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