A Weakly Penalized Discontinuous Galerkin
Method for Radiation in Dense, Scattering
Media
We review the derivation of weakly penalized
discontinuous Galerkin methods for scattering
dominated radiation transport and extend the
asymptotic analysis to non-isotropic scattering.
Multilevel Schwarz preconditioners for singularly
perturbed symmetric reaction-diffusion systems
We present robust and highly parallel multilevel
non-overlapping Schwarz preconditioners, to solve an
interior penalty discontinuous Galerkin finite element
discretization of a system of steady state, singularly
perturbed reaction-diffusion equations with a singular
reaction operator, using a GMRES solver. We provide proofs
of convergence for the two-level setting and the multigrid
V-cycle as well as numerical results for a wide range of
regimes.