A Two-Dimensional Discontinuous Heterogeneous Finite Element Method for Neutron Transport Calculations

A discontinuous heterogeneous finite element method is presented and discussed. The method is intended for realistic numerical pin-by-pin lattice calculations when an exact representation of the geometric shape of the pins is made without need for homogenization. The method keeps the advantages of conventional discrete ordinate methods, such as fast execution together with the possibility to deal with a large number of spatial meshes, while minimizing the need for geometric modeling. It also provides a complete factorization in space, angle, and energy for the discretized matrices and minimizes, thus, storage requirements. An angular multigrid acceleration technique has also been developed to speed up the rate of convergence of the inner iterations. A particular aspect of this acceleration is the introduction of boundary restriction and prolongation operators that minimize oscillatory behavior and enhance positivity. Numerical tests are presented that show the high precision of the method and the efficiency of the angular multigrid acceleration.