Mixed-Hybrid Discretization Methods for the Linear Boltzmann Transport Equation

By: Serge Van Criekingen, Robert Beauwens, Joseph W. Jerome, and Elmer Lewis

The linear Boltzmann transport equation is discretized, using a finite element technique for the spatial variable, and a spherical harmonic technique for the angular variable. Based on an even- and odd- parity flux decomposition, mixed hybrid methods combine the advantages of mixed (approximation of even- and odd- parity fluxes) and hybrid (use of Lagrange multipliers to enforce interface regularity conditions) methods. Existence and uniqueness are proved for the resulting problems. Beside the well known primal/dual distinction induced by the spatial variable, the angular variable yields an even/odd distinction for the spherical expansion order.
This paper has appeared: CMAME, vol. 195 (2006), 2719--2741, and can be viewed in the following format: