Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system

Cross-diffusion systems arise as hydrodynamic limits of lattice multi-species interacting particle models. The objective of this work is to provide a numerical scheme for the simulation of the cross-diffusion system identified in [J. Quastel, Comm. Pure Appl. Math. , 45 (1992), pp. 623–679]. To simu...

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Bibliographic Details
Published in:ESAIM. Proceedings and surveys 2023, Vol.73, p.173-186
Main Authors: Dabaghi, Jad, Ehrlacher, Virginie, Strössner, Christoph
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Computation
Diffusion coefficient
Finite volume method
Mathematical analysis
Optimization
Partial differential equations
Photovoltaic cells
Self diffusion
Simulation
Tensors
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Summary:Cross-diffusion systems arise as hydrodynamic limits of lattice multi-species interacting particle models. The objective of this work is to provide a numerical scheme for the simulation of the cross-diffusion system identified in [J. Quastel, Comm. Pure Appl. Math. , 45 (1992), pp. 623–679]. To simulate this system, it is necessary to provide an approximation of the so-called self-diffusion coefficient matrix of the tagged particle process. Classical algorithms for the computation of this matrix are based on the estimation of the long-time limit of the average mean square displacement of the particle. In this work, as an alternative, we propose a novel approach for computing the self-diffusion coefficient using deterministic low-rank approximation techniques, as the minimum of a high-dimensional optimization problem. The computed self-diffusion coefficient is then used for the simulation of the cross-diffusion system using an implicit finite volume scheme.
ISSN:2267-3059
2267-3059
DOI:10.1051/proc/202373173