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Title: Fast stable finite difference schemes for nonlinear cross-diffusion
Authors: Lobo, Diogo de Castro 
Keywords: Fast numerical schemes; Image processing; Matrix factorization; Nonlinear cross-diffusion; Operator splitting
Issue Date: 2021
Publisher: Elsevier
Project: CMUC-UIDB/00324/2020 
Serial title, monograph or event: Computers and Mathematics with Applications
Volume: 101
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 on-the-fly applications.
ISSN: 08981221
DOI: 10.1016/j.camwa.2021.06.011
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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