An efficient adaptive algorithm for photon-electron coupled Boltzmann equation in radiation therapy

In this paper, we propose an efficient adaptive algorithm for the photon-electron coupled Boltzmann equations in radiation therapy. The algorithm employs adaptive mesh technologies for both angular and spatial discretization and effectively solves the equation across various domains with a reduced number of degrees of freedom and computational time while maintaining accuracy. For spatial discretization, we employ an adaptive discontinuous Galerkin scheme based on material redefinition to automatically conduct adaptive refinement during the computation process. For angular discretization, we utilize high-order discretization near the incident direction, while low-order discretization is applied to other directions. We compare its performance with the classical Monte Carlo simulations for both mono-energetic and multi-energetic photon beams in various media. Numerical results demonstrate the efficiency and accuracy of the algorithm.