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
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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.
Affiliations des auteurs :
Jad Dabaghi 1, 2 ; Virginie Ehrlacher 1, 2 ; Christoph Strössner 3
@article{EP_2023_73_a9,
author = {Jad Dabaghi and Virginie Ehrlacher and Christoph Str\"ossner},
title = {Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system},
journal = {ESAIM. Proceedings},
pages = {173--186},
year = {2023},
volume = {73},
doi = {10.1051/proc/202373173},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/202373173/}
}
TY - JOUR AU - Jad Dabaghi AU - Virginie Ehrlacher AU - Christoph Strössner TI - Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system JO - ESAIM. Proceedings PY - 2023 SP - 173 EP - 186 VL - 73 UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/202373173/ DO - 10.1051/proc/202373173 LA - en ID - EP_2023_73_a9 ER -
%0 Journal Article %A Jad Dabaghi %A Virginie Ehrlacher %A Christoph Strössner %T Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system %J ESAIM. Proceedings %D 2023 %P 173-186 %V 73 %U http://geodesic.mathdoc.fr/articles/10.1051/proc/202373173/ %R 10.1051/proc/202373173 %G en %F EP_2023_73_a9
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
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