## Multigrid algorithms for solving the linear Boltzmann equation using first-order system least-squares finite element methods

Solving the linear Boltzmann equation in neutron scattering phenomena presents many challenges to standard numerical schemes in computational physics. For an SN discretization, the so-called ray effects pollute the numerical solution. This pollution can be viewed mathematically as ''contamination'' from a poorly chosen approximating basis set for the angle component of the discretization-i.e., collocation in angle is equivalent to discretization with delta basis functions, which form a poor approximating basis set. Fortunately, a PN discretization, which uses a better approximating basis set (i.e., spherical harmonics), eliminates these ray effects. Unfortunately, solving for the moments or PN equations is difficult. Momentsmore »