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Abstract : |
Multi-dimensional integrals of products of several arrays arise in certain scientific computations. To optimize the performance of such computations on parallel computers, the total number of arithmetic operations and the total amount of communication need to be minimized. This paper addresses the operation minimization sub-problem and the communication minimization sub-problem. Earlier work had addressed these problems in a restricted context of dense arrays, with additional constraints. In this paper, general solutions are developed that handle sparse arrays and other features such as fast Fourier transforms and multiple use of arrays, that are characteristics of real computational physics. The new algorithm for the operation minimization subproblem has been implemented and used to generate solutions that improve over the best manually-optimized ones by a factor of two. 1, |
