All-at-once preconditioning in PDE-constrained optimization
The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle p...
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| Format: | Journal article |
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2009
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| _version_ | 1797102773278343168 |
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| author | Rees, T Stoll, M Wathen, A |
| author_facet | Rees, T Stoll, M Wathen, A |
| author_sort | Rees, T |
| collection | OXFORD |
| description | The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound constraints for the control are introduced. Numerical results will illustrate the competitiveness of our techniques. |
| first_indexed | 2024-03-07T06:10:34Z |
| format | Journal article |
| id | oxford-uuid:ef57366d-a414-425c-af79-5ae0ea1ff7c1 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:10:34Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:ef57366d-a414-425c-af79-5ae0ea1ff7c12022-03-27T11:39:31ZAll-at-once preconditioning in PDE-constrained optimizationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:ef57366d-a414-425c-af79-5ae0ea1ff7c1Mathematical Institute - ePrints2009Rees, TStoll, MWathen, A The optimization of functions subject to partial differential equations (PDE) plays an important role in many areas of science and industry. In this paper we introduce the basic concepts of PDE-constrained optimization and show how the all-at-once approach will lead to linear systems in saddle point form. We will discuss implementation details and different boundary conditions. We then show how these system can be solved efficiently and discuss methods and preconditioners also in the case when bound constraints for the control are introduced. Numerical results will illustrate the competitiveness of our techniques. |
| spellingShingle | Rees, T Stoll, M Wathen, A All-at-once preconditioning in PDE-constrained optimization |
| title | All-at-once preconditioning in PDE-constrained optimization |
| title_full | All-at-once preconditioning in PDE-constrained optimization |
| title_fullStr | All-at-once preconditioning in PDE-constrained optimization |
| title_full_unstemmed | All-at-once preconditioning in PDE-constrained optimization |
| title_short | All-at-once preconditioning in PDE-constrained optimization |
| title_sort | all at once preconditioning in pde constrained optimization |
| work_keys_str_mv | AT reest allatoncepreconditioninginpdeconstrainedoptimization AT stollm allatoncepreconditioninginpdeconstrainedoptimization AT wathena allatoncepreconditioninginpdeconstrainedoptimization |