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

The phase space finite element method when applied to the first order transport equation results in a matrix equation that can only be solved directly. While the direct solution procedure is competitive with more established transport methods for one-dimensional geometries, it is much too slow in two or more dimensions. This summary presents two alternative implementations of the finite element method. Both reduce the size of the matrix to be solved by dividing the spatial domain into smaller regions, and both realize increased efficiency in multi-dimensional applications. Following brief derivations of the methods, computational results for both one-dimensional and two-dimensional applications will be presented and compared for the two distinct approaches