A Radial Basis Function Method for Solving PDE Constrained Optimization Problems
In this article, we apply the theory of meshfree methods to the problem of PDE constrained optimization. We derive new collocation-type methods to solve the distributed control problem with Dirichlet boundary conditions and the Neumann boundary control problem, both involving Poisson's equation...
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| Format: | Report |
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Springer
2011
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| _version_ | 1826299512373641216 |
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| author | Pearson, J |
| author_facet | Pearson, J |
| author_sort | Pearson, J |
| collection | OXFORD |
| description | In this article, we apply the theory of meshfree methods to the problem of PDE constrained optimization. We derive new collocation-type methods to solve the distributed control problem with Dirichlet boundary conditions and the Neumann boundary control problem, both involving Poisson's equation. We prove results concerning invertibility of the matrix systems we generate, and discuss a modication to guarantee invertibility. We implement these methods using MATLAB, and produce numerical results to demonstrate the methods' capability. We also comment on the methods' effectiveness in comparison to the widely-used finite element formulation of the problem, and make some recommendations as to how this work may be extended. |
| first_indexed | 2024-03-07T05:03:04Z |
| format | Report |
| id | oxford-uuid:d8f95776-3af7-4798-b633-7d5c3338ab8a |
| institution | University of Oxford |
| last_indexed | 2024-03-07T05:03:04Z |
| publishDate | 2011 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:d8f95776-3af7-4798-b633-7d5c3338ab8a2022-03-27T08:52:38ZA Radial Basis Function Method for Solving PDE Constrained Optimization ProblemsReporthttp://purl.org/coar/resource_type/c_93fcuuid:d8f95776-3af7-4798-b633-7d5c3338ab8aMathematical Institute - ePrintsSpringer2011Pearson, JIn this article, we apply the theory of meshfree methods to the problem of PDE constrained optimization. We derive new collocation-type methods to solve the distributed control problem with Dirichlet boundary conditions and the Neumann boundary control problem, both involving Poisson's equation. We prove results concerning invertibility of the matrix systems we generate, and discuss a modication to guarantee invertibility. We implement these methods using MATLAB, and produce numerical results to demonstrate the methods' capability. We also comment on the methods' effectiveness in comparison to the widely-used finite element formulation of the problem, and make some recommendations as to how this work may be extended. |
| spellingShingle | Pearson, J A Radial Basis Function Method for Solving PDE Constrained Optimization Problems |
| title | A Radial Basis Function Method for Solving PDE Constrained Optimization Problems |
| title_full | A Radial Basis Function Method for Solving PDE Constrained Optimization Problems |
| title_fullStr | A Radial Basis Function Method for Solving PDE Constrained Optimization Problems |
| title_full_unstemmed | A Radial Basis Function Method for Solving PDE Constrained Optimization Problems |
| title_short | A Radial Basis Function Method for Solving PDE Constrained Optimization Problems |
| title_sort | radial basis function method for solving pde constrained optimization problems |
| work_keys_str_mv | AT pearsonj aradialbasisfunctionmethodforsolvingpdeconstrainedoptimizationproblems AT pearsonj radialbasisfunctionmethodforsolvingpdeconstrainedoptimizationproblems |