Combining the Augmented Lagrangian Preconditioner with the Simple Schur Complement Approximation

A preconditioner for the Schur complement matrix

A preconditioner for iterative solution of the interface problem in Schur Complement Domain Decomposition Methods is presented. This preconditioner is based on solving a problem in a narrow strip around the interface. It requires much less memory and computing time than classical Neumann-Neumann preconditioner and its variants, and handles correctly the flux splitting among subdomains that shar...

SchurRAS: A Restricted Version of the Overlapping Schur Complement Preconditioner

This paper presents a preconditioner based on solving approximate Schur complement systems with overlapping restricted additive Schwarz methods (RAS). The construction of the preconditoner, called SchurRAS, is as simple as in the standard RAS. The communication requirements for each application of the preconditioning operation are similar with those of the standard RAS approach. In the particul...

A preconditioner for the Schur complement domain decomposition method

Combining stabilized SQP with the augmented Lagrangian algorithm

For an optimization problem with general equality and inequality constraints, we propose an algorithm which uses subproblems of the stabilized SQP (sSQP) type for approximately solving subproblems of the augmented Lagrangian method. The motivation is to take advantage of the well-known robust behavior of the augmented Lagrangian algorithm, including on problems with degenerate constraints, and ...

Incomplete Augmented Lagrangian Preconditioner for Steady Incompressible Navier-Stokes Equations

An incomplete augmented Lagrangian preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable finite elements, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented Lagrangian-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton li...