All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems
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...
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| Format: | Journal article |
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2010
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| _version_ | 1826257465223675904 |
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| author | Stoll, M Wathen, A |
| author_facet | Stoll, M Wathen, A |
| author_sort | Stoll, M |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T18:18:38Z |
| format | Journal article |
| id | oxford-uuid:0582e39a-5746-405d-870c-6d1fe1597db6 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:18:38Z |
| publishDate | 2010 |
| record_format | dspace |
| spelling | oxford-uuid:0582e39a-5746-405d-870c-6d1fe1597db62022-03-26T08:57:35ZAll-at-Once Solution if Time-Dependent PDE-Constrained Optimisation ProblemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0582e39a-5746-405d-870c-6d1fe1597db6Mathematical Institute - ePrints2010Stoll, MWathen, ATime-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. |
| spellingShingle | Stoll, M Wathen, A All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems |
| title | All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems |
| title_full | All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems |
| title_fullStr | All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems |
| title_full_unstemmed | All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems |
| title_short | All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems |
| title_sort | all at once solution if time dependent pde constrained optimisation problems |
| work_keys_str_mv | AT stollm allatoncesolutioniftimedependentpdeconstrainedoptimisationproblems AT wathena allatoncesolutioniftimedependentpdeconstrainedoptimisationproblems |