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A Fast Solver for an H₁ Regularized PDE-Constrained Optimization Problem

Publisher： Cambridge University Press

E-ISSN： 1991-7120|19|1|143-167

ISSN： 1815-2406

Source： Communications in Computational Physics, Vol.19, Iss.1, 2016-01, pp. : 143-167

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

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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.

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