Regularization-Robust Preconditioners for Time-Dependent PDE-Constrained Optimization Problems

J.W. Pearson, M. Stoll, A.J. Wathen

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we motivate, derive, and test effective preconditioners to be used with the Minres algorithm for solving a number of saddle point systems which arise in PDE-constrained optimization problems. We consider the distributed control problem involving the heat equation and the Neumann boundary control problem involving Poisson's equation and the heat equation. Crucial to the effectiveness of our preconditioners in each case is an effective approximation of the Schur complement of the matrix system. In each case, we state the problem being solved, propose the preconditioning approach, prove relevant eigenvalue bounds, and provide numerical results which demonstrate that our solvers are effective for a wide range of regularization parameter values, as well as mesh sizes and time-steps.
Original languageEnglish
Pages (from-to)1126-1152
Number of pages27
JournalSIAM Journal on Matrix Analysis and Applications
Volume33
Issue number4
DOIs
Publication statusPublished - 1 Jan 2012

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