Partitioning PDE computations: Methods and performance evaluation

We consider modeling, predicting and evaluating the perfonnance of methods for solving PDEs in parallel architectures. We have developed a method for coarse grain partitioning of computations for parallel architectures and we apply it to three PDE applications: (a) Cholesky factorization, (b) spline collocation, and (c) an application complete from processing text input to plotting the PDE solution. OUf partitioning method is oriented to minimizing interprocessor communication and we review some "unifonn" architectures and models of their communication. We apply this method to the three applications implemented on the FLEX/32 multicomputer. We review the architecture on the FLEX/32 and the results of applying the partitioning method to computation running on the FLEX/32. We observe that the FLEX/32 does not have any communication bottleneck and probably will not suffer substantial perfonnance degradation if the processor speeds are increased by a factor of 10. Our partitioning method works reasonably well even here where communication costs are negligible. The coarse grain structure of two of these applications is not highly parallel and we observe speedups of about k/2 for k processors. The other application is highly parallel and we observe optimal speedups for any number of processors as the problem size increases. 'loThis research supported in part by NSF grant DMC-8508684. *"'This research supponed in pan by AFOSR granl 84·0385. This paper will appear in the January 1987 issue of Parallel Computing.