Model reduction using a posteriori analysis
Mathematical models in biology and physiology are often represented by large systems of non–linear ordinary differential equations. In many cases, an observed behaviour may be written as a linear functional of the solution of this system of equations. A technique is presented in this study for autom...
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| Format: | Journal article |
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2009
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| _version_ | 1797055178158899200 |
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| author | Whiteley, J |
| author_facet | Whiteley, J |
| author_sort | Whiteley, J |
| collection | OXFORD |
| description | Mathematical models in biology and physiology are often represented by large systems of non–linear ordinary differential equations. In many cases, an observed behaviour may be written as a linear functional of the solution of this system of equations. A technique is presented in this study for automatically identifying key terms in the system of equations that are responsible for a given linear functional of the solution. This technique is underpinned by ideas drawn from a posteriori error analysis. This concept has been used in finite element analysis to identify regions of the computational domain and components of the solution where a fine computational mesh should be used to ensure accuracy of the numerical solution. We use this concept to identify regions of the computational domain and components of the solution where accurate representation of the mathematical model is required for accuracy of the solution. The technique presented is demonstrated by application to a model problem, and then to automatically deduce known results from a cell–level cardiac electrophysiology model. |
| first_indexed | 2024-03-06T19:07:26Z |
| format | Journal article |
| id | oxford-uuid:15a18f8f-2b28-4818-b841-b8414a0b4bec |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:07:26Z |
| publishDate | 2009 |
| record_format | dspace |
| spelling | oxford-uuid:15a18f8f-2b28-4818-b841-b8414a0b4bec2022-03-26T10:26:36ZModel reduction using a posteriori analysisJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:15a18f8f-2b28-4818-b841-b8414a0b4becMathematical Institute - ePrints2009Whiteley, JMathematical models in biology and physiology are often represented by large systems of non–linear ordinary differential equations. In many cases, an observed behaviour may be written as a linear functional of the solution of this system of equations. A technique is presented in this study for automatically identifying key terms in the system of equations that are responsible for a given linear functional of the solution. This technique is underpinned by ideas drawn from a posteriori error analysis. This concept has been used in finite element analysis to identify regions of the computational domain and components of the solution where a fine computational mesh should be used to ensure accuracy of the numerical solution. We use this concept to identify regions of the computational domain and components of the solution where accurate representation of the mathematical model is required for accuracy of the solution. The technique presented is demonstrated by application to a model problem, and then to automatically deduce known results from a cell–level cardiac electrophysiology model. |
| spellingShingle | Whiteley, J Model reduction using a posteriori analysis |
| title | Model reduction using a posteriori analysis |
| title_full | Model reduction using a posteriori analysis |
| title_fullStr | Model reduction using a posteriori analysis |
| title_full_unstemmed | Model reduction using a posteriori analysis |
| title_short | Model reduction using a posteriori analysis |
| title_sort | model reduction using a posteriori analysis |
| work_keys_str_mv | AT whiteleyj modelreductionusingaposteriorianalysis |