Multidimensional nodal transport methods for multiple-instruction multiple-data, distributed memory machines

As computer hardware technology approaches the physical limits (on size and speed) of the electronic components of computer systems, it has become evident in recent years that any significant improvements in the performance of future systems must be rooted in advanced architectures. Efforts in this direction have resulted in numerous ideas and designs for vector and parallel processors. Among the many problems that have been implemented on the new systems is the neutron and photon transport equation. Monte Carlo-type methods have been implemented on shared-memory (SM) and distributed-memory (DM) multiple-instruction multiple-data (MIMD) machines. On the other hand, implementation of discrete ordinates-type methods on SM MIMD systems has been considered for general codes as well as special one-dimensional, multigroup codes. More recently, implementation of the latter code on the hypercube and the comparison between two chaotic and one ordered iterative schemes have been reported. In this paper the authors present the implementation of the zeroth and first-order two-dimensional nodal transport methods on the hypercube. The objective is to study the effect of the various parameters in a simple test problem on speedup and efficiency in order to determine the cases most suitable for solving on a DM machine, such as the hypercube