High-Order Mixed Finite Element Variable Eddington Factor Methods

We apply high-order mixed finite element discretization techniques and their associated preconditioned iterative solvers to the Variable Eddington Factor (VEF) equations in two spatial dimensions. The VEF discretizations are coupled a Discontinuous Galerkin (DG) of discrete ordinates transport equation form effective linear algorithms that compatible with (curved) meshes. This combination is motivated by use methods hydrodynamics calculations at Lawrence Livermore National Laboratory (LLNL). Due mathematical structure equations, standard Raviart Thomas (RT) elements cannot be used approximate vector variable equations. Instead, we investigate three alternatives based on continuous for each component, non-conforming RT approach where DG-like used, hybridized method. present numerical results demonstrate accuracy, compatibility curved meshes, robust efficient convergence iteratively solving transport-VEF system invert discretized