Projection Techniques for Iterative Solution of Ax = B with Successive Right-hand Sides

Projection techniques are developed for computing approximate solutions to linear systems of the form Ax n = b n , for a sequence n = 1; 2; :::, e.g., arising from time discretization of a partial diierential equation. The approximate solutions are based upon previous solutions, and can be used as initial guesses for iterative solution of the system, resulting in signiicantly reduced computational expense. Examples of two-and three-dimensional incompressible Navier-Stokes calculations are presented in which x n represents the pressure at time level t n , and A is a consistent discrete Poisson operator. In ows containing signiicant dynamic activity, these projection techniques lead to as much as a twofold reduction in solution time.