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Reference: M. Stoll and A. J. Wathen, (2010). All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems.Citable link to this page:

 

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

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.

Bibliographic Details

Issue Date: 2010Identifiers

Urn: uuid:0582e39a-5746-405d-870c-6d1fe1597db6 Item Description

Type: Article;

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Author: M. Stoll - - - A. J. Wathen - - - - Bibliographic Details Issue Date: 2010 - Identifiers Urn: uuid:0582e39a-5746-405d-870c-6d1fe1

Source: https://ora.ox.ac.uk/objects/uuid:0582e39a-5746-405d-870c-6d1fe1597db6



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