Krylov Subspace Solvers and Indefinite Preconditioning of Saddle Point Algebraic Linear Systems

Valeria Simoncini* and Mattia Tani

Symmetric linear systems in saddle point form arise in a wide variety of applications, including fluid dynamics, elasticity and constrained optimization problems in general. Indefinite preconditioners can lead to effective strategies for solving these systems. When selecting the Krylov subspace solver, current strategies rely either on nonsymmetric methods such as GMRES, or on the Conjugate Gradients in a non-standard inner product. In this talk we discuss some of the pros and cons of these two alternatives.

Mathematics Subject Classification: 65F08

Keywords: saddle point linear systems; preconditioning; iterative solvers

Minisymposion: Preconditioning for PDE-Constrained Optimization