Even/odd parity transport with internal voids

The even/odd parity form of the transport equation is well suited for finite element (FE) solutions because the resulting problem is symmetric positive definite (SPD) and can, therefore, be solved with highly efficient conjugate gradient (CG) algorithms with Galerkin FE. The authors have been investigating a new approach for solving the transport equation: a simultaneous space/direction solution instead of the traditional source iteration approach. For problems containing internal void regions, the even/odd parity form breaks down. They investigate a method for handling internal voids, using the classic Reed problem for the evaluation. Although the Reed problem is one-dimensional, the method is valid for multidimensional problems as well