| 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 (and 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. |
