The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks when time is of the essence. We propose the use of two operator splitting schemes for nonlinear cross-diffusion processes in order to lower the computational load, and establish their stability properties using discrete $L^2$ energy methods. Furthermore, by attaining a stable factorization of the system matrix as a forward-backward pass, corresponding to the Thomas algorithm for self-diffusion processes, we show that the use of implicit cross-diffusion can be competitive in terms of execution time, widening the range of viable cross-diffusion coefficients for on-the-fly applications.

翻译：交叉扩散模型的动态导致隐含差异方案在计算上高度复杂,使其在时间紧迫时不适合任务。我们提议对非线性交叉扩散进程采用两种操作员分割计划,以降低计算负荷,并使用离散的2美元能源方法建立其稳定性特性。此外,通过实现系统矩阵的稳定化,作为前向后向传递,与Thomas自我扩散过程的算法相对应,我们表明,隐含交叉扩散的使用在实施时间方面可以具有竞争力,可以扩大在飞上应用的可行交叉扩散系数的范围。