Uzawa-Type and Augmented Lagrangian Methods for Double Saddle Point Systems

We study different types of stationary iterative methods for solving a class of large, sparse linear systems with double saddle point structure. In particular, we propose a class of Uzawa-like methods including a generalized (block) Gauss-Seidel (GGS) scheme and a generalized (block) successive overrelaxation (GSOR) method. Both schemes rely on a relaxation parameter, and we establish convergence intervals for these parameters. Additionally, we investigate the performance of these methods in combination with an augmented Lagrangian approach. Numerical experiments are reported for test problems from two different applications, a mixed-hybrid discretization of the potential fluid flow problem and finite element modeling of liquid crystal directors. Our results show that fast convergence can be achieved with a suitable choice of parameters.