Title: Preconditioners for Generalized Saddle-Point Problems Brief Abstract: Generalized saddle point problems arise in a number of applications, ranging from optimization and metal deformation to fluid flow and PDE-governed optimal control. We examine two types of preconditioners for these problems, one block-diagonal and one indefinite, and present analyses of the eigenvalue distributions of the preconditioned matrices. We also investigate the use of approximations for the Schur complement matrix in these preconditioners and develop eigenvalue analysis accordingly. We examine new developments in probing methods (derived from graph coloring methods for sparse Jacobians) for building approximations to the Schur complement and consider their effect in the context of our preconditioners. To illustrate our results, we consider a model Navier-Stokes problem as well as a real-world application involving the deformation of aluminum strips. CSRI POC: Ray Tuminaro, (925) 294-2564 |