An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem
We propose and analyze an interior penalty method for a finite-dimensional large-scale bounded Nonlinear Complementarity Problem (NCP) arising from the discretization of a differential double obstacle problem in engineering. Our approach is to approximate the bounded NCP by a nonlinear algebraic equ...
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| Format: | Journal Article |
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Elsevier
2018
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| Online Access: | http://hdl.handle.net/20.500.11937/66879 |
| _version_ | 1848761416661598208 |
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| author | Wang, Song |
| author_facet | Wang, Song |
| author_sort | Wang, Song |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We propose and analyze an interior penalty method for a finite-dimensional large-scale bounded Nonlinear Complementarity Problem (NCP) arising from the discretization of a differential double obstacle problem in engineering. Our approach is to approximate the bounded NCP by a nonlinear algebraic equation containing a penalty function with a penalty parameter µ > 0. The penalty equation is shown to be uniquely solvable. We also prove that the solution to the penalty equation converges to the exact one at the rate O(µ 1/2 ) as µ ? 0. A smooth Newton method is proposed for solving the penalty equation and it is shown that the linearized system is reducible to two decoupled subsystems. Numerical experiments, performed on some non-trivial test examples, demonstrate the computed rate of convergence matches the theoretical one. |
| first_indexed | 2025-11-14T10:31:20Z |
| format | Journal Article |
| id | curtin-20.500.11937-66879 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:31:20Z |
| publishDate | 2018 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-668792018-10-12T01:35:06Z An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem Wang, Song We propose and analyze an interior penalty method for a finite-dimensional large-scale bounded Nonlinear Complementarity Problem (NCP) arising from the discretization of a differential double obstacle problem in engineering. Our approach is to approximate the bounded NCP by a nonlinear algebraic equation containing a penalty function with a penalty parameter µ > 0. The penalty equation is shown to be uniquely solvable. We also prove that the solution to the penalty equation converges to the exact one at the rate O(µ 1/2 ) as µ ? 0. A smooth Newton method is proposed for solving the penalty equation and it is shown that the linearized system is reducible to two decoupled subsystems. Numerical experiments, performed on some non-trivial test examples, demonstrate the computed rate of convergence matches the theoretical one. 2018 Journal Article http://hdl.handle.net/20.500.11937/66879 10.1016/j.apm.2017.07.038 Elsevier fulltext |
| spellingShingle | Wang, Song An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem |
| title | An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem |
| title_full | An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem |
| title_fullStr | An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem |
| title_full_unstemmed | An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem |
| title_short | An interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem |
| title_sort | interior penalty method for a large-scale finite-dimensional nonlinear double obstacle problem |
| url | http://hdl.handle.net/20.500.11937/66879 |