| EPSRC Reference: |
EP/H026053/1 |
| Title: |
Iterative Methods for PDE-Constrained Optimization |
| Principal Investigator: |
Gould, Professor N |
| Other Investigators: |
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| Department: |
Computational Sci and Eng - RAL |
| Organisation: |
STFC Laboratories (Grouped) |
| Scheme: |
Standard Research |
| Starts: |
18 January 2010 |
Ends: |
17 June 2010 |
Value (£): |
12,104
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| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Nonlinear optimization is a fundamental branch of numerical analysis andis ubiquitous in science and engineering. It allows one, for example, todetermine an optimal flight plan under specified circumstances, to findthe shortest paths between fixed positions on a given manifold(geodesics), to predict the shape and layout of telescope arrays thatmaximize light intensity, or to find an optimal design among infinitelymany possible elastic structures. Recent progress in large-scalenonlinear optimization and linear algebra opens new perspectives on thesolution of optimization problems whose constraints are defined bydiscretized sets of partial-differential equations (PDEs). Such problemsare challenging both because of the structural properties present in thecontinuous equations and because of their sheer intimidating size. Theyare important because of their wide-ranging application; a particularlyvital instance is the Navier-Stokes equations, the basic equations offluid mechanics. Challenging as such equations may be, theirdiscretization by the finite-element method leads to a consistentstructure that can be exploited by numerical algorithms.Our proposed research is to design and analyse numerical methodsfor solving PDE-constrained optimization problems, and to buildhigh-quality software to allow others to use our work. We shallparticularly be concerned with methods which are guaranteed toconverge to a locally-best solution, and which ultimately convergerapidly to this solution fast. We shall address the issues ofadditional side constraints that might be imposed physically andof natural rank-deficiencies that arise from the differential equations.
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Key Findings |
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Potential use in non-academic contexts |
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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