Parallel implementation of recursive spectral bisection on the connection machine CM-5 system

Abstract

This chapter presents the description of the parallel implementation of the recursive spectral bisection (RSB) algorithm, followed by two decomposition examples. The purpose of the recursive spectral bisection algorithm is to generate a reordering of the elements based on idual such that nicely shaped partitions of adjacent elements are obtained. These partitions are then mapped to the vector units of the CM-5 system with the constraint of having at most one partition per vector unit. The partitioning procedure follows exactly the array block distribution format used by the CM-5 run-time system. In this format, all partitions contain the same number of elements except the last one, which has whatever elements remain. It should be noted that the parallel implementation of the RSB algorithm is tightly linked to the data mapping format. The implementation of the algorithm is done such that all elements of the mesh are treated in parallel. It implies a two-level parallelization; one level on the partitions generated at a given stage of the recursive process and the other on the elements in each partition. One should note that there is no performance loss during the recursive process because the CM-5 system always processes the same number of data—namely, the number of elements in the whole mesh. This discussion concludes that the computing power of the CM-5 system has made possible the decomposition of large three-dimensional unstructured meshes in a reasonable time.