The explicitly-interfaced method and the response matrix method: two methods for the solution of the transport equation

Two alternative implementations of the phase space finite element method for the solution of the transport equation are presented. Both rely on dividing the spatial domain into smaller regions to increase computational efficiency. The explicitly-interfaced method results in a series of matrix equations that are solved iteratively to find a flux distribution over the entire spatial domain. The response matrix method results in the familiar response matrix equations through direct inversion of each region's finite element matrix. The global flux distribution is again found iteratively. Both methods are applied to one- and two-dimensional test problems. For most one-dimensional applications the new methods are no more efficient than the conventional procedure. In two dimensions, however, the new methods are significantly more efficient