Orthogonalization-based Iterative Solvers for Generalized Stokes Problems

Two methods for solving the generalized Stokes problems that occur in viscous, incompressible ows are described and tested. Both are based on some type of linear algebraic orthogonaliza-tion process. The rst, EMGS, is a preconditioner derived from an incomplete Gram{Schmidt factorization, and it is proven to exist whenever the matrix being preconditioned can be factored using Gaussian elimination. For M{matrices, EMGS is proven to give a better approximate fac-torization than ILU preconditioning, but this requires a large amount of intermediate storage for computing the preconditioner. The second orthogonalization approach gives a derived system which eliminates the indeeniteness of the generalized Stokes problem, and keeps the velocity eld in the space of discrete null{divergence vectors. Both methods are tested on problems extracted from a nite element uid ow solver.