An efficient operator-splitting FEM-FCT algorithm for 3D chemotaxis models

An efficient operator-splitting finite element method (FEM) combined with the flux-corrected transport (FCT) algorithm is presented to reduce the computation and storage of solving three-dimensional (3D) chemotaxis models. Firstly, the 3D coupled and positivity-preserving problem is split into a ser...

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Bibliographic Details
Published in:Engineering with computers Vol. 36; no. 4; pp. 1393 - 1404
Main Authors: Huang, Xueling, Xiao, Xufeng, Zhao, Jianping, Feng, Xinlong
Format: Journal Article
Language:English
Published: London Springer London 01.10.2020
Springer Nature B.V
Subjects:
Algorithms
CAE) and Design
Calculus of Variations and Optimal Control; Optimization
Classical Mechanics
Computer Science
Computer simulation
Computer-Aided Engineering (CAD
Control
Finite element method
Flux corrected transport
Math. Applications in Chemistry
Mathematical and Computational Engineering
Original Article
Splitting
Systems Theory
Three dimensional models
Finite element method
Chemotaxis models
Operator-splitting method
Flux-corrected transport algorithm
92C15
65M60
92C17
ISSN:0177-0667, 1435-5663
Online Access:Get full text
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Summary:An efficient operator-splitting finite element method (FEM) combined with the flux-corrected transport (FCT) algorithm is presented to reduce the computation and storage of solving three-dimensional (3D) chemotaxis models. Firstly, the 3D coupled and positivity-preserving problem is split into a series of 1D subproblems in three spatial directions. Then each 1D subproblem is solved by the FEM-FCT algorithm which guarantees the positivity of numerical solutions. As the 1D subproblems in one direction are spatially independent, they can be calculated in parallel. Additionally, the accuracy and efficiency of the proposed method are investigated by numerical tests. Furthermore, we employ the proposed method to simulate 3D chemotaxis phenomena, including the typical blow-up effect, the more complex pattern formation and aggregating behavior of cell distribution.
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ISSN:0177-0667
1435-5663
DOI:10.1007/s00366-019-00771-8