A Numerical Approach for a System of Transport Equations in the Field of Radiotherapy
| dc.contributor.author | PICHARD, Teddy | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRULL, Stéphane | |
| hal.structure.identifier | Laboratoire des Composites Thermostructuraux [LCTS] | |
| dc.contributor.author | DUBROCA, Bruno | |
| dc.date.accessioned | 2024-04-04T02:45:48Z | |
| dc.date.available | 2024-04-04T02:45:48Z | |
| dc.date.issued | 2019 | |
| dc.identifier.issn | 1815-2406 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191499 | |
| dc.description.abstractEn | Numerical schemes for systems of transport equations are commonly constrained by a stability condition of Courant-Friedrichs-Lewy (CFL) type. We consider a system modeling the steady transport of photons and electrons in the field of radiotherapy. Naive discretizations of such a system are commonly constrained by a very restrictive CFL condition. This issue is circumvented by constructing an implicit scheme based on a relaxation approach.We use an entropy-based moment model, namely the M1 model. Such a system of equations possesses the non-linear flux terms of a hyperbolic system but no time derivative. The flux terms are well-defined only under a condition on the unknowns, called realizability, which corresponds to the positivity of an underlying kinetic distribution function.The present numerical approach is applicable to non-linear systems which possess no hyperbolic operator, and it preserves the realizability property. However, the discrete equations are non-linear, and we propose a numerical method to solve such non-linear systems.Our approach is tested on academic and practical cases in 1D, 2D, and 3D and it is shown to require significantly less computational power than reference methods. | |
| dc.language.iso | en | |
| dc.publisher | Global Science Press | |
| dc.subject.en | Implicit scheme | |
| dc.subject.en | relaxation scheme | |
| dc.subject.en | M 1 model | |
| dc.subject.en | radiotherapy dose computation | |
| dc.title.en | A Numerical Approach for a System of Transport Equations in the Field of Radiotherapy | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.4208/cicp.OA-2017-0245 | |
| dc.subject.hal | Chimie/Matériaux | |
| bordeaux.journal | Communications in Computational Physics | |
| bordeaux.page | 1097-1126 | |
| bordeaux.volume | 25 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 4 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03334377 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03334377v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Communications%20in%20Computational%20Physics&rft.date=2019&rft.volume=25&rft.issue=4&rft.spage=1097-1126&rft.epage=1097-1126&rft.eissn=1815-2406&rft.issn=1815-2406&rft.au=PICHARD,%20Teddy&BRULL,%20St%C3%A9phane&DUBROCA,%20Bruno&rft.genre=article |
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