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

Abstract : 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. This approach is then used for the simulation of the cross-diffusion system using an implicit finite volume scheme.
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https://hal.archives-ouvertes.fr/hal-03441986
Contributor : Jad Dabaghi Connect in order to contact the contributor
Submitted on : Monday, April 4, 2022 - 6:23:35 PM
Last modification on : Monday, May 16, 2022 - 7:10:01 PM

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  • HAL Id : hal-03441986, version 2
  • ARXIV : 2111.11349

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Jad Dabaghi, Virginie Ehrlacher, Christoph Strössner. Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system. 2022. ⟨hal-03441986v2⟩

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