Terascale Spectral Element Algorithms and Implementations

We describe the development and implementation of an efficient spectral element code for multimillion gridpoint simulations of incompressible flows in general two- and three-dimensional domains. Key to this effort has been the development of scalable solvers for elliptic problems and a stabilization scheme that admits full use of the method’s high-order accuracy. We review these and other recently developed algorithmic underpinnings that have resulted in good parallel and vector performance on a broad range of architectures and that, with sustained performance of 319 GFLOPS on 2048 nodes of the Intel ASCI-Red machine at Sandia, readies us for the multithousand node terascale computing systems now coming on line at the DOE labs.