Parallel Numerical Algorithms for Simulation of Multidimensional Ill-Posed Nonlinear Diffusion-Advection-Reaction Models

摘要

This paper presents finite difference approximations of two dimensional in space mathematical model of a bacterial self-organization. Due to the chemotaxis process some instability of the solution can be developed in the system, in this paper we show that such instability can be connected to the ill-posed problem defined by the backward in time diffusion process. The ADI and splitting type methods are used to construct robust parallel numerical approximations. Domain decomposition method is applied to distribute subtasks among processors. The scalability analysis of the parallel algorithm is done and results of computational experiments are presented.