The Finite Element Response Matrix Method for the Solution of the Neutron Transport Equation

-The finite element response matrix method has been applied to the solution of the neutron transport equation. This method has previously been applied to the neutron diffusion equation for coarse mesh reactor analysis with excellent results. As with the diffusion equation implementation, the transport method employs a local-global projection technique to allow treatment of internal heterogeneities that would normally not be resolved by the coarse global mesh that is needed for computational efficiency. However, since the transport equation includes the angular domain, the local~lobal projection technique has been extended to angle as well as space. Since the response matrices do not depend on the multiplication factor, a conventional fission source iteration method is utilized for criticality problems. The method has been applied to the one-dimensional and twodimensional neutron transport equations. For one-dimensional geometries, the local global projection method yields excellent results, indicating the potential of this approach as a viable coarse mesh transport method. Numerical results are presented for several one-dimensional configurations that were analyzed with varying choices of local and global meshes in the spatial domain. Preliminary results with two-dimensional applications indicate that computational times may be an order of magnitude faster than with the conventional finite element solution of the two-dimensional transport equation.