Discretization of Neutron Transport by FOSLS and Piecewise Constant Functions on the Sphere

Discretization of Neutron Transport by FOSLS and Piecewise Constant Functions on the Sphere:

C. Pflaum
This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.

Abstract: The approximation of the function space on the sphere plays an important role in the discretization of transport equation. We will present a discretization that employs piecewise constant functions on the sphere and the FOSLS formulation of the Boltzmann transport equation. The discrete equation system is solved by a multigrid process in space and on the sphere. Numerical results show an ameloriation of the ray effect. For the implementation of the discretization and the multigrid algorithm, we used the parallel version of the library EXPDE (Expression Templates for Partial Differential Equations).