application to radiotherapy dose calculation
dc.typeArticle de revue
dc.identifier.doi10.4208/cicp.121114.210415a
dc.subject.halMathématiques [math]/Equations aux dérivées partielles [math.AP]
dc.subject.halMathématiques [math]/Analyse numérique [math.NA]
bordeaux.journalCommunications in Computational Physics
bordeaux.page168-191
bordeaux.volume19
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-01934314
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-01934314v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Computational%20Physics&rft.date=2016&rft.volume=19&rft.issue=1&rft.spage=168-191&rft.epage=168-191&rft.eissn=1815-2406&rft.issn=1815-2406&rft.au=PICHARD,%20Teddy&AREGBA-DRIOLLET,%20Denise&BRULL,%20St%C3%A9phane&DUBROCA,%20Bruno&FRANK,%20Martin&rft.genre=article


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