Fast stable finite difference schemes for nonlinear cross-diffusion

Diogo Lobo

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arXiv · 2105.04043

Fast stable finite difference schemes for nonlinear cross-diffusion

Diogo Lobo

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Abstract

The dynamics of cross-diffusion models leads to a high computational complexity for implicit difference schemes, turning them unsuitable for tasks that require results in real-time. 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 \textit{on-the-fly} applications.

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Diogo Lobo. 2021-05-09. Fast stable finite difference schemes for nonlinear cross-diffusion. https://arxiv.org/abs/2105.04043

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