The Parallel Solution of Partial Differential Equations on Transputer Networks

We present an implementation of a finite-difference approximation for the solution of partial differential equations on transputer networks. The grid structure associated with the finite-difference approximation is exploited by using geometric partitioning of the data among the processors. This provides a very low degree of communication between the processors. The resultant system of linear equations is then solved by a variety of Conjugate Gradient methods. Care has been taken to ensure that the basic linear algebra operations are implemented as efficiently as possible for the particular geometric partitioning used.