COARSE-GRAIN DEFLATION FOR PRECONDITIONED CONJUGATE GRADIENT SOLVERS: APPLICATION TO THE PRESSURE POISSON EQUATION

A deflated preconditioned conjugate gradient technique has been developed for the so-lution of the Pressure-Poisson equation within an incompressible flow solver. The deflation is done using a region-based decomposition of the unknowns, making it extremely simple to implement. This procedure belongs to the family of hybrid methods (making use of both direct and iterative solvers) and the preconditioner obtained belongs to the class of optimal ones just as Multigrid and Domain Decomposition Methods. The procedure has shown a considerable reduction in the number of iterations. For grids with large graph-depth the savings exceed an order of magnitude. Furthermore, the technique has shown a remark-able insensitivity to the number of groups/regions chosen, and to the way the groups are formed. I