Abstract

Parallel processing is maturing with the ability to program heterogeneous environments and the help of networking systems such as PVM. Heterogeneous multiprocessing has been revolutionized due to tools such as PVM which allows the user to develop code independent of the machine arthitecture. This thesis develops a load balancing algorithm to handle the time march problem, heat conduction. It is based on the speeds of the machines in the current environment.

The heat equation algorithm is enhanced by the Psi Calculus of a Mathematics of Arrays. \l' Calculus allows the indexing of the heat matrix in terms of starts, stops and strides. This eliminates the necessity to compute the Cartesian coordinates at each timestep. Furthermore, our design is independent of the dimension of the heat matrix. The same program can run the heat equation on a 1-D, 2-D, and 3-D problem. This work has been carried out in conjunction with the Psi Group at University of Missouri - Rolla.

The tests for this thesis run in 4 different environments. Differences in the speed and real memory of the machines produce valuable information pertaining to the partitioning of very large matrices. Because speed is the only factor of the load balancer of this thesis, these tests are able to analyze the effect of memory on performance. Machines that do not have enough memory to "carry their weight" severely hinder performance. This is due to the very large matrix sizes and the amount of memory necessary to process large matrices.

Department(s)

Computer Science

Comments

The first Author is a Graduate Student.

This report is substantially the M.S. thesis of the first author, completed May, 1994

Report Number

CSc-94-11

Document Type

Technical Report

Document Version

Final Version

File Type

text

Language(s)

English

Rights

© 1994 University of Missouri - Rolla, All rights reserved

Publication Date

1 May, 1994

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