Spectral element methods for large scale parallel Navier-Stokes calculations

We analyze the computational complexity of a recently developed two-level iteration scheme for spectral element solution of the time-dependent incompressible Navier-Stokes equations in complex domains. We present several algorithmic advances which significantly enhance the scalability of this approach, including: implementation of an advanced combine operation for degrees-of-freedom on subdomain edges, parallel solution of the (fine-grained) coarse-grid problem, and implementation of local low-order finite element preconditioners for the find-grid problem. Timings on the 512 node Intel Delta machine show that the combined improvements lead to a fourfold reduction in Navier-Stokes solution time for the particular case of a three-dimensional boundary layer calculation consisting of one million degrees-of-freedom.