Inexact Factorization Sample Clauses

Inexact Factorization. Using the exact inverse of Aε, with ε > 0 as a preconditioner as done in Figure 6.4, is clearly not practical if the problem is large. The efficient solution of the linear system requires an approximation of the inverse which can be computed at a relatively low cost in terms of memory and CPU time and which significantly reduces the number of iterations of the linear iterative solver. Many options exist how to obtain such an approximation. We consider first inexact factorization methods for preconditioning the linear system. While we will not follow this approach in this thesis, we believe that these methods are worth mentioning here since they have been shown to be very efficient when applied to the unsteady Navier-Xxxxxx equations for incompressible fluids [74, 77, 78] and their applicability to the Xxxxxxx flow (or Non-Newtonian fluid flow in general) should be investigated in the future. We begin by recalling two important types of inexact factorization methods applied to the unsteady Navier- Xxxxxx equations (for Newtonian fluids) before presenting some ideas how this may be used for the twofold saddle point problem (4.21) for Non-Newtonian fluids.