  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.
