Résumé : Radiotherapy treatments consists in irradiating the patient with beams of energetic particles (typically photons) targeting the tumor. Such particles are transported through the medium deposit energy in the medium. This deposited energy is the so-called dose, responsible for the biological effect of the radiations. The present work aim to develop numerical methods for dose computation and optimization that are competitive in terms of computational cost and accuracy compared to reference method. The motion of particles is first studied through a system of linear transport equations at the kinetic level. Then the method of moment is used to reduce the computational costs leading to the so-called Mn models. Standard numerical schemes for moment equations are constrained by stability conditions which happen to be very restrictive when the medium contains low density regions. Inconditionally stable numerical schemes adapted to moment equations are developed.
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