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

Abstract

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.