Numerical Methods for Balance Laws with Space Dependent Flux: Application to Radiotherapy Dose Calculation (Communications in Computational Physics, 2011)
The present work is concerned with the derivation of numerical methodsto approximate the radiation dose in external beam radiotherapy. To address this issue,we consider a moment approximation of radiative transfer, closed by an entropyminimization principle. The model under consideration is governed by a system ofhyperbolic equations in conservation form supplemented by source terms. The maindifficulty coming from the numerical approximation of this system is an explicit spacedependence in the flux function. Indeed, this dependence will be seen to be stiff andspecific numerical strategies must be derived in order to obtain the needed accuracy. Afirst approach is developed considering the 1D case, where a judicious change of variablesallows to eliminate the space dependence in the flux function. This is not possiblein multi-D. We therefore reinterpret the 1D scheme as a scheme on two meshes, andgeneralize this to 2D by alternating transformations between separate meshes. We callthis procedure projection method. Several numerical experiments, coming from medicalphysics, illustrate the potential applicability of the developed method.