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

Jad Dabaghi; Virginie Ehrlacher; Christoph Strössner

doi:10.1051/proc/202373173

Geodesic

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

Jad Dabaghi ^1,² ; Virginie Ehrlacher ^1,² ; Christoph Strössner ³

¹ Ecole des Ponts ParisTech, Marne-la-Vallée, France
² INRIA Paris, France
³ Institute of Mathematics, EPF Lausanne, Switzerland

ESAIM. Proceedings, Tome 73 (2023), pp. 173-186.

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Résumé

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.

DOI : 10.1051/proc/202373173

Affiliations des auteurs :

Jad Dabaghi ^{1, 2} ; Virginie Ehrlacher ^{1, 2} ; Christoph Strössner ³

¹ Ecole des Ponts ParisTech, Marne-la-Vallée, France
² INRIA Paris, France
³ Institute of Mathematics, EPF Lausanne, Switzerland

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     title = {Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system},
     journal = {ESAIM. Proceedings},
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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. ESAIM. Proceedings, Tome 73 (2023), pp. 173-186. doi : 10.1051/proc/202373173. http://geodesic.mathdoc.fr/articles/10.1051/proc/202373173/

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