Fast iterative solution of reaction-diffusion control problems arising from chemical processes
PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix...
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| Formato: | Report |
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SIAM
2012
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| _version_ | 1826268733681696768 |
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| author | Pearson, J Stoll, M |
| author_facet | Pearson, J Stoll, M |
| author_sort | Pearson, J |
| collection | OXFORD |
| description | PDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs. |
| first_indexed | 2024-03-06T21:14:08Z |
| format | Report |
| id | oxford-uuid:3f317dfe-0165-4df4-a80f-7ca579edd64b |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:14:08Z |
| publishDate | 2012 |
| publisher | SIAM |
| record_format | dspace |
| spelling | oxford-uuid:3f317dfe-0165-4df4-a80f-7ca579edd64b2022-03-26T14:30:24ZFast iterative solution of reaction-diffusion control problems arising from chemical processesReporthttp://purl.org/coar/resource_type/c_93fcuuid:3f317dfe-0165-4df4-a80f-7ca579edd64bMathematical Institute - ePrintsSIAM2012Pearson, JStoll, MPDE-constrained optimization problems, and the development of preconditioned iterative methods for the efficient solution of the arising matrix system, is a field of numerical analysis that has recently been attracting much attention. In this paper, we analyze and develop preconditioners for matrix systems that arise from the optimal control of reaction-diffusion equations, which themselves result from chemical processes. Important aspects in our solvers are saddle point theory, mass matrix representation and effective Schur complement approximation, as well as the outer (Newton) iteration to take account of the nonlinearity of the underlying PDEs. |
| spellingShingle | Pearson, J Stoll, M Fast iterative solution of reaction-diffusion control problems arising from chemical processes |
| title | Fast iterative solution of reaction-diffusion control problems arising from chemical processes |
| title_full | Fast iterative solution of reaction-diffusion control problems arising from chemical processes |
| title_fullStr | Fast iterative solution of reaction-diffusion control problems arising from chemical processes |
| title_full_unstemmed | Fast iterative solution of reaction-diffusion control problems arising from chemical processes |
| title_short | Fast iterative solution of reaction-diffusion control problems arising from chemical processes |
| title_sort | fast iterative solution of reaction diffusion control problems arising from chemical processes |
| work_keys_str_mv | AT pearsonj fastiterativesolutionofreactiondiffusioncontrolproblemsarisingfromchemicalprocesses AT stollm fastiterativesolutionofreactiondiffusioncontrolproblemsarisingfromchemicalprocesses |