Numerical linear algebra problems solved on transputer farms.

Ole Tingleff / Section for Numerical Analysis


This paper describes a communication harness for a network of transputers with ternary tree structure. The system has beeen used for matrix-matrix products, for Sturmian sequences and for Romberg integration. We also describe a comunication harness for a transputer farm with cube structure. The language is occam 2.

1. Introduction Many computational problems can be split into subtaskes which can be treated independently. Such problems are suited for parallel computations in a processor farm with slave processors controlled by a master processor. A tree structured processor farm is well suited for such a situation.
In other problems, the subtaskes are not mutually independent, they have to exchange data during the parallel computations. In this situation we should choose a processor farm where the distance from any processor to any orther processor is small. A cube structure is a good choice here.
The work on automatic adressing methods for tree structures has been continued. The effort has been concentrated on the ternary tree. The tree has been expanded to 13 transputers, and methods for implementing more levels of the tree have been examined.
The ternary tree was used for further tests with the BLAS3 problem, a matrix-matrix product. It has also been used for determination of all eigenvalues of a tridiagonal matrix. We have performed tests with Romberg integration of functions of one variable.

IMM Technical Report 5/95