Implementation of the conjugate gradient algorithm on a vector hypercube multiprocessor

In this paper, parallel implementation and vectorization of the Scaled Conjugate Gradient (SCG) algorithm for the solution of large sparse linear system of equations, on a vector hypercube multiprocessor (iPSC- VX), is described. Computations in the SCG algorithm consist mainly of matrix operations that can be vectorized and are implemented on the Vector Processor on each node of the hypercube. The implementation described here achieves efficient parallelization by overlapping vectorized computations with inter-node communication. A speed-up of 58 over a µVax II is obtained for large finite element meshes.