Parallel multi-level solvers for spectral element methods

Efficient solution of the Navier-Stokes equations in complex domains is dependent upon the availability of fast solvers for sparse linear systems. For unsteady incompressible flows, the pressure operator is the leading contributor to stiffness, as the characteristic propagation speed is infinite. In the context of operator splitting formulations, it is the pressure solve which is the most computationally challenging, despite its elliptic origins. We seek to improve existing spectral element iterative methods for the pressure solve in order to overcome the slow convergence frequently observed in the presence of highly refined grids or highaspect ratio elements. The new algorithm incorporates an enriched coarse-grid operator which admits anisotropic resolution within elements, and a new parallel solution technique which mitigates the additional overhead of the enlarged coarse-grid system.