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 simul...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2023-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://www.esaim-proc.org/articles/proc/pdf/2023/02/proc2307309.pdf |
| _version_ | 1797673434332790784 |
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| author | Dabaghi Jad Ehrlacher Virginie Strössner Christoph |
| author_facet | Dabaghi Jad Ehrlacher Virginie Strössner Christoph |
| author_sort | Dabaghi Jad |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T21:45:27Z |
| format | Article |
| id | doaj.art-4ffda14efc4e4542b806799fe1eadefc |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-03-11T21:45:27Z |
| publishDate | 2023-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-4ffda14efc4e4542b806799fe1eadefc2023-09-26T10:13:00ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592023-01-017317318610.1051/proc/202373173proc2307309Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion systemDabaghi Jad0Ehrlacher Virginie1Strössner Christoph2Ecole des Ponts ParisTechEcole des Ponts ParisTechInstitute of Mathematics, EPF LausanneCross-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.https://www.esaim-proc.org/articles/proc/pdf/2023/02/proc2307309.pdf |
| spellingShingle | Dabaghi Jad Ehrlacher Virginie Strössner Christoph Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system ESAIM: Proceedings and Surveys |
| title | Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system |
| title_full | Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system |
| title_fullStr | Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system |
| title_full_unstemmed | Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system |
| title_short | Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system |
| title_sort | computation of the self diffusion coefficient with low rank tensor methods application to the simulation of a cross diffusion system |
| url | https://www.esaim-proc.org/articles/proc/pdf/2023/02/proc2307309.pdf |
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