Parallel discrete ordinates methods in the SCEPTRE project

Although the transport of photons and electrons/positrons can be described by the same Boltzmann transport equation, the cross sections are very different, resulting in very different iterative convergence properties for the two particle types. The SCEPTRE project contains a suite of deterministic codes for solving the linear steady-state Boltzmann transport equation, including two very different solution algorithms: a sweeps-based approach for solving the first-order transport equation that is efficient for photon transport, and a conjugate-gradient algorithm for solving the second-order transport equation that is efficient for electron/positron transport. These two solution algorithms are coupled through a common set of interfaces to handle the finite element approximation in space, the discrete-ordinates method in angle, the scattering source terms, input parsing, pre- and post-processing capabilities. We evaluate the two solution algorithms by comparing the run times for photon- and electron-transport problems, investigating parallel performance and effects from finite-element basis function types, preconditioning, and scaling with angular quadrature order and Legendre cross section expansion order. (authors)