Abstract:

Saddle point linear systems arise in a variety of constrained PDE and
optimization problems. When these systems are very large and sparse,
iterative methods must be used to compute a solution. A challenge here is
to derive and apply preconditioners that exploit the properties and the
structure of the given discrete operators, and yield fast convergence
while imposing reasonable storage requirements. In this talk I will
provide an overview of preconditioners and discuss their spectral
properties, bounds on convergence, and computational qualities. We will
look at a variety of such techniques and focus on Schur complement-based
approaches and augmentation techniques.