A Fast Solver for an H1 Regularized PDE-Constrained Optimization Problem. (15th January 2016)

• Record Type: Journal Article
• Authors: Barker, Andrew T.; Rees, Tyrone; Stoll, Martin
• Is Part Of: Communications in computational physics. Volume 19:Number 1(2016:Jan.)
• Page Start: 143
• Page End: 167
• Publication Date: 2016-01-15
• Subjects: 49M25, -- 49K20, -- 65F10, -- 65N22, -- 65F50, -- 65N55; Preconditioning, -- Krylov methods, -- PDE-constrained optimization, -- optimal control of PDEs; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.190914.080415a
• Languages: English
• ISSNs: 1815-2406

Abstract

Abstract: In this paper we consider PDE-constrained optimization problems which incorporate an H1 regularization control term. We focus on a time-dependent PDE, and consider both distributed and boundary control. The problems we consider include bound constraints on the state, and we use a Moreau-Yosida penalty function to handle this. We propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.