Constrained partial differential equations and optimization problems typically require the need to solve special linear systems known as saddle-point systems. When the matrices are very large and sparse, iterative methods must be used. A challenge here is to derive and apply solution methods that exploit the properties and the structure of the underlying discrete operators, and yield fast convergence without imposing unreasonable computer storage requirements. In this talk I will provide an overview of solution techniques. We will discuss effective preconditioners and their spectral properties for Krylov subspace solvers, bounds on convergence rates, and computational challenges.
This seminar is organized jointly with the Montreal section of CORS and financially supported by the CORS Traveling Speakers Program.