Abstract:
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 differential equation. The approximate solutions are based upon previous solutions, and can be used as initial guesses for iterative solution of the system, resulting in significantly 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 flows containing significant dynamic activity, these projection techniques lead to as much as a two-fold reduction in solution time.
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