NumericalMethods for Balance Laws with Space Dependent Flux:Application to Radiotherapy Dose Calculation  

作　　者：Christophe Berthon Martin Frank Celine Sarazin Rodolphe Turpault 

机构地区：[1]Universite de Nantes,Laboratoire de Mathematiques Jean Leray,UMR6629,2 rue de la Houssiniere,BP 92208,44322 Nantes Cedex 3,France [2]RWTH Aachen University,Mathematics,Center for Computational Engineering Science,Schinkelstrasse 2,52062 Aachen,Germany

出　　处：《Communications in Computational Physics》2011年第10期1184-1210,共27页计算物理通讯（英文）

基　　金：supported by the Federation de Recherche des Pays de Loire FR9962 of the Centre National de la Recherche Scientifique(CNRS);by the German Research Foundation DFG under grant KL 1105/14/2;and by German Academic Exchange Service DAAD under grant D/0707534;The third author would like to thank the Fraunhofer ITWM for its financial support.

摘　　要：The present work is concerned with the derivation of numerical methods to approximate the radiation dose in external beam radiotherapy.To address this issue,we consider a moment approximation of radiative transfer,closed by an entropy minimization principle.The model under consideration is governed by a system of hyperbolic equations in conservation form supplemented by source terms.The main difficulty coming from the numerical approximation of this system is an explicit space dependence in the flux function.Indeed,this dependence will be seen to be stiff and specific numerical strategiesmust be derived in order to obtain the needed accuracy.A first approach is developed considering the 1D case,where a judicious change of variables allows to eliminate the space dependence in the flux function.This is not possible in multi-D.We therefore reinterpret the 1D scheme as a scheme on two meshes,and generalize this to 2D by alternating transformations between separate meshes.We call this procedure projection method.Several numerical experiments,coming from medical physics,illustrate the potential applicability of the developed method.

关 键 词：RADIOTHERAPY hyperbolic system of conservation laws source term approximations finite volume methods 

分 类 号：O17[理学—数学]