Radiative transport equation (RTE) is a fundamental equation for particles, such photon or neutron, transport in complex medium. Analytical solution is rarely available unless in very special setup. Numerically it is vey challenging due to (1) high dimensionality, which includes both physical and angular space, (2) multiple scattering, which couples the solution in space and directions and causes the solution to behave differently in different regimes, e.g., transport and diffusion regimes. I will present an efficient forward solver for steady-state RTE on structured and unstructured meshes with general boundary condition. In our algorithm we (1) use a direct angular discretization combined with discontinuous Galerkin spatial discretization, and (2) construct an improved source iteration used as the relaxation for multigrid methods in both angular and physical space. Our algorithm can deal with different scattering regimes effectively. We show both convergence and error estimate for our algorithm. If time permits, I will also show some application in optical imaging, in which RTE is regarded as a golden standard.
Copyright. All Rights Reserved.