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    Model reduction using a posteriori analysis

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    Type
    Article
    Authors
    Whiteley, Jonathan P.
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2010-05
    Permanent link to this record
    http://hdl.handle.net/10754/598851
    
    Metadata
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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 functional of interest. 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. © 2010 Elsevier Inc.
    Citation
    Whiteley JP (2010) Model reduction using a posteriori analysis. Mathematical Biosciences 225: 44–52. Available: http://dx.doi.org/10.1016/j.mbs.2010.01.008.
    Sponsors
    This publication is based on work supported by Award No. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
    Publisher
    Elsevier BV
    Journal
    Mathematical Biosciences
    DOI
    10.1016/j.mbs.2010.01.008
    PubMed ID
    20117117
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.mbs.2010.01.008
    Scopus Count
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