Cang, Songluan.

We propose a new minimum total communication distance (TCD) algorithm and an optimal TCD algorithm for broadcast in a 2-dimensional mesh (2-D mesh). The former generates a minimum TCD from a given source node, and the latter guarantees a minimum TCD among all the possible source nodes. These algorithms are based on a divide-and-conquer approach where a 2-D mesh is partitioned into four submeshes of equal size. The source node sends the broadcast message to a special node called an eye in each submesh. The above procedure is then recursively applied in each submesh. These algorithms are extended to a 3-dimensional mesh (3-D mesh), and are generalized to a d-dimensional mesh or torus. In addition, the proposed approach can potentially be used to solve optimization problems in other collective communication operations.

The embedded cluster Monte Carlo (ECMC) method which combines the Korringa-Kohn-Rostoker coherent potential approximation embedded cluster method (KKR-CPA-ECM) and the Monte Carlo method has been developed in order to study phase diagrams of binary alloys. The KKR-CPA-ECM provides interchange energies to the Monte Carlo code. In this thesis, a pair-interaction (PI) method is used to provide interchange energies to the Monte Carlo code. The code of the PI method is obtained based on the KKR-CPA-ECM code. The interchange energies of Cu0.5 Zn0.5 alloys are calculated with the PI method. The critical temperature and the phase boundary of Cu-Zn alloys are obtained by carrying out both Monte Carlo calculations with above interchange energies and the ECMC calculations. A comparison between the results of both methods is made.