An Inherently Parallel Multigroup Nodal Diffusion Method for Hexagonal-Z Geometry

Abstract

An inherently parallel analytical nodal method for the solution of the multigroup neutron diffusion equations in hexagonal-z geometry has been developed and implemented in the code HEXPEDITE. The method is based on a hexagonal-z variant of the transverse integration procedure. The transverse - integrated diffusion equation is similar in shape to the one solved in the ILLICO method, and hence a solution method similar to that of ILLICO is adopted. The local solution for the fluxes is done analytically, whereas the global discrete coupling is achieved using net currents that are solved for by the direct inversion of independent tri-diagonal matrix equations. This approach results in a method that is inherently parallel and vectorizable. The code has been tested on a number of benchmark problems. The results demonstrate that the method is highly accurate as well as computationally efficient. The method was tested in two types of parallel environments: two distributed processing environments and a shared memory multiprocessor computer. In the two distributed processing environments it was found that the communication overhead for such an efficient algorithm offsets any gain derived from the use of multiple machines. The implementation on a shared memory parallel computer displayed a speedup factor as high as 5.9 on 8 processors.