Efficient Numerical Algorithms based on Difference Potentials for Chemotaxis Systems in 3D
This work provides a practical numerical tool for simulating chemotaxis systems in complex 3D geometries, which is relevant for biological and medical applications.
The paper develops efficient numerical algorithms based on the Difference Potentials Method for solving chemotaxis systems in 3D irregular geometries using Cartesian meshes and Fast Poisson Solvers, with a domain decomposition approach for mesh adaptivity and parallelization. Numerical experiments demonstrate accuracy, efficiency, and robustness.
In this work, we propose efficient and accurate numerical algorithms based on Difference Potentials Method for numerical solution of chemotaxis systems and related models in 3D. The developed algorithms handle 3D irregular geometry with the use of only Cartesian meshes and employ Fast Poisson Solvers. In addition, to further enhance computational efficiency of the methods, we design a Difference-Potentials-based domain decomposition approach which allows mesh adaptivity and easy parallelization of the algorithm in space. Extensive numerical experiments are presented to illustrate the accuracy, efficiency and robustness of the developed numerical algorithms.