Parallel Algorithms for the Spectral Transform Method

The spectral transform method is a standard numerical technique for solving partial diierential equations on a sphere and is widely used in atmospheric circulation models. Recent research has identiied several promising algorithms for implementing this method on massively parallel computers; however, no detailed comparison of the diierent algorithms has previously been attempted. In this paper, we describe these diierent parallel algorithms and report on computational experiments that we have conducted to evaluate their eeciency on parallel computers. The experiments used a testbed code that solves the nonlinear shallow water equations on a sphere; considerable care was taken to ensure that the experiments provide a fair comparison of the diierent algorithms and that the results are relevant to global models. We focus on hypercube-and mesh-connected multicomputers with cut-through routing, such as the Intel iPSC/860, DELTA, and Paragon, and the nCUBE/2, but also indicate how the results extend to other parallel computer architectures. The results of this study are relevant not only to the spectral transform method but also to multidimensional FFTs and other parallel transforms.