Abstract

. 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. 1 Introduction We consider the solution of the non-singular system of N linear equations, Ax = b (1) derived from a finite-difference approximation to a partial differential equation (PDE), using parallel implementations of various Conjugate Gradient iterative methods. Systems like (1) are characterized by being large, structured and sparse. Because of the very low d...

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