Experiences with Parallel Block Preconditioning of the Linearized Incompressible Navier-Stokes Equations

Victoria E. Howle
Sandia National Laboratory
MS 9217, PO Box 969
Livermore, CA 94551

Ray Tuminaro, Sandia National Laboratory
John Shadid, Sandia National Laboratory
Howard Elman, Univ. of Maryland


We consider the use of parallel block preconditioning techniques for the Navier-Stokes equations. These block techniques correspond to those of Kay & Loghin and result in methods that can be effective and robust over a variety of Reynolds numbers. The basic idea is to approximate the Schur complement operator for the Pressure equation based on the notion that certain differential operators approximately commute. The resulting preconditioner requires two block `solves' at each invocation: one for the pressure unknowns and the other for the velocities. A multigrid V cycle is then used to approximate each of these block solves, which makes the cost per iteration proportional to the number of unknowns. Numerical studies on the ASCI Red machine demonstrate that the preconditioner is effective in terms of both convergence rate and parallel performance.