The Mathematical Institute, University of Oxford, Eprints Archive

Model reduction using a posteriori analysis

Whiteley, J. P. (2009) Model reduction using a posteriori analysis. Not specified . (Submitted)

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Abstract

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.

Item Type:Article
Subjects:H - N > Numerical analysis
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:811
Deposited By:Dr M. Stoll
Deposited On:23 Sep 2009 08:28
Last Modified:23 Sep 2009 08:28

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