In this paper we analyze communication patterns in the parallel three-dimensional Navier-Stokes solver Prism , and present performance results on the IBM SP2, the Cray T3D and the SGI P ow er Challenge XL. Prism is used for direct n umerical simulation of turbulence in non-separable and multiply-connected domains. The n umerical method used in the solver is based on mixed spectral element-F ourierexpansions in (x ; y) planes and z;direction, respectively. Each (or a group) of F ouriermodes is computed on a separate processor as the linear contributions (Helmholtz solves) are completely uncoupled in the incompressible Navier-Stokes equations coupling is obtained via the nonlinear contributions (convectiv e terms).The transfer of data betw eenphysical and Fourier space requires a series of complete exc hange operations, which dominate the communication cost for small numberof processors. As the number of processors increases, global reduction and gather operations become important while complete exc hangebecomes more latency dominated. Predictive models for these communication operations are proposed and tested against measurements. A relatively large variation in communication timings per iteration is observed in simulations and quanti ed in terms of speci c operations. A n umberof improvements are proposed that could signi cantly reduce the communications overheadwith increasing n umbersof processors, and generic predictive maps are developed for the complete exchange operation, which remains the fundamental communication in Prism . Results presented in this paper are representativ eof a wider class of parallel spectral and nite element codes for computational mechanics which require similar communication operations.Corresponding Author 1 0-89791-854-1/1996/$5.00 © 1996 IEEE Figure 2: Data Layout in Prism. Here we h a ve c hosen to store a Fourier mode (2 \Fourier planes") pernode. This also means that we keep 2 \Physical Planes" pernode. Because this is a Real-to-Complex FFT, N z = 2 m = 2P \Physical Planes" map to P + 1 independent Fourier modes (0 to N z =2 = P) as the other P ; 1 modes (N z =2 + 1 to N z ; 1 are xed by symmetry. Of these P + 1 modes, the rst and last one have vanishing imaginary parts, hence by \packing" the real part of mode P in place of the imaginary part of mode 0 we are left with N z = 2 P \Fourier planes" as well.The communication that the code is based on is the Global or Complete Exchange. This is a communication pattern of great importance to any 2-D or 3-D FFT-based solver as well, since it lies behind the transposition of a distributed matrix. It is also used in multiplying distributed matrices when one or more of the matrices is speci ed to be in transposed form. In the case of Prism it is used to move the data between Fourier and Physical space: For most of the calculation, the ow variables are in Fourier Space distributed in \Fourier planes" among the nodes, arranged according to the Fourier mode they correspond to. However when the need to form the non-linear products (Pass I) ...