Model reduction using a posteriori analysis

Type
Article

Authors
Whiteley, Jonathan P.

KAUST Grant Number
KUK-C1-013-04

Date
2010-05

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.

Acknowledgements
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

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