4-INDEX TRANSFORMATION ON DISTRIBUTED-MEMORY PARALLEL COMPUTERS

Because it has 𝒪(N5) operations, a low computation to data transfer ratio, and is a compact piece of code, the four‐index transformation is a good test case for parallel algorithm development of electronic structure calculations. We present an algorithm primarily designed for distributed‐memory machines. Unlike the previous algorithm of Whiteside et al., ours is not designed with a particular architecture in mind. It is a general algorithm in the sense that not only can it be used on some common architectures but it can utilize some of the advantages inherent in each. In addition, we present formulas predicting that there would be a twofold decrease in communication time if our algorithm was used instead of that of Whiteside et al., on a square array of processors and up to an N‐fold decrease if the two algorithms were implemented on a hypercube. Copyright © 1990 John Wiley & Sons, Inc.