The Mathematical Institute, University of Oxford, Eprints Archive

All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems

Stoll, M. and Wathen, A. J. (2010) All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems. SIAM Journal on Scientific Computing . (Submitted)

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Abstract

Time-dependent partial differential equations (PDEs) play an important role in applied mathematics and many other areas of science. One-shot methods try to compute the solution to these problems in a single iteration that solves for all time-steps at the same time. In this paper, we look at one-shot approaches for the optimal control of time-dependent PDEs and focus on the fast solution of these problems. The use of Krylov subspace solvers together with an efficient preconditioner allows for minimal storage requirements. We solve only approximate time-evolutions for both forward and adjoint problem and compute accurate solutions of a given control problem only at convergence of the overall Krylov subspace iteration. We show that our approach can give competitive results for a variety of problem formulations.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1019
Deposited By:Peter Hudston
Deposited On:27 Nov 2010 09:35
Last Modified:09 Feb 2012 15:53

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