An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations
In the presence of nonaffine and highly nonlinear terms in parametrized partial differential equations, the standard Galerkin reduced-order approach is no longer efficient, because the evaluation of these terms involves high computational complexity. An efficient reduced-order approach is developed...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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2007
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| Online Access: | http://hdl.handle.net/1721.1/35822 |
| _version_ | 1811091199870631936 |
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| author | Nguyen, N. C. Peraire, Jaime |
| author_facet | Nguyen, N. C. Peraire, Jaime |
| author_sort | Nguyen, N. C. |
| collection | MIT |
| description | In the presence of nonaffine and highly nonlinear terms in parametrized partial differential equations, the standard Galerkin reduced-order approach is no longer efficient, because the evaluation of these terms involves high computational complexity. An efficient reduced-order approach is developed to deal with “nonaffineness” and nonlinearity. The efficiency and accuracy of the approach are demonstrated on several test cases, which show significant computational savings relative to classical numerical methods and relative to the standard Galerkin reduced-order approach. |
| first_indexed | 2024-09-23T14:58:31Z |
| format | Article |
| id | mit-1721.1/35822 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T14:58:31Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | mit-1721.1/358222019-04-12T08:35:47Z An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations Nguyen, N. C. Peraire, Jaime Nonaffine Equations Nonlinear Equations Reduced-Order Approximation Best Points Interpolation Method In the presence of nonaffine and highly nonlinear terms in parametrized partial differential equations, the standard Galerkin reduced-order approach is no longer efficient, because the evaluation of these terms involves high computational complexity. An efficient reduced-order approach is developed to deal with “nonaffineness” and nonlinearity. The efficiency and accuracy of the approach are demonstrated on several test cases, which show significant computational savings relative to classical numerical methods and relative to the standard Galerkin reduced-order approach. Singapore-MIT Alliance (SMA) 2007-01-31T14:39:20Z 2007-01-31T14:39:20Z 2007-01 Article http://hdl.handle.net/1721.1/35822 en Computational Engineering (CE) 456635 bytes application/pdf application/pdf |
| spellingShingle | Nonaffine Equations Nonlinear Equations Reduced-Order Approximation Best Points Interpolation Method Nguyen, N. C. Peraire, Jaime An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations |
| title | An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations |
| title_full | An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations |
| title_fullStr | An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations |
| title_full_unstemmed | An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations |
| title_short | An Efficient Reduced-Order Approach for Nonaffine and Nonlinear Partial Differential Equations |
| title_sort | efficient reduced order approach for nonaffine and nonlinear partial differential equations |
| topic | Nonaffine Equations Nonlinear Equations Reduced-Order Approximation Best Points Interpolation Method |
| url | http://hdl.handle.net/1721.1/35822 |
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