@Article{CiCP-19-1,
author = {Teddy, Pichard and Denise, Aregba-Driollet and Stéphane, Brull and Dubroca, Bruno and Martin, Frank},
title = {Relaxation Schemes for the $M_1$ Model with Space-Dependent Flux: Application to Radiotherapy Dose Calculation},
journal = {Communications in Computational Physics},
year = {2016},
volume = {19},
number = {1},
pages = {168--191},
abstract = {<p style="text-align: justify;">Because of stability constraints, most numerical schemes applied to hyperbolic
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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.121114.210415a},
url = {https://global-sci.com/article/80249/relaxation-schemes-for-the-m-1-model-with-space-dependent-flux-application-to-radiotherapy-dose-calculation}
}