A robust collision source method for rank adaptive dynamical low-rankapproximation in radiation therapy

Deterministic models for radiation transport describe the density of particles moving through a background material. In therapy applications, phase space this is composed energy, spatial position and direction flight. The resulting six-dimensional prohibits fine numerical discretizations, which are essential construction accurate reliable treatment plans. work, we tackle high dimensional dynamical low-rank approximation particle density. Dynamical (DLRA) evolves solution on manifold in time. Interpreting energy variable as pseudo-time lets us employ DLRA framework to represent equation every energy. Stiff scattering terms treated an efficient implicit discretization rank adaptive integrator chosen dynamically adapt To facilitate use boundary conditions reduce overall rank, split into collided uncollided collision source method. Uncollided described by directed quadrature set guaranteeing low computational costs, whereas represented solution. It can be shown that presented method L 2 -stable under time step restriction does not depend stiff terms. Moreover, require inversions matrices. Numerical results configurations well line benchmark underline efficiency proposed