A parallel, adaptive finite element scheme for modeling chemotactic biological systems

This paper considers the numerical approximation of complex spatial patterns and rapidly evolving transients in chemotactic biological systems using parallel adaptive multiscale schemes and algorithms. Transport processes in such biological systems are typically modeled by coupled systems of nonline...

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Bibliographic Details
Published in:Communications in numerical methods in engineering Vol. 25; no. 12; pp. 1162 - 1185
Main Authors: Kirk, Benjamin S., Carey, Graham F.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 01.12.2009
Wiley
Subjects:
adaptive mesh refinement
Bacteriology
Biological and medical sciences
chemotaxis
Classical transport
Exact sciences and technology
Fluid dynamics
Fundamental and applied biological sciences. Psychology
Fundamental areas of phenomenology (including applications)
General theory
Microbiology
Motility, taxis
parallel finite elements
Physics
reaction-diffusion
Statistical physics, thermodynamics, and nonlinear dynamical systems
Transport processes
Transient response
Adaptive systems
parallel finite elements
Adaptive algorithm
Step method
adaptive mesh refinement
Reaction diffusion equation
Parallel algorithms
Biological system
Finite element method
reaction-diffusion
Multiscale method
Bacteria
Variational calculus
Biological models
Modelling
Transport processes
Non linear effect
Time integration
chemotaxis
ISSN:1069-8299, 1099-0887
Online Access:Get full text
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Summary:This paper considers the numerical approximation of complex spatial patterns and rapidly evolving transients in chemotactic biological systems using parallel adaptive multiscale schemes and algorithms. Transport processes in such biological systems are typically modeled by coupled systems of nonlinear reaction–diffusion equations. For example, a model of this form has been proposed for studying chemotaxis in bacteria colonies. In the present study, we develop a variational formulation for this model leading to an approximate finite element scheme with adaptive time stepping and local adaptive mesh refinement/coarsening algorithms. The parallel adaptive solution algorithm is presented in detail and applied to investigate the effect of chemotaxis in spot formation behind concentric advancing concentrations fronts. Numerical results concerning the accuracy, efficiency, and performance of the algorithm are also presented. Copyright © 2008 John Wiley & Sons, Ltd.
Bibliography:istex:643E4D92E6A28879B9CAB18E6F77B22AF4799C44
ark:/67375/WNG-6XFS6C0D-5
ArticleID:CNM1173
ISSN:1069-8299
1099-0887
DOI:10.1002/cnm.1173