Clinical Adaptive Radiation Transport Algorithms

The aim of this project is to develop adaptive numerical methods for the approximation of continuum linear Boltzmann transport models, with a specific emphasis on applications in clinical radiotherapy, and to compare the robustness, precision and efficiency of such methods against current leading Monte Carlo methods. In particular, a hp-adaptive discontinuous Galerkin finite element method (DGFEM) tailored to the neutron transport equation will be formulated, with an emphasis on employing such methods on general polytopic meshes. With this in mind, efficient numerical cubature schemes on polytopes will be exploited, and computable a posteriori error bounds will be derived and utilised in automatic hp-adaptive algorithms that allow multiple quantities of clinical interest to be approximated to within a given error tolerance whilst minimising computational cost.