Hypercube applications of the x-y geometry nodal method for the neutron diffusion equation

The role that nodal methods play in neutron diffusion theory is highly important. With the advent of high-speed computers, these methods become valuable computational tools. Indeed, implementation of diffusion equation methods on parallel machines has been reported. Solving the one-group neutron diffusion equation by the nodal method requires finding the solution of a system of three equations: the x- and y-current continuity and the conservation equations. This requires matrix inversion. For a very coarse mesh size, the solution may take only a few seconds. As the mesh gets finer, the system of equations grows in the number of unknowns resulting in a matrix of very high order. On serial computers, matrix inversion is limited by the amount of memory. The CPU time for large systems of equations can also become prohibitive. Thus, a new parallelized iterative algorithm is developed