KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the … Read more

Constraint-Preconditioned Krylov Solvers for Regularized Saddle-Point Systems

We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (SIAM J. Matrix Anal. Appl., 28(1), 2006) describe how to apply the conjugate gradient (CG) method coupled with a constraint preconditioner, a choice that has proved to be … Read more